|\^/|     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_y := proc(x)
> return(c(-2.0)/exp(c(x)));
> end;
           exact_soln_y := proc(x) return c(-2.0)/exp(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
>     ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
    if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
        rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
            (array_x[1] - array_given_rad_poles[1, 1])
             + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
        omniout_float(ALWAYS,
            "Radius of convergence (given) for eq  1           ", 4,
            rad_given, 4, " ");
        omniout_float(ALWAYS,
            "Order of pole (given)                             ", 4,
            array_given_ord_poles[1, 1], 4, " ");
        if rad_given < glob_least_given_sing then
            glob_least_given_sing := rad_given
        end if
    elif glob_type_given_pole = 3 then
        omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
    elif glob_type_given_pole = 5 then
        omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
    else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
    end if;
    if array_rad_test_poles[1, 1] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (ratio test) for eq  1      ", 4,
            array_rad_test_poles[1, 1], 4, " ");
        if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
            glob_least_ratio_sing := array_rad_test_poles[1, 1]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (ratio test)                        ", 4,
            array_ord_test_poles[1, 1], 4, " ")
    else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
    end if;
    if glob__small < array_rad_test_poles[1, 2] and
    array_rad_test_poles[1, 2] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (three term test) for eq 1  ", 4,
            array_rad_test_poles[1, 2], 4, " ");
        if array_rad_test_poles[1, 2] < glob_least_3_sing then
            glob_least_3_sing := array_rad_test_poles[1, 2]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (three term test)                   ", 4,
            array_ord_test_poles[1, 2], 4, " ")
    else omniout_str(ALWAYS,
        "NO REAL POLE (three term test) for Equation 1")
    end if;
    if glob__small < array_rad_test_poles[1, 3] and
    array_rad_test_poles[1, 3] < glob_large_float then
        omniout_float(ALWAYS,
            "Radius of convergence (six term test) for eq 1    ", 4,
            array_rad_test_poles[1, 3], 4, " ");
        if array_rad_test_poles[1, 3] < glob_least_6_sing then
            glob_least_6_sing := array_rad_test_poles[1, 3]
        end if;
        omniout_float(ALWAYS,
            "Order of pole (six term test)                     ", 4,
            array_ord_test_poles[1, 3], 4, " ")
    else omniout_str(ALWAYS,
        "NO COMPLEX POLE (six term test) for Equation 1")
    end if
end proc

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

# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local min_size;
>     min_size := glob_estimated_size_answer;
>     if (float_abs(array_y[1]) < min_size) then # if number 3
>         min_size := float_abs(array_y[1]);
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 3;
>     if (min_size < glob__1) then # if number 3
>         min_size := glob__1;
>         omniout_float(ALWAYS,"min_size",32,min_size,32,"");
>     fi;# end if 3;
>     min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    min_size := glob_estimated_size_answer;
    if float_abs(array_y[1]) < min_size then
        min_size := float_abs(array_y[1]);
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    if min_size < glob__1 then
        min_size := glob__1;
        omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
    end if;
    min_size
end proc

# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     max_estimated_step_error  := glob__small;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
>     omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
>     est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
>     if (est_tmp >= max_estimated_step_error) then # if number 3
>         max_estimated_step_error := est_tmp;
>     fi;# end if 3;
>     omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
>     max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    max_estimated_step_error := glob__small;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
    omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
    est_tmp := float_abs(array_y[no_terms - 3]
         + array_y[no_terms - 2]*hn_div_ho
         + array_y[no_terms - 1]*hn_div_ho_2
         + array_y[no_terms]*hn_div_ho_3);
    if max_estimated_step_error <= est_tmp then
        max_estimated_step_error := est_tmp
    end if;
    omniout_float(ALWAYS, "max_estimated_step_error", 32,
        max_estimated_step_error, 32, "");
    max_estimated_step_error
end proc

# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
>     no_terms := ATS_MAX_TERMS;
>     hn_div_ho := glob__0_5;
>     hn_div_ho_2 := glob__0_25;
>     hn_div_ho_3 := glob__0_125;
>     est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
>     if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
>         est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
>     fi;# end if 3;
>     if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
>         array_max_est_error[1] := c(est_tmp);
>     fi;# end if 3
>     ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    no_terms := ATS_MAX_TERMS;
    hn_div_ho := glob__0_5;
    hn_div_ho_2 := glob__0_25;
    hn_div_ho_3 := glob__0_125;
    est_tmp := c(float_abs(array_y[no_terms - 3]))
         + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
         + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
         + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
    if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
        est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
    end if;
    if c(array_max_est_error[1]) <= c(est_tmp) then
        array_max_est_error[1] := c(est_tmp)
    end if
end proc

# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local ret;
>     if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
>         ret := true;
>     else
>         ret := false;
>     fi;# end if 3;
>     return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    if glob_check_sign*glob_next_display - glob_h/glob__10 <=
    glob_check_sign*array_x[1] then ret := true
    else ret := false
    end if;
    return ret
end proc

# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
>     #TOP DISPLAY ALOT
>     if (reached_interval())  then # if number 3
>         if (iter >= 0)  then # if number 4
>             ind_var := array_x[1];
>             omniout_float(ALWAYS,"x[1]                             ",33,ind_var,20," ");
>             closed_form_val_y := evalf(exact_soln_y(ind_var));
>             omniout_float(ALWAYS,"y[1] (closed_form)               ",33,closed_form_val_y,20," ");
>             term_no   :=  1;
>             numeric_val := array_y[term_no];
>             abserr := float_abs(numeric_val - closed_form_val_y);
>             omniout_float(ALWAYS,"y[1] (numeric)                   ",33,numeric_val,20," ");
>             if (c(float_abs(closed_form_val_y)) > c(glob_prec))  then # if number 5
>                 relerr := abserr*glob__100/float_abs(closed_form_val_y);
>                 if (c(relerr) > c(glob_prec)) then # if number 6
>                     glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
>                 else
>                     glob_good_digits := Digits;
>                 fi;# end if 6;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_good_digits := -16;
>             fi;# end if 5;
>             if (glob_good_digits < glob_min_good_digits) then # if number 5
>                 glob_min_good_digits  := glob_good_digits;
>             fi;# end if 5;
>             if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
>                 glob_min_apfp_est_good_digits  := glob_apfp_est_good_digits;
>             fi;# end if 5;
>             if (evalf(float_abs(numeric_val)) > glob_prec)  then # if number 5
>                 est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*19*ATS_MAX_TERMS/float_abs(numeric_val));
>                 if (evalf(est_rel_err) > glob_prec) then # if number 6
>                     glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
>                 else
>                     glob_est_digits := Digits;
>                 fi;# end if 6;
>             else
>                 relerr :=  glob__m1  ;
>                 glob_est_digits := -16;
>             fi;# end if 5;
>             array_est_digits[1] := glob_est_digits;
>             if (glob_iter  = 1) then # if number 5
>                 array_1st_rel_error[1] := relerr;
>             else
>                 array_last_rel_error[1] := relerr;
>             fi;# end if 5;
>             array_est_rel_error[1] := est_rel_err;
>             omniout_float(ALWAYS,"absolute error                   ",4,abserr,20," ");
>             omniout_float(ALWAYS,"relative error                   ",4,relerr,20,"%");
>             omniout_int(INFO,"Desired digits                   ",32,glob_desired_digits_correct,4," ");
>             omniout_int(INFO,"Estimated correct digits         ",32,glob_est_digits,4," ");
>             omniout_int(INFO,"Correct digits                   ",32,glob_good_digits,4," ")
>             ;
>             omniout_float(ALWAYS,"h                                ",4,glob_h,20," ");
>         fi;# end if 4;
>         #BOTTOM DISPLAY ALOT
>     fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    if reached_interval() then
        if 0 <= iter then
            ind_var := array_x[1];
            omniout_float(ALWAYS, "x[1]                             ", 33,
                ind_var, 20, " ");
            closed_form_val_y := evalf(exact_soln_y(ind_var));
            omniout_float(ALWAYS, "y[1] (closed_form)               ", 33,
                closed_form_val_y, 20, " ");
            term_no := 1;
            numeric_val := array_y[term_no];
            abserr := float_abs(numeric_val - closed_form_val_y);
            omniout_float(ALWAYS, "y[1] (numeric)                   ", 33,
                numeric_val, 20, " ");
            if c(glob_prec) < c(float_abs(closed_form_val_y)) then
                relerr := abserr*glob__100/float_abs(closed_form_val_y);
                if c(glob_prec) < c(relerr) then
                    glob_good_digits := -int_trunc(log10(c(relerr))) + 3
                else glob_good_digits := Digits
                end if
            else relerr := glob__m1; glob_good_digits := -16
            end if;
            if glob_good_digits < glob_min_good_digits then
                glob_min_good_digits := glob_good_digits
            end if;
            if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
            then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
            end if;
            if glob_prec < evalf(float_abs(numeric_val)) then
                est_rel_err := evalf(array_max_est_error[1]*100.0*
                    sqrt(glob_iter)*19*ATS_MAX_TERMS/float_abs(numeric_val))
                    ;
                if glob_prec < evalf(est_rel_err) then
                    glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
                else glob_est_digits := Digits
                end if
            else relerr := glob__m1; glob_est_digits := -16
            end if;
            array_est_digits[1] := glob_est_digits;
            if glob_iter = 1 then array_1st_rel_error[1] := relerr
            else array_last_rel_error[1] := relerr
            end if;
            array_est_rel_error[1] := est_rel_err;
            omniout_float(ALWAYS, "absolute error                   ", 4,
                abserr, 20, " ");
            omniout_float(ALWAYS, "relative error                   ", 4,
                relerr, 20, "%");
            omniout_int(INFO, "Desired digits                   ", 32,
                glob_desired_digits_correct, 4, " ");
            omniout_int(INFO, "Estimated correct digits         ", 32,
                glob_est_digits, 4, " ");
            omniout_int(INFO, "Correct digits                   ", 32,
                glob_good_digits, 4, " ");
            omniout_float(ALWAYS, "h                                ", 4,
                glob_h, 20, " ")
        end if
    end if
end proc

# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
>     #TOP PROGRESS REPORT
>     clock_sec1   := elapsed_time_seconds();
>     total_clock_sec   :=  (clock_sec1) - (glob_orig_start_sec);
>     glob_clock_sec   :=  (clock_sec1) - (glob_clock_start_sec);
>     left_sec   :=  (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
>     expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h)  ,( clock_sec1) - (glob_orig_start_sec));
>     opt_clock_sec   := ( clock_sec1) - (glob_optimal_clock_start_sec);
>     glob_optimal_expect_sec   :=  comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
>     glob_total_exp_sec   := glob_optimal_expect_sec + c(total_clock_sec);
>     percent_done   :=  comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
>     glob_percent_done := percent_done;
>     omniout_str_noeol(INFO,"Total Elapsed Time              ");
>     omniout_timestr((total_clock_sec));
>     omniout_str_noeol(INFO,"Elapsed Time(since restart)     ");
>     omniout_timestr((glob_clock_sec));
>     if (c(percent_done) < glob__100)  then # if number 3
>         omniout_str_noeol(INFO,"Expected Time Remaining         ");
>         omniout_timestr((expect_sec));
>         omniout_str_noeol(INFO,"Optimized Time Remaining        ");
>         omniout_timestr((glob_optimal_expect_sec));
>         omniout_str_noeol(INFO,"Expected Total Time             ");
>         omniout_timestr((glob_total_exp_sec));
>     fi;# end if 3;
>     omniout_str_noeol(INFO,"Time to Timeout                 ");
>     omniout_timestr((left_sec));
>     omniout_float(INFO,    "Percent Done                    ",33,percent_done,4,"%");
>     #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    clock_sec1 := elapsed_time_seconds();
    total_clock_sec := clock_sec1 - glob_orig_start_sec;
    glob_clock_sec := clock_sec1 - glob_clock_start_sec;
    left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
    expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
        clock_sec1 - glob_orig_start_sec);
    opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
    glob_optimal_expect_sec :=
        comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
        ;
    glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
    percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
    glob_percent_done := percent_done;
    omniout_str_noeol(INFO, "Total Elapsed Time              ");
    omniout_timestr(total_clock_sec);
    omniout_str_noeol(INFO, "Elapsed Time(since restart)     ");
    omniout_timestr(glob_clock_sec);
    if c(percent_done) < glob__100 then
        omniout_str_noeol(INFO, "Expected Time Remaining         ");
        omniout_timestr(expect_sec);
        omniout_str_noeol(INFO, "Optimized Time Remaining        ");
        omniout_timestr(glob_optimal_expect_sec);
        omniout_str_noeol(INFO, "Expected Total Time             ");
        omniout_timestr(glob_total_exp_sec)
    end if;
    omniout_str_noeol(INFO, "Time to Timeout                 ");
    omniout_timestr(left_sec);
    omniout_float(INFO, "Percent Done                    ", 33,
        percent_done, 4, "%")
end proc

# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14,  rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
>     #TOP CHECK FOR POLE
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,1] :=  glob_larger_float;
>     array_ord_test_poles[1,1] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 3;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 4
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 5
>             found_sing := 0;
>         fi;# end if 5;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 5
>         if (rad_c  < array_rad_test_poles[1,1]) then # if number 6
>             array_rad_test_poles[1,1] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,1] := rad_c;
>             array_ord_test_poles[1,1] := tmp_ord;
>         fi;# end if 6;
>     fi;# end if 5;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,2] :=  glob_larger_float;
>     array_ord_test_poles[1,2] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 5;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 6
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 7
>             found_sing := 0;
>         fi;# end if 7;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 7
>         if (rad_c  < array_rad_test_poles[1,2]) then # if number 8
>             array_rad_test_poles[1,2] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,2] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 9
>                 glob_min_pole_est := rad_c;
>             fi;# end if 9;
>             array_ord_test_poles[1,2] := tmp_ord;
>         fi;# end if 8;
>     fi;# end if 7;
>     #BOTTOM general radius test1
>     tmp_rad :=  glob_larger_float;
>     prev_tmp_rad :=  glob_larger_float;
>     tmp_ratio :=  glob_larger_float;
>     rad_c :=  glob_larger_float;
>     array_rad_test_poles[1,3] :=  glob_larger_float;
>     array_ord_test_poles[1,3] :=  glob_larger_float;
>     found_sing := 1;
>     last_no :=  ATS_MAX_TERMS - 1 - 10;
>     cnt :=  0;
>     while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
>         tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>         if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
>             tmp_ratio :=  tmp_rad / prev_tmp_rad;
>         else
>             tmp_ratio :=  glob_large_float;
>         fi;# end if 7;
>         if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
>             rad_c := tmp_rad;
>         elif
>         (cnt = 0) then # if number 8
>             rad_c := tmp_rad;
>         elif
>         (cnt > 0) then # if number 9
>             found_sing := 0;
>         fi;# end if 9;
>         prev_tmp_rad := tmp_rad;;
>         cnt :=  cnt + 1;
>         last_no := last_no + 1;
>     od;# end do number 1;
>     if (found_sing = 1) then # if number 9
>         if (rad_c  < array_rad_test_poles[1,3]) then # if number 10
>             array_rad_test_poles[1,3] := rad_c;
>             last_no := last_no - 1;
>             tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
>             array_rad_test_poles[1,3] := rad_c;
>             if (rad_c  <  glob_min_pole_est) then # if number 11
>                 glob_min_pole_est := rad_c;
>             fi;# end if 11;
>             array_ord_test_poles[1,3] := tmp_ord;
>         fi;# end if 10;
>     fi;# end if 9;
>     #BOTTOM general radius test1
>     #START ADJUST ALL SERIES
>     if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
>         h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
>         omniout_str(ALWAYS,"SETTING H FOR POLE");
>         glob_h_reason := 6;
>         if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
>             omniout_str(ALWAYS,"SETTING H FOR MIN H");
>             h_new := glob_min_h;
>             glob_h_reason := 5;
>         fi;# end if 10;
>         term := 1;
>         ratio := c(1.0);
>         while (term <= ATS_MAX_TERMS)  do # do number 1
>             array_y[term] := array_y[term]* ratio;
>             array_y_higher[1,term] := array_y_higher[1,term]* ratio;
>             array_x[term] := array_x[term]* ratio;
>             ratio := ratio * h_new / float_abs(glob_h);
>             term := term + 1;
>         od;# end do number 1;
>         glob_h := h_new;
>     fi;# end if 9;
>     #BOTTOM ADJUST ALL SERIES
>     ;
>     if (reached_interval())  then # if number 9
>         display_poles();
>     fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 1] := glob_larger_float;
    array_ord_test_poles[1, 1] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
        tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
            array_y_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 1] then
            array_rad_test_poles[1, 1] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
                array_y_higher[1, last_no], last_no);
            array_rad_test_poles[1, 1] := rad_c;
            array_ord_test_poles[1, 1] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 2] := glob_larger_float;
    array_ord_test_poles[1, 2] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
        tmp_rad := comp_rad_from_three_terms(
            array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
            array_y_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 2] then
            array_rad_test_poles[1, 2] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_three_terms(
                array_y_higher[1, last_no - 2],
                array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
                last_no);
            array_rad_test_poles[1, 2] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 2] := tmp_ord
        end if
    end if;
    tmp_rad := glob_larger_float;
    prev_tmp_rad := glob_larger_float;
    tmp_ratio := glob_larger_float;
    rad_c := glob_larger_float;
    array_rad_test_poles[1, 3] := glob_larger_float;
    array_ord_test_poles[1, 3] := glob_larger_float;
    found_sing := 1;
    last_no := ATS_MAX_TERMS - 11;
    cnt := 0;
    while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
        tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
            array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
            array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
            array_y_higher[1, last_no], last_no);
        if glob__0 < float_abs(prev_tmp_rad) then
            tmp_ratio := tmp_rad/prev_tmp_rad
        else tmp_ratio := glob_large_float
        end if;
        if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
        glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
        elif cnt = 0 then rad_c := tmp_rad
        elif 0 < cnt then found_sing := 0
        end if;
        prev_tmp_rad := tmp_rad;
        cnt := cnt + 1;
        last_no := last_no + 1
    end do;
    if found_sing = 1 then
        if rad_c < array_rad_test_poles[1, 3] then
            array_rad_test_poles[1, 3] := rad_c;
            last_no := last_no - 1;
            tmp_ord := comp_ord_from_six_terms(
                array_y_higher[1, last_no - 5],
                array_y_higher[1, last_no - 4],
                array_y_higher[1, last_no - 3],
                array_y_higher[1, last_no - 2],
                array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
                last_no);
            array_rad_test_poles[1, 3] := rad_c;
            if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
            end if;
            array_ord_test_poles[1, 3] := tmp_ord
        end if
    end if;
    if
    float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
    then
        h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
        omniout_str(ALWAYS, "SETTING H FOR POLE");
        glob_h_reason := 6;
        if glob_check_sign*h_new < glob_check_sign*glob_min_h then
            omniout_str(ALWAYS, "SETTING H FOR MIN H");
            h_new := glob_min_h;
            glob_h_reason := 5
        end if;
        term := 1;
        ratio := c(1.0);
        while term <= ATS_MAX_TERMS do
            array_y[term] := array_y[term]*ratio;
            array_y_higher[1, term] := array_y_higher[1, term]*ratio;
            array_x[term] := array_x[term]*ratio;
            ratio := ratio*h_new/float_abs(glob_h);
            term := term + 1
        end do;
        glob_h := h_new
    end if;
    if reached_interval() then display_poles() end if
end proc

# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
>     local kkk, order_d, adj2, adj3 , temporary, term;
>     #TOP ATOMALL
>     # before write maple main top matter
>     # before generate constants assign
>     # before generate globals assign
>     #END OUTFILE1
>     #BEGIN OUTFILE2
>     #END OUTFILE2
>     #BEGIN ATOMHDR1
>     #emit pre exp 1 $eq_no = 1
>     array_tmp1[1] :=  exp(array_x[1]);
>     #emit pre div CONST FULL $eq_no = 1 i = 1
>     array_tmp2[1] := array_const_2D0[1] / 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_y_set_initial[1,2]) then # if number 1
>         if (1 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
>             if (2 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[2] := temporary;
>                 array_y_higher[1,2] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(1);
>             array_y_higher[2,1] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre exp ID_LINEAR iii = 2 $eq_no = 1
>     array_tmp1[2] := array_tmp1[1] * array_x[2] / c(1);
>     #emit pre div CONST FULL $eq_no = 1 i = 2
>     array_tmp2[2] := neg(ats(2,array_tmp1,array_tmp2,2)) / array_tmp1[1];
>     #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_y_set_initial[1,3]) then # if number 1
>         if (2 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
>             if (3 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[3] := temporary;
>                 array_y_higher[1,3] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(2);
>             array_y_higher[2,2] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 3;
>     #END ATOMHDR2
>     #BEGIN ATOMHDR3
>     #emit pre exp ID_LINEAR iii = 3 $eq_no = 1
>     array_tmp1[3] := array_tmp1[2] * array_x[2] / c(2);
>     #emit pre div CONST FULL $eq_no = 1 i = 3
>     array_tmp2[3] := neg(ats(3,array_tmp1,array_tmp2,2)) / array_tmp1[1];
>     #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_y_set_initial[1,4]) then # if number 1
>         if (3 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
>             if (4 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[4] := temporary;
>                 array_y_higher[1,4] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(3);
>             array_y_higher[2,3] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 4;
>     #END ATOMHDR3
>     #BEGIN ATOMHDR4
>     #emit pre exp ID_LINEAR iii = 4 $eq_no = 1
>     array_tmp1[4] := array_tmp1[3] * array_x[2] / c(3);
>     #emit pre div CONST FULL $eq_no = 1 i = 4
>     array_tmp2[4] := neg(ats(4,array_tmp1,array_tmp2,2)) / array_tmp1[1];
>     #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_y_set_initial[1,5]) then # if number 1
>         if (4 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
>             if (5 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[5] := temporary;
>                 array_y_higher[1,5] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(4);
>             array_y_higher[2,4] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 5;
>     #END ATOMHDR4
>     #BEGIN ATOMHDR5
>     #emit pre exp ID_LINEAR iii = 5 $eq_no = 1
>     array_tmp1[5] := array_tmp1[4] * array_x[2] / c(4);
>     #emit pre div CONST FULL $eq_no = 1 i = 5
>     array_tmp2[5] := neg(ats(5,array_tmp1,array_tmp2,2)) / array_tmp1[1];
>     #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_y_set_initial[1,6]) then # if number 1
>         if (5 <= ATS_MAX_TERMS) then # if number 2
>             temporary := c(array_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
>             if (6 <= ATS_MAX_TERMS) then # if number 3
>                 array_y[6] := temporary;
>                 array_y_higher[1,6] := temporary;
>             fi;# end if 3;
>             temporary := c(temporary) / c(glob_h) * c(5);
>             array_y_higher[2,5] := c(temporary);
>         fi;# end if 2;
>     fi;# end if 1;
>     kkk := 6;
>     #END ATOMHDR5
>     #BEGIN OUTFILE3
>     #Top Atomall While Loop-- outfile3
>     while (kkk <= ATS_MAX_TERMS) do # do number 1
>         #END OUTFILE3
>         #BEGIN OUTFILE4
>         #emit exp LINEAR $eq_no = 1
>         array_tmp1[kkk] := array_tmp1[kkk - 1] * array_x[2] / c(kkk - 1);
>         #emit div CONST FULL $eq_no = 1 i = 1
>         array_tmp2[kkk] := neg(ats(kkk,array_tmp1,array_tmp2,2)) / array_tmp1[1];
>         #emit NOT FULL - FULL add $eq_no = 1
>         array_tmp3[kkk] := array_tmp2[kkk];
>         #emit assign $eq_no = 1
>         order_d  := 1;
>         if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
>             if ( not  array_y_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_y[kkk + order_d] := c(temporary);
>                 array_y_higher[1,kkk + order_d] := c(temporary);
>                 term := kkk + order_d - 1;
>                 adj2 := kkk + order_d - 1;
>                 adj3 := 2;
>                 while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
>                     if (adj3 <= order_d + 1) then # if number 3
>                         if (adj2 > 0) then # if number 4
>                             temporary := c(temporary) / c(glob_h) * c(adj2);
>                         else
>                             temporary := c(temporary);
>                         fi;# end if 4;
>                         array_y_higher[adj3,term] := c(temporary);
>                     fi;# end if 3;
>                     term  := term - 1;
>                     adj2 := adj2 - 1;
>                     adj3 := adj3 + 1;
>                 od;# end do number 1
>             fi;# end if 2
>         fi;# end if 1;
>         kkk   :=  kkk + 1;
>     od;# end do number 1;
>     #BOTTOM ATOMALL
>     #END OUTFILE4
>     #BEGIN OUTFILE5
>     #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    array_tmp1[1] := exp(array_x[1]);
    array_tmp2[1] := array_const_2D0[1]/array_tmp1[1];
    array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
    if not array_y_set_initial[1, 2] then
        if 1 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
            if 2 <= ATS_MAX_TERMS then
                array_y[2] := temporary; array_y_higher[1, 2] := temporary
            end if;
            temporary := c(temporary)*c(1)/c(glob_h);
            array_y_higher[2, 1] := c(temporary)
        end if
    end if;
    kkk := 2;
    array_tmp1[2] := array_tmp1[1]*array_x[2]/c(1);
    array_tmp2[2] := neg(ats(2, array_tmp1, array_tmp2, 2))/array_tmp1[1];
    array_tmp3[2] := array_tmp2[2];
    if not array_y_set_initial[1, 3] then
        if 2 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
            if 3 <= ATS_MAX_TERMS then
                array_y[3] := temporary; array_y_higher[1, 3] := temporary
            end if;
            temporary := c(temporary)*c(2)/c(glob_h);
            array_y_higher[2, 2] := c(temporary)
        end if
    end if;
    kkk := 3;
    array_tmp1[3] := array_tmp1[2]*array_x[2]/c(2);
    array_tmp2[3] := neg(ats(3, array_tmp1, array_tmp2, 2))/array_tmp1[1];
    array_tmp3[3] := array_tmp2[3];
    if not array_y_set_initial[1, 4] then
        if 3 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
            if 4 <= ATS_MAX_TERMS then
                array_y[4] := temporary; array_y_higher[1, 4] := temporary
            end if;
            temporary := c(temporary)*c(3)/c(glob_h);
            array_y_higher[2, 3] := c(temporary)
        end if
    end if;
    kkk := 4;
    array_tmp1[4] := array_tmp1[3]*array_x[2]/c(3);
    array_tmp2[4] := neg(ats(4, array_tmp1, array_tmp2, 2))/array_tmp1[1];
    array_tmp3[4] := array_tmp2[4];
    if not array_y_set_initial[1, 5] then
        if 4 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
            if 5 <= ATS_MAX_TERMS then
                array_y[5] := temporary; array_y_higher[1, 5] := temporary
            end if;
            temporary := c(temporary)*c(4)/c(glob_h);
            array_y_higher[2, 4] := c(temporary)
        end if
    end if;
    kkk := 5;
    array_tmp1[5] := array_tmp1[4]*array_x[2]/c(4);
    array_tmp2[5] := neg(ats(5, array_tmp1, array_tmp2, 2))/array_tmp1[1];
    array_tmp3[5] := array_tmp2[5];
    if not array_y_set_initial[1, 6] then
        if 5 <= ATS_MAX_TERMS then
            temporary :=
                c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
            if 6 <= ATS_MAX_TERMS then
                array_y[6] := temporary; array_y_higher[1, 6] := temporary
            end if;
            temporary := c(temporary)*c(5)/c(glob_h);
            array_y_higher[2, 5] := c(temporary)
        end if
    end if;
    kkk := 6;
    while kkk <= ATS_MAX_TERMS do
        array_tmp1[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1);
        array_tmp2[kkk] :=
            neg(ats(kkk, array_tmp1, array_tmp2, 2))/array_tmp1[1];
        array_tmp3[kkk] := array_tmp2[kkk];
        order_d := 1;
        if kkk + order_d <= ATS_MAX_TERMS then
            if not array_y_set_initial[1, kkk + order_d] then
                temporary := c(array_tmp3[kkk])*expt(glob_h, c(order_d))*
                    c(factorial_3(kkk - 1, kkk + order_d - 1));
                array_y[kkk + order_d] := c(temporary);
                array_y_higher[1, kkk + order_d] := c(temporary);
                term := kkk + order_d - 1;
                adj2 := kkk + order_d - 1;
                adj3 := 2;
                while
                1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
                do
                    if adj3 <= order_d + 1 then
                        if 0 < adj2 then
                            temporary := c(temporary)*c(adj2)/c(glob_h)
                        else temporary := c(temporary)
                        end if;
                        array_y_higher[adj3, term] := c(temporary)
                    end if;
                    term := term - 1;
                    adj2 := adj2 - 1;
                    adj3 := adj3 + 1
                end do
            end if
        end if;
        kkk := kkk + 1
    end do
end proc

# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
>     #BEGIN OUTFIEMAIN
>     local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
>     term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
>     rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
>     x_start,x_end
>     ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
>     global
>     ALWAYS,
>     INFO,
>     DEBUGL,
>     DEBUGMASSIVE,
>     glob_iolevel,
>     glob_yes_pole,
>     glob_no_pole,
>     glob_not_given,
>     glob_no_sing_tests,
>     glob_ratio_test,
>     glob_three_term_test,
>     glob_six_term_test,
>     glob_log_10,
>     #Top Generate Globals Decl
>     MAX_UNCHANGED,
>     glob__small,
>     glob_small_float,
>     glob_smallish_float,
>     glob_large_float,
>     glob_larger_float,
>     glob__m2,
>     glob__m1,
>     glob__0,
>     glob__1,
>     glob__2,
>     glob__3,
>     glob__4,
>     glob__5,
>     glob__8,
>     glob__10,
>     glob__100,
>     glob__pi,
>     glob__0_5,
>     glob__0_8,
>     glob__m0_8,
>     glob__0_25,
>     glob__0_125,
>     glob_prec,
>     glob_check_sign,
>     glob_desired_digits_correct,
>     glob_max_estimated_step_error,
>     glob_ratio_of_radius,
>     glob_percent_done,
>     glob_total_exp_sec,
>     glob_optimal_expect_sec,
>     glob_estimated_size_answer,
>     glob_almost_1,
>     glob_clock_sec,
>     glob_clock_start_sec,
>     glob_disp_incr,
>     glob_h,
>     glob_diff_rc_fm,
>     glob_diff_rc_fmm1,
>     glob_diff_rc_fmm2,
>     glob_diff_ord_fm,
>     glob_diff_ord_fmm1,
>     glob_diff_ord_fmm2,
>     glob_six_term_ord_save,
>     glob_guess_error_rc,
>     glob_guess_error_ord,
>     glob_least_given_sing,
>     glob_least_ratio_sing,
>     glob_least_3_sing,
>     glob_least_6_sing,
>     glob_last_good_h,
>     glob_max_h,
>     glob_min_h,
>     glob_display_interval,
>     glob_abserr,
>     glob_relerr,
>     glob_min_pole_est,
>     glob_max_rel_trunc_err,
>     glob_max_trunc_err,
>     glob_max_hours,
>     glob_optimal_clock_start_sec,
>     glob_optimal_start,
>     glob_upper_ratio_limit,
>     glob_lower_ratio_limit,
>     glob_max_sec,
>     glob_orig_start_sec,
>     glob_normmax,
>     glob_max_minutes,
>     glob_next_display,
>     glob_est_digits,
>     glob_subiter_method,
>     glob_html_log,
>     glob_min_good_digits,
>     glob_good_digits,
>     glob_min_apfp_est_good_digits,
>     glob_apfp_est_good_digits,
>     glob_max_opt_iter,
>     glob_dump,
>     glob_djd_debug,
>     glob_display_flag,
>     glob_djd_debug2,
>     glob_h_reason,
>     glob_sec_in_minute,
>     glob_min_in_hour,
>     glob_hours_in_day,
>     glob_days_in_year,
>     glob_sec_in_hour,
>     glob_sec_in_day,
>     glob_sec_in_year,
>     glob_not_yet_finished,
>     glob_initial_pass,
>     glob_not_yet_start_msg,
>     glob_reached_optimal_h,
>     glob_optimal_done,
>     glob_type_given_pole,
>     glob_optimize,
>     glob_look_poles,
>     glob_dump_closed_form,
>     glob_max_iter,
>     glob_no_eqs,
>     glob_unchanged_h_cnt,
>     glob_warned,
>     glob_warned2,
>     glob_start,
>     glob_iter,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_1,
>     array_const_0D0,
>     array_const_2D0,
>     #END CONST
>     array_y_init,
>     array_norms,
>     array_fact_1,
>     array_1st_rel_error,
>     array_last_rel_error,
>     array_est_rel_error,
>     array_max_est_error,
>     array_type_pole,
>     array_type_real_pole,
>     array_type_complex_pole,
>     array_est_digits,
>     array_y,
>     array_x,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_m1,
>     array_y_higher,
>     array_y_higher_work,
>     array_y_higher_work2,
>     array_y_set_initial,
>     array_given_rad_poles,
>     array_given_ord_poles,
>     array_rad_test_poles,
>     array_ord_test_poles,
>     array_fact_2,
>     ATS_MAX_TERMS,
>     glob_last;
>     ATS_MAX_TERMS := 30;
>     # before first input block
>     #BEGIN FIRST INPUT BLOCK
>     #BEGIN BLOCK 1
>     #BEGIN FIRST INPUT BLOCK
>     Digits:=32;
>     max_terms:=30;
>     #END BLOCK 1
>     #END FIRST INPUT BLOCK
>     #START OF INITS AFTER INPUT BLOCK
>     glob_html_log := true;
>     #END OF INITS AFTER INPUT BLOCK
>     # before generate arrays
>     array_y_init:= Array(0..(30),[]);
>     array_norms:= Array(0..(30),[]);
>     array_fact_1:= Array(0..(30),[]);
>     array_1st_rel_error:= Array(0..(2),[]);
>     array_last_rel_error:= Array(0..(2),[]);
>     array_est_rel_error:= Array(0..(2),[]);
>     array_max_est_error:= Array(0..(2),[]);
>     array_type_pole:= Array(0..(2),[]);
>     array_type_real_pole:= Array(0..(2),[]);
>     array_type_complex_pole:= Array(0..(2),[]);
>     array_est_digits:= Array(0..(2),[]);
>     array_y:= Array(0..(30),[]);
>     array_x:= Array(0..(30),[]);
>     array_tmp0:= Array(0..(30),[]);
>     array_tmp1:= Array(0..(30),[]);
>     array_tmp2:= Array(0..(30),[]);
>     array_tmp3:= Array(0..(30),[]);
>     array_m1:= Array(0..(30),[]);
>     array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
>     array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
>     array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
>     array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
>     array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
>     array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
>     array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
>     array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
>     array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
>     # before generate constants
>     # before generate globals definition
>     #Top Generate Globals Definition
>     #Bottom Generate Globals Deninition
>     # before generate const definition
>     # before arrays initialized
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_y_init[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_norms[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_fact_1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_1st_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_last_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_est_rel_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_max_est_error[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_real_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_type_complex_pole[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 2) do # do number 1
>         array_est_digits[term] := 0;
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_y[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_x[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp0[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp2[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_tmp3[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     term := 1;
>     while (term <= 30) do # do number 1
>         array_m1[term] := c(0.0);
>         term := term + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 30) do # do number 2
>             array_y_higher[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 30) do # do number 2
>             array_y_higher_work[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 30) do # do number 2
>             array_y_higher_work2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 30) do # do number 2
>             array_y_set_initial[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_rad_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 3) do # do number 2
>             array_given_ord_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_rad_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=2) do # do number 1
>         term := 1;
>         while (term <= 4) do # do number 2
>             array_ord_test_poles[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     ord := 1;
>     while (ord <=30) do # do number 1
>         term := 1;
>         while (term <= 30) do # do number 2
>             array_fact_2[ord,term] := c(0.0);
>             term := term + 1;
>         od;# end do number 2;
>         ord := ord + 1;
>     od;# end do number 1;
>     # before symbols initialized
>     #BEGIN SYMBOLS INITIALIZATED
>     zero_ats_ar(array_y);
>     zero_ats_ar(array_x);
>     zero_ats_ar(array_tmp0);
>     zero_ats_ar(array_tmp1);
>     zero_ats_ar(array_tmp2);
>     zero_ats_ar(array_tmp3);
>     zero_ats_ar(array_m1);
>     zero_ats_ar(array_const_1);
>     array_const_1[1]   := c(1);
>     zero_ats_ar(array_const_0D0);
>     array_const_0D0[1]   := c(0.0);
>     zero_ats_ar(array_const_2D0);
>     array_const_2D0[1]   := c(2.0);
>     zero_ats_ar(array_m1);
>     array_m1[1]   := glob__m1;
>     #END SYMBOLS INITIALIZATED
>     # before generate factorials init
>     #Initing Factorial Tables
>     iiif := 0;
>     while (iiif <= ATS_MAX_TERMS) do # do number 1
>         jjjf := 0;
>         while (jjjf <= ATS_MAX_TERMS) do # do number 2
>             array_fact_1[iiif] := 0;
>             array_fact_2[iiif,jjjf] := 0;
>             jjjf := jjjf + 1;
>         od;# end do number 2;
>         iiif := iiif + 1;
>     od;# end do number 1;
>     #Done Initing Factorial Table
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     glob_iolevel := 5;
>     glob_yes_pole := 4;
>     glob_no_pole := 3;
>     glob_not_given := 0;
>     glob_no_sing_tests := 4;
>     glob_ratio_test := 1;
>     glob_three_term_test := 2;
>     glob_six_term_test := 3;
>     glob_log_10 := log(c(10.0));
>     MAX_UNCHANGED := 10;
>     glob__small := c(0.1e-50);
>     glob_small_float := c(0.1e-50);
>     glob_smallish_float := c(0.1e-60);
>     glob_large_float := c(1.0e100);
>     glob_larger_float := c(1.1e100);
>     glob__m2 := c(-2);
>     glob__m1 := c(-1);
>     glob__0 := c(0);
>     glob__1 := c(1);
>     glob__2 := c(2);
>     glob__3 := c(3);
>     glob__4 := c(4);
>     glob__5 := c(5);
>     glob__8 := c(8);
>     glob__10 := c(10);
>     glob__100 := c(100);
>     glob__pi := c(0.0);
>     glob__0_5 := c(0.5);
>     glob__0_8 := c(0.8);
>     glob__m0_8 := c(-0.8);
>     glob__0_25 := c(0.25);
>     glob__0_125 := c(0.125);
>     glob_prec := c(1.0e-16);
>     glob_check_sign := c(1.0);
>     glob_desired_digits_correct := c(8.0);
>     glob_max_estimated_step_error := c(0.0);
>     glob_ratio_of_radius := c(0.1);
>     glob_percent_done := c(0.0);
>     glob_total_exp_sec := c(0.1);
>     glob_optimal_expect_sec := c(0.1);
>     glob_estimated_size_answer := c(100.0);
>     glob_almost_1 := c(0.9990);
>     glob_clock_sec := c(0.0);
>     glob_clock_start_sec := c(0.0);
>     glob_disp_incr := c(0.1);
>     glob_h := c(0.1);
>     glob_diff_rc_fm := c(0.1);
>     glob_diff_rc_fmm1 := c(0.1);
>     glob_diff_rc_fmm2 := c(0.1);
>     glob_diff_ord_fm := c(0.1);
>     glob_diff_ord_fmm1 := c(0.1);
>     glob_diff_ord_fmm2 := c(0.1);
>     glob_six_term_ord_save := c(0.1);
>     glob_guess_error_rc := c(0.1);
>     glob_guess_error_ord := c(0.1);
>     glob_least_given_sing := c(9.9e200);
>     glob_least_ratio_sing := c(9.9e200);
>     glob_least_3_sing := c(9.9e100);
>     glob_least_6_sing := c(9.9e100);
>     glob_last_good_h := c(0.1);
>     glob_max_h := c(0.1);
>     glob_min_h := c(0.000001);
>     glob_display_interval := c(0.1);
>     glob_abserr := c(0.1e-10);
>     glob_relerr := c(0.1e-10);
>     glob_min_pole_est := c(0.1e+10);
>     glob_max_rel_trunc_err := c(0.1e-10);
>     glob_max_trunc_err := c(0.1e-10);
>     glob_max_hours := c(0.0);
>     glob_optimal_clock_start_sec := c(0.0);
>     glob_optimal_start := c(0.0);
>     glob_upper_ratio_limit := c(1.0001);
>     glob_lower_ratio_limit := c(0.9999);
>     glob_max_sec := c(10000.0);
>     glob_orig_start_sec := c(0.0);
>     glob_normmax := c(0.0);
>     glob_max_minutes := c(0.0);
>     glob_next_display := c(0.0);
>     glob_est_digits := 1;
>     glob_subiter_method := 3;
>     glob_html_log := true;
>     glob_min_good_digits := 99999;
>     glob_good_digits := 0;
>     glob_min_apfp_est_good_digits := 99999;
>     glob_apfp_est_good_digits := 0;
>     glob_max_opt_iter := 10;
>     glob_dump := false;
>     glob_djd_debug := true;
>     glob_display_flag := true;
>     glob_djd_debug2 := true;
>     glob_h_reason := 0;
>     glob_sec_in_minute := 60 ;
>     glob_min_in_hour := 60;
>     glob_hours_in_day := 24;
>     glob_days_in_year := 365;
>     glob_sec_in_hour := 3600;
>     glob_sec_in_day := 86400;
>     glob_sec_in_year := 31536000;
>     glob_not_yet_finished := true;
>     glob_initial_pass := true;
>     glob_not_yet_start_msg := true;
>     glob_reached_optimal_h := false;
>     glob_optimal_done := false;
>     glob_type_given_pole := 0;
>     glob_optimize := false;
>     glob_look_poles := false;
>     glob_dump_closed_form := false;
>     glob_max_iter := 1000;
>     glob_no_eqs := 0;
>     glob_unchanged_h_cnt := 0;
>     glob_warned := false;
>     glob_warned2 := false;
>     glob_start := 0;
>     glob_iter := 0;
>     # before generate set diff initial
>     array_y_set_initial[1,1] := true;
>     array_y_set_initial[1,2] := false;
>     array_y_set_initial[1,3] := false;
>     array_y_set_initial[1,4] := false;
>     array_y_set_initial[1,5] := false;
>     array_y_set_initial[1,6] := false;
>     array_y_set_initial[1,7] := false;
>     array_y_set_initial[1,8] := false;
>     array_y_set_initial[1,9] := false;
>     array_y_set_initial[1,10] := false;
>     array_y_set_initial[1,11] := false;
>     array_y_set_initial[1,12] := false;
>     array_y_set_initial[1,13] := false;
>     array_y_set_initial[1,14] := false;
>     array_y_set_initial[1,15] := false;
>     array_y_set_initial[1,16] := false;
>     array_y_set_initial[1,17] := false;
>     array_y_set_initial[1,18] := false;
>     array_y_set_initial[1,19] := false;
>     array_y_set_initial[1,20] := false;
>     array_y_set_initial[1,21] := false;
>     array_y_set_initial[1,22] := false;
>     array_y_set_initial[1,23] := false;
>     array_y_set_initial[1,24] := false;
>     array_y_set_initial[1,25] := false;
>     array_y_set_initial[1,26] := false;
>     array_y_set_initial[1,27] := false;
>     array_y_set_initial[1,28] := false;
>     array_y_set_initial[1,29] := false;
>     array_y_set_initial[1,30] := false;
>     # before generate init omniout const
>     ALWAYS := 1;
>     INFO := 2;
>     DEBUGL := 3;
>     DEBUGMASSIVE := 4;
>     ATS_MAX_TERMS := 30;
>     glob_iolevel := INFO;
>     # set default block
>     #Write Set Defaults
>     glob_orig_start_sec   :=  elapsed_time_seconds();
>     glob_display_flag   :=   true;
>     glob_no_eqs   := 1;
>     glob_iter   :=  -1;
>     opt_iter   :=  -1;
>     glob_max_iter   :=  50000;
>     glob_max_hours   :=  (0.0);
>     glob_max_minutes   :=  (15.0);
>     omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
>     omniout_str(ALWAYS,"##############temp/div_c_exppostode.ode#################");
>     omniout_str(ALWAYS,"diff  (  y  ,  x  ,  1  )   =   2.0  /  exp ( x )  ; ");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"Digits:=32;");
>     omniout_str(ALWAYS,"max_terms:=30;");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>     omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>     omniout_str(ALWAYS,"x_start := c(1.0);");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"x_end := c(5.0) ;");
>     omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
>     omniout_str(ALWAYS,"glob_look_poles := true;");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"");
>     omniout_str(ALWAYS,"glob_type_given_pole := 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(0.005);");
>     omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
>     omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>     omniout_str(ALWAYS,"!");
>     omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>     omniout_str(ALWAYS,"exact_soln_y := proc(x)");
>     omniout_str(ALWAYS,"return(c(-2.0)/exp(c(x)));");
>     omniout_str(ALWAYS,"end;");
>     omniout_str(ALWAYS,"#END USER DEF BLOCK");
>     omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>     glob_unchanged_h_cnt   :=  0;
>     glob_warned   :=  false;
>     glob_warned2   :=  false;
>     glob_small_float   := glob__0;
>     glob_smallish_float   := glob__0;
>     glob_large_float   :=  c(1.0e100);
>     glob_larger_float   := c( 1.1e100);
>     glob_almost_1   := c( 0.99);
>     # before second block
>     #TOP SECOND INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     #BEGIN BLOCK 2
>     #END FIRST INPUT BLOCK
>     #BEGIN SECOND INPUT BLOCK
>     x_start := c(1.0);
>     x_end := c(5.0) ;
>     array_y_init[0 + 1] := exact_soln_y(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(0.005);
>     glob_display_interval:=c(0.01);
>     #END OVERRIDE BLOCK
>     #END BLOCK 2
>     #END SECOND INPUT BLOCK
>     #BEGIN INITS AFTER SECOND INPUT BLOCK
>     glob_last_good_h := glob_h;
>     glob_max_sec   := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
>     #  after second input block
>     glob_check_sign := c(my_check_sign(x_start,x_end));
>     glob__pi := arccos(glob__m1);
>     glob_prec = expt(10.0,c(-Digits));
>     if (glob_optimize)  then # if number 9
>         #BEGIN OPTIMIZE CODE
>         omniout_str(ALWAYS,"START of Optimize");
>         #Start Series -- INITIALIZE FOR OPTIMIZE
>         found_h := false;
>         glob_min_pole_est :=  glob_larger_float;
>         last_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         glob_min_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_max_h := float_abs(glob_max_h) * glob_check_sign;
>         glob_h := float_abs(glob_min_h) * glob_check_sign;
>         glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
>         display_max := c(x_end) - c(x_start)/glob__10;
>         if ((glob_display_interval) > (display_max)) then # if number 10
>             glob_display_interval := c(display_max);
>         fi;# end if 10;
>         chk_data();
>         min_value := glob_larger_float;
>         est_answer := est_size_answer();
>         opt_iter := 1;
>         est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>         omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>         estimated_step_error  := glob_small_float;
>         while ((opt_iter <= 100) and ( not found_h)) do # do number 1
>             omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
>             array_x[1]   := c(x_start);
>             array_x[2]   :=  c(glob_h);
>             glob_next_display := c(x_start);
>             order_diff := 1;
>             #Start Series array_y
>             term_no   :=  1;
>             while (term_no <= order_diff) do # do number 2
>                 array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             rows   :=  order_diff;
>             r_order   :=  1;
>             while (r_order <= rows) do # do number 2
>                 term_no   :=  1;
>                 while (term_no <= (rows - r_order + 1)) do # do number 3
>                     it  := term_no + r_order - 1;
>                     if (term_no < ATS_MAX_TERMS) then # if number 10
>                         array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                     fi;# end if 10;
>                     term_no   :=  term_no + 1;
>                 od;# end do number 3;
>                 r_order   :=  r_order + 1;
>             od;# end do number 2
>             ;
>             atomall();
>             if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
>                 omniout_str(ALWAYS,"SETTING H FOR MIN H");
>                 glob_h := glob_check_sign * float_abs(glob_min_h);
>                 glob_h_reason := 1;
>                 found_h := true;
>             fi;# end if 10;
>             if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
>                 omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
>                 glob_h_reason := 2;
>                 glob_h := glob_display_interval;
>                 found_h := true;
>             fi;# end if 10;
>             if (glob_look_poles)  then # if number 10
>                 check_for_pole();
>             fi;# end if 10;
>             if ( not found_h) then # if number 10
>                 est_answer := est_size_answer();
>                 est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
>                 omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
>                 estimated_step_error := test_suggested_h();
>                 omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
>                 if (estimated_step_error < est_needed_step_err) then # if number 11
>                     omniout_str(ALWAYS,"Double H and LOOP");
>                     glob_h := glob_h*glob__2;
>                 else
>                     omniout_str(ALWAYS,"Found H for OPTIMAL");
>                     found_h := true;
>                     glob_h_reason := 3;
>                     glob_h := glob_h/glob__2;
>                 fi;# end if 11;
>             fi;# end if 10;
>             opt_iter := opt_iter + 1;
>         od;# end do number 1;
>         if (( not found_h) and (opt_iter = 1)) then # if number 10
>             omniout_str(ALWAYS,"Beginning glob_h too large.");
>             found_h := false;
>         fi;# end if 10;
>         if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
>             omniout_str(ALWAYS,"SETTING H FOR MAX H");
>             glob_h := glob_check_sign * float_abs(glob_max_h);
>             glob_h_reason := 1;
>             found_h := true;
>         fi;# end if 10;
>     else
>         found_h := true;
>         glob_h := glob_h * glob_check_sign;
>     fi;# end if 9;
>     #END OPTIMIZE CODE
>     if (glob_html_log)  then # if number 9
>         html_log_file := fopen("entry.html",WRITE,TEXT);
>     fi;# end if 9;
>     #BEGIN SOLUTION CODE
>     if (found_h) then # if number 9
>         omniout_str(ALWAYS,"START of Soultion");
>         #Start Series -- INITIALIZE FOR SOLUTION
>         array_x[1]   := c(x_start);
>         array_x[2]   :=  c(glob_h);
>         glob_next_display := c(x_start);
>         glob_min_pole_est :=  glob_larger_float;
>         glob_least_given_sing := glob_larger_float;
>         glob_least_ratio_sing := glob_larger_float;
>         glob_least_3_sing := glob_larger_float;
>         glob_least_6_sing := glob_larger_float;
>         order_diff := 1;
>         #Start Series array_y
>         term_no   :=  1;
>         while (term_no <= order_diff) do # do number 1
>             array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
>             term_no   :=  term_no + 1;
>         od;# end do number 1;
>         rows   :=  order_diff;
>         r_order   :=  1;
>         while (r_order <= rows) do # do number 1
>             term_no   :=  1;
>             while (term_no <= (rows - r_order + 1)) do # do number 2
>                 it  := term_no + r_order - 1;
>                 if (term_no < ATS_MAX_TERMS) then # if number 10
>                     array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
>                 fi;# end if 10;
>                 term_no   :=  term_no + 1;
>             od;# end do number 2;
>             r_order   :=  r_order + 1;
>         od;# end do number 1
>         ;
>         current_iter   :=  1;
>         glob_clock_start_sec   := elapsed_time_seconds();
>         glob_clock_sec   :=  elapsed_time_seconds();
>         glob_iter   :=  0;
>         omniout_str(DEBUGL," ");
>         glob_reached_optimal_h   :=  true;
>         glob_optimal_clock_start_sec := elapsed_time_seconds();
>         while ((glob_iter < glob_max_iter)  and (glob_check_sign * array_x[1] < glob_check_sign * x_end )  and  (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
>             #left paren 0001C
>             if (reached_interval()) then # if number 10
>                 omniout_str(INFO," ");
>                 omniout_str(INFO,"TOP MAIN SOLVE Loop");
>             fi;# end if 10;
>             glob_iter   :=  glob_iter + 1;
>             glob_clock_sec   := elapsed_time_seconds();
>             track_estimated_error();
>             atomall();
>             track_estimated_error();
>             display_alot(current_iter);
>             if (glob_look_poles)  then # if number 10
>                 check_for_pole();
>             fi;# end if 10;
>             if (reached_interval()) then # if number 10
>                 glob_next_display  := glob_next_display + glob_display_interval;
>             fi;# end if 10;
>             array_x[1]   := array_x[1] + glob_h;
>             array_x[2]   :=  glob_h;
>             #Jump Series array_y;
>             order_diff  := 2;
>             #START PART 1  SUM AND ADJUST
>             #START SUM AND ADJUST EQ =1
>             #sum_and_adjust array_y
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 2;
>             calc_term := 1;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 2;
>             calc_term := 1;
>             #sum_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 2;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 2;
>             #sum_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #BEFORE ADJUST SUBSERIES EQ =1
>             ord := 1;
>             calc_term := 1;
>             #adjust_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii  - 1));
>                 iii  := iii - 1;
>             od;# end do number 2;
>             #AFTER ADJUST SUBSERIES EQ =1
>             #BEFORE SUM SUBSERIES EQ =1
>             temp_sum := glob__0;
>             ord := 1;
>             calc_term := 1;
>             #sum_subseriesarray_y
>             iii  := ATS_MAX_TERMS;
>             while (iii >= calc_term)   do # do number 2
>                 temp_sum := temp_sum + array_y_higher_work[ord,iii];
>                 iii  := iii - 1;
>             od;# end do number 2;
>             array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
>             #AFTER SUM SUBSERIES EQ =1
>             #END SUM AND ADJUST EQ =1
>             #END PART 1
>             #START PART 2  MOVE TERMS to REGULAR Array
>             term_no := ATS_MAX_TERMS;
>             while (term_no >= 1) do # do number 2
>                 array_y[term_no] := array_y_higher_work2[1,term_no];
>                 ord := 1;
>                 while (ord <= order_diff)  do # do number 3
>                     array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
>                     ord := ord + 1;
>                 od;# end do number 3;
>                 term_no   :=  term_no - 1;
>             od;# end do number 2;
>             #END PART 2 HEVE MOVED TERMS to REGULAR Array
>             ;
>         od;# end do number 1;#right paren 0001C
>         omniout_str(ALWAYS,"Finished!");
>         if (glob_iter >= glob_max_iter)  then # if number 10
>             omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
>         fi;# end if 10;
>         if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec  )) then # if number 10
>             omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
>         fi;# end if 10;
>         glob_clock_sec   := elapsed_time_seconds();
>         omniout_str(INFO,"diff  (  y  ,  x  ,  1  )   =   2.0  /  exp ( x )  ; ");
>         omniout_int(INFO,"Iterations                      ",32,glob_iter,4," ")
>         ;
>         prog_report(x_start,x_end);
>         if (glob_html_log)  then # if number 10
>             logstart(html_log_file);
>             logitem_str(html_log_file,"2015-05-02T21:26:35-05:00")
>             ;
>             logitem_str(html_log_file,"Maple")
>             ;
>             logitem_str(html_log_file,"<a href=\"div_c_exp.ode.txt\">div_c_exp</a>")
>             ;
>             logitem_str(html_log_file,"diff  (  y  ,  x  ,  1  )   =   2.0  /  exp ( 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 11
>                 logitem_integer(html_log_file,array_est_digits[1])
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             if (glob_min_good_digits <> -16) then # if number 11
>                 logitem_integer(html_log_file,glob_min_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             if (glob_good_digits <> -16) then # if number 11
>                 logitem_integer(html_log_file,glob_good_digits)
>                 ;
>             else
>                 logitem_str(html_log_file,"Unknown")
>                 ;
>             fi;# end if 11;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_str(html_log_file,"NA")
>             ;
>             logitem_integer(html_log_file,ATS_MAX_TERMS)
>             ;
>             if (glob_type_given_pole  = 0) then # if number 11
>                 logitem_str(html_log_file,"Not Given")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 4) then # if number 12
>                 logitem_str(html_log_file,"No Solution")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 5) then # if number 13
>                 logitem_str(html_log_file,"Some Pole")
>                 ;
>                 logitem_str(html_log_file,"????")
>                 ;
>             elif
>             (glob_type_given_pole  = 3) then # if number 14
>                 logitem_str(html_log_file,"No Pole")
>                 ;
>                 logitem_str(html_log_file,"NA")
>                 ;
>             elif
>             (glob_type_given_pole  = 1) then # if number 15
>                 logitem_str(html_log_file,"Real Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             elif
>             (glob_type_given_pole  = 2) then # if number 16
>                 logitem_str(html_log_file,"Complex Sing")
>                 ;
>                 logitem_float(html_log_file,glob_least_given_sing)
>                 ;
>             fi;# end if 16;
>             if (glob_least_ratio_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_ratio_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             if (glob_least_3_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_3_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             if (glob_least_6_sing < glob_large_float) then # if number 16
>                 logitem_float(html_log_file,glob_least_6_sing)
>                 ;
>             else
>                 logitem_str(html_log_file,"NONE")
>                 ;
>             fi;# end if 16;
>             logitem_integer(html_log_file,glob_iter)
>             ;
>             logitem_time(html_log_file,(glob_clock_sec))
>             ;
>             if (c(glob_percent_done) < glob__100)  then # if number 16
>                 logitem_time(html_log_file,(glob_total_exp_sec))
>                 ;
>                 0;
>             else
>                 logitem_str(html_log_file,"Done")
>                 ;
>                 0;
>             fi;# end if 16;
>             log_revs(html_log_file,"<td> 308.maple.seems.ok </td>")
>             ;
>             logitem_str(html_log_file,"<a href=\"diffeq.div_c_exp.mxt.txt\">div_c_exp diffeq.mxt</a>")
>             ;
>             logitem_str(html_log_file,"<a href=\"results.div_c_exp.mxt.txt\">div_c_exp maple results</a>")
>             ;
>             logitem_str(html_log_file,"OK")
>             ;
>             logend(html_log_file)
>             ;
>             ;
>         fi;# end if 15;
>         if (glob_html_log)  then # if number 15
>             fclose(html_log_file);
>         fi;# end if 15
>         ;
>         ;;
>     fi;# end if 14
>     #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
    ATS_MAX_TERMS := 30;
    Digits := 32;
    max_terms := 30;
    glob_html_log := true;
    array_y_init := Array(0 .. 30, []);
    array_norms := Array(0 .. 30, []);
    array_fact_1 := Array(0 .. 30, []);
    array_1st_rel_error := Array(0 .. 2, []);
    array_last_rel_error := Array(0 .. 2, []);
    array_est_rel_error := Array(0 .. 2, []);
    array_max_est_error := Array(0 .. 2, []);
    array_type_pole := Array(0 .. 2, []);
    array_type_real_pole := Array(0 .. 2, []);
    array_type_complex_pole := Array(0 .. 2, []);
    array_est_digits := Array(0 .. 2, []);
    array_y := Array(0 .. 30, []);
    array_x := Array(0 .. 30, []);
    array_tmp0 := Array(0 .. 30, []);
    array_tmp1 := Array(0 .. 30, []);
    array_tmp2 := Array(0 .. 30, []);
    array_tmp3 := Array(0 .. 30, []);
    array_m1 := Array(0 .. 30, []);
    array_y_higher := Array(0 .. 2, 0 .. 31, []);
    array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
    array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
    array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
    array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
    array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
    array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
    array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
    array_fact_2 := Array(0 .. 30, 0 .. 31, []);
    term := 1;
    while term <= 30 do array_y_init[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
    ;
    term := 1;
    while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do
        array_last_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
    term := 1;
    while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
    end do;
    term := 1;
    while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
    ;
    term := 1;
    while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
    term := 1;
    while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 30 do
            array_y_higher[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 30 do
            array_y_higher_work[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 30 do
            array_y_higher_work2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 30 do
            array_y_set_initial[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_given_rad_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_given_ord_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 4 do
            array_rad_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 4 do
            array_ord_test_poles[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 30 do
        term := 1;
        while term <= 30 do
            array_fact_2[ord, term] := c(0.); term := term + 1
        end do;
        ord := ord + 1
    end do;
    zero_ats_ar(array_y);
    zero_ats_ar(array_x);
    zero_ats_ar(array_tmp0);
    zero_ats_ar(array_tmp1);
    zero_ats_ar(array_tmp2);
    zero_ats_ar(array_tmp3);
    zero_ats_ar(array_m1);
    zero_ats_ar(array_const_1);
    array_const_1[1] := c(1);
    zero_ats_ar(array_const_0D0);
    array_const_0D0[1] := c(0.);
    zero_ats_ar(array_const_2D0);
    array_const_2D0[1] := c(2.0);
    zero_ats_ar(array_m1);
    array_m1[1] := glob__m1;
    iiif := 0;
    while iiif <= ATS_MAX_TERMS do
        jjjf := 0;
        while jjjf <= ATS_MAX_TERMS do
            array_fact_1[iiif] := 0;
            array_fact_2[iiif, jjjf] := 0;
            jjjf := jjjf + 1
        end do;
        iiif := iiif + 1
    end do;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    glob_iolevel := 5;
    glob_yes_pole := 4;
    glob_no_pole := 3;
    glob_not_given := 0;
    glob_no_sing_tests := 4;
    glob_ratio_test := 1;
    glob_three_term_test := 2;
    glob_six_term_test := 3;
    glob_log_10 := log(c(10.0));
    MAX_UNCHANGED := 10;
    glob__small := c(0.1*10^(-50));
    glob_small_float := c(0.1*10^(-50));
    glob_smallish_float := c(0.1*10^(-60));
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob__m2 := c(-2);
    glob__m1 := c(-1);
    glob__0 := c(0);
    glob__1 := c(1);
    glob__2 := c(2);
    glob__3 := c(3);
    glob__4 := c(4);
    glob__5 := c(5);
    glob__8 := c(8);
    glob__10 := c(10);
    glob__100 := c(100);
    glob__pi := c(0.);
    glob__0_5 := c(0.5);
    glob__0_8 := c(0.8);
    glob__m0_8 := c(-0.8);
    glob__0_25 := c(0.25);
    glob__0_125 := c(0.125);
    glob_prec := c(0.10*10^(-15));
    glob_check_sign := c(1.0);
    glob_desired_digits_correct := c(8.0);
    glob_max_estimated_step_error := c(0.);
    glob_ratio_of_radius := c(0.1);
    glob_percent_done := c(0.);
    glob_total_exp_sec := c(0.1);
    glob_optimal_expect_sec := c(0.1);
    glob_estimated_size_answer := c(100.0);
    glob_almost_1 := c(0.9990);
    glob_clock_sec := c(0.);
    glob_clock_start_sec := c(0.);
    glob_disp_incr := c(0.1);
    glob_h := c(0.1);
    glob_diff_rc_fm := c(0.1);
    glob_diff_rc_fmm1 := c(0.1);
    glob_diff_rc_fmm2 := c(0.1);
    glob_diff_ord_fm := c(0.1);
    glob_diff_ord_fmm1 := c(0.1);
    glob_diff_ord_fmm2 := c(0.1);
    glob_six_term_ord_save := c(0.1);
    glob_guess_error_rc := c(0.1);
    glob_guess_error_ord := c(0.1);
    glob_least_given_sing := c(0.99*10^201);
    glob_least_ratio_sing := c(0.99*10^201);
    glob_least_3_sing := c(0.99*10^101);
    glob_least_6_sing := c(0.99*10^101);
    glob_last_good_h := c(0.1);
    glob_max_h := c(0.1);
    glob_min_h := c(0.1*10^(-5));
    glob_display_interval := c(0.1);
    glob_abserr := c(0.1*10^(-10));
    glob_relerr := c(0.1*10^(-10));
    glob_min_pole_est := c(0.1*10^10);
    glob_max_rel_trunc_err := c(0.1*10^(-10));
    glob_max_trunc_err := c(0.1*10^(-10));
    glob_max_hours := c(0.);
    glob_optimal_clock_start_sec := c(0.);
    glob_optimal_start := c(0.);
    glob_upper_ratio_limit := c(1.0001);
    glob_lower_ratio_limit := c(0.9999);
    glob_max_sec := c(10000.0);
    glob_orig_start_sec := c(0.);
    glob_normmax := c(0.);
    glob_max_minutes := c(0.);
    glob_next_display := c(0.);
    glob_est_digits := 1;
    glob_subiter_method := 3;
    glob_html_log := true;
    glob_min_good_digits := 99999;
    glob_good_digits := 0;
    glob_min_apfp_est_good_digits := 99999;
    glob_apfp_est_good_digits := 0;
    glob_max_opt_iter := 10;
    glob_dump := false;
    glob_djd_debug := true;
    glob_display_flag := true;
    glob_djd_debug2 := true;
    glob_h_reason := 0;
    glob_sec_in_minute := 60;
    glob_min_in_hour := 60;
    glob_hours_in_day := 24;
    glob_days_in_year := 365;
    glob_sec_in_hour := 3600;
    glob_sec_in_day := 86400;
    glob_sec_in_year := 31536000;
    glob_not_yet_finished := true;
    glob_initial_pass := true;
    glob_not_yet_start_msg := true;
    glob_reached_optimal_h := false;
    glob_optimal_done := false;
    glob_type_given_pole := 0;
    glob_optimize := false;
    glob_look_poles := false;
    glob_dump_closed_form := false;
    glob_max_iter := 1000;
    glob_no_eqs := 0;
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_start := 0;
    glob_iter := 0;
    array_y_set_initial[1, 1] := true;
    array_y_set_initial[1, 2] := false;
    array_y_set_initial[1, 3] := false;
    array_y_set_initial[1, 4] := false;
    array_y_set_initial[1, 5] := false;
    array_y_set_initial[1, 6] := false;
    array_y_set_initial[1, 7] := false;
    array_y_set_initial[1, 8] := false;
    array_y_set_initial[1, 9] := false;
    array_y_set_initial[1, 10] := false;
    array_y_set_initial[1, 11] := false;
    array_y_set_initial[1, 12] := false;
    array_y_set_initial[1, 13] := false;
    array_y_set_initial[1, 14] := false;
    array_y_set_initial[1, 15] := false;
    array_y_set_initial[1, 16] := false;
    array_y_set_initial[1, 17] := false;
    array_y_set_initial[1, 18] := false;
    array_y_set_initial[1, 19] := false;
    array_y_set_initial[1, 20] := false;
    array_y_set_initial[1, 21] := false;
    array_y_set_initial[1, 22] := false;
    array_y_set_initial[1, 23] := false;
    array_y_set_initial[1, 24] := false;
    array_y_set_initial[1, 25] := false;
    array_y_set_initial[1, 26] := false;
    array_y_set_initial[1, 27] := false;
    array_y_set_initial[1, 28] := false;
    array_y_set_initial[1, 29] := false;
    array_y_set_initial[1, 30] := false;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    ATS_MAX_TERMS := 30;
    glob_iolevel := INFO;
    glob_orig_start_sec := elapsed_time_seconds();
    glob_display_flag := true;
    glob_no_eqs := 1;
    glob_iter := -1;
    opt_iter := -1;
    glob_max_iter := 50000;
    glob_max_hours := 0.;
    glob_max_minutes := 15.0;
    omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
    omniout_str(ALWAYS,
        "##############temp/div_c_exppostode.ode#################");
    omniout_str(ALWAYS,
        "diff  (  y  ,  x  ,  1  )   =   2.0  /  exp ( x )  ; ");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits:=32;");
    omniout_str(ALWAYS, "max_terms:=30;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "x_start := c(1.0);");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "x_end := c(5.0) ;");
    omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "");
    omniout_str(ALWAYS, "glob_type_given_pole := 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(0.005);");
    omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_y := proc(x)");
    omniout_str(ALWAYS, "return(c(-2.0)/exp(c(x)));");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := glob__0;
    glob_smallish_float := glob__0;
    glob_large_float := c(0.10*10^101);
    glob_larger_float := c(0.11*10^101);
    glob_almost_1 := c(0.99);
    x_start := c(1.0);
    x_end := c(5.0);
    array_y_init[1] := exact_soln_y(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(0.005);
    glob_display_interval := c(0.01);
    glob_last_good_h := glob_h;
    glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
    glob_check_sign := c(my_check_sign(x_start, x_end));
    glob__pi := arccos(glob__m1);
    glob_prec = expt(10.0, c(-Digits));
    if glob_optimize then
        omniout_str(ALWAYS, "START of Optimize");
        found_h := false;
        glob_min_pole_est := glob_larger_float;
        last_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        glob_min_h := float_abs(glob_min_h)*glob_check_sign;
        glob_max_h := float_abs(glob_max_h)*glob_check_sign;
        glob_h := float_abs(glob_min_h)*glob_check_sign;
        glob_display_interval :=
            c(float_abs(c(glob_display_interval))*glob_check_sign);
        display_max := c(x_end) - c(x_start)/glob__10;
        if display_max < glob_display_interval then
            glob_display_interval := c(display_max)
        end if;
        chk_data();
        min_value := glob_larger_float;
        est_answer := est_size_answer();
        opt_iter := 1;
        est_needed_step_err :=
            estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
            ;
        omniout_float(ALWAYS, "est_needed_step_err", 32,
            est_needed_step_err, 16, "");
        estimated_step_error := glob_small_float;
        while opt_iter <= 100 and not found_h do
            omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
            array_x[1] := c(x_start);
            array_x[2] := c(glob_h);
            glob_next_display := c(x_start);
            order_diff := 1;
            term_no := 1;
            while term_no <= order_diff do
                array_y[term_no] := array_y_init[term_no]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1));
                term_no := term_no + 1
            end do;
            rows := order_diff;
            r_order := 1;
            while r_order <= rows do
                term_no := 1;
                while term_no <= rows - r_order + 1 do
                    it := term_no + r_order - 1;
                    if term_no < ATS_MAX_TERMS then
                        array_y_higher[r_order, term_no] :=
                        array_y_init[it]*expt(glob_h, c(term_no - 1))/
                        c(factorial_1(term_no - 1))
                    end if;
                    term_no := term_no + 1
                end do;
                r_order := r_order + 1
            end do;
            atomall();
            if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
                omniout_str(ALWAYS, "SETTING H FOR MIN H");
                glob_h := float_abs(glob_min_h)*glob_check_sign;
                glob_h_reason := 1;
                found_h := true
            end if;
            if
            glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
            then
                omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
                glob_h_reason := 2;
                glob_h := glob_display_interval;
                found_h := true
            end if;
            if glob_look_poles then check_for_pole() end if;
            if not found_h then
                est_answer := est_size_answer();
                est_needed_step_err := estimated_needed_step_error(x_start,
                    x_end, glob_h, est_answer);
                omniout_float(ALWAYS, "est_needed_step_err", 32,
                    est_needed_step_err, 16, "");
                estimated_step_error := test_suggested_h();
                omniout_float(ALWAYS, "estimated_step_error", 32,
                    estimated_step_error, 32, "");
                if estimated_step_error < est_needed_step_err then
                    omniout_str(ALWAYS, "Double H and LOOP");
                    glob_h := glob_h*glob__2
                else
                    omniout_str(ALWAYS, "Found H for OPTIMAL");
                    found_h := true;
                    glob_h_reason := 3;
                    glob_h := glob_h/glob__2
                end if
            end if;
            opt_iter := opt_iter + 1
        end do;
        if not found_h and opt_iter = 1 then
            omniout_str(ALWAYS, "Beginning glob_h too large.");
            found_h := false
        end if;
        if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
            omniout_str(ALWAYS, "SETTING H FOR MAX H");
            glob_h := float_abs(glob_max_h)*glob_check_sign;
            glob_h_reason := 1;
            found_h := true
        end if
    else found_h := true; glob_h := glob_check_sign*glob_h
    end if;
    if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
    end if;
    if found_h then
        omniout_str(ALWAYS, "START of Soultion");
        array_x[1] := c(x_start);
        array_x[2] := c(glob_h);
        glob_next_display := c(x_start);
        glob_min_pole_est := glob_larger_float;
        glob_least_given_sing := glob_larger_float;
        glob_least_ratio_sing := glob_larger_float;
        glob_least_3_sing := glob_larger_float;
        glob_least_6_sing := glob_larger_float;
        order_diff := 1;
        term_no := 1;
        while term_no <= order_diff do
            array_y[term_no] := array_y_init[term_no]*
                expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
            term_no := term_no + 1
        end do;
        rows := order_diff;
        r_order := 1;
        while r_order <= rows do
            term_no := 1;
            while term_no <= rows - r_order + 1 do
                it := term_no + r_order - 1;
                if term_no < ATS_MAX_TERMS then
                    array_y_higher[r_order, term_no] := array_y_init[it]*
                    expt(glob_h, c(term_no - 1))/
                    c(factorial_1(term_no - 1))
                end if;
                term_no := term_no + 1
            end do;
            r_order := r_order + 1
        end do;
        current_iter := 1;
        glob_clock_start_sec := elapsed_time_seconds();
        glob_clock_sec := elapsed_time_seconds();
        glob_iter := 0;
        omniout_str(DEBUGL, " ");
        glob_reached_optimal_h := true;
        glob_optimal_clock_start_sec := elapsed_time_seconds();
        while glob_iter < glob_max_iter and
        glob_check_sign*array_x[1] < glob_check_sign*x_end and
        glob_clock_sec - glob_orig_start_sec < glob_max_sec do
            if reached_interval() then
                omniout_str(INFO, " ");
                omniout_str(INFO, "TOP MAIN SOLVE Loop")
            end if;
            glob_iter := glob_iter + 1;
            glob_clock_sec := elapsed_time_seconds();
            track_estimated_error();
            atomall();
            track_estimated_error();
            display_alot(current_iter);
            if glob_look_poles then check_for_pole() end if;
            if reached_interval() then glob_next_display :=
                glob_next_display + glob_display_interval
            end if;
            array_x[1] := array_x[1] + glob_h;
            array_x[2] := glob_h;
            order_diff := 2;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 2;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 2;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
                    expt(glob_h, c(calc_term - 1))*
                    c(factorial_3(iii - calc_term, iii - 1)));
                iii := iii - 1
            end do;
            temp_sum := glob__0;
            ord := 1;
            calc_term := 1;
            iii := ATS_MAX_TERMS;
            while calc_term <= iii do
                temp_sum := temp_sum + array_y_higher_work[ord, iii];
                iii := iii - 1
            end do;
            array_y_higher_work2[ord, calc_term] := temp_sum*
                expt(glob_h, c(calc_term - 1))/
                c(factorial_1(calc_term - 1));
            term_no := ATS_MAX_TERMS;
            while 1 <= term_no do
                array_y[term_no] := array_y_higher_work2[1, term_no];
                ord := 1;
                while ord <= order_diff do
                    array_y_higher[ord, term_no] :=
                        array_y_higher_work2[ord, term_no];
                    ord := ord + 1
                end do;
                term_no := term_no - 1
            end do
        end do;
        omniout_str(ALWAYS, "Finished!");
        if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
            "Maximum Iterations Reached before Solution Completed!")
        end if;
        if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
        then omniout_str(ALWAYS,
            "Maximum Time Reached before Solution Completed!")
        end if;
        glob_clock_sec := elapsed_time_seconds();
        omniout_str(INFO,
            "diff  (  y  ,  x  ,  1  )   =   2.0  /  exp ( x )  ; ");
        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, "2015-05-02T21:26:35-05:00");
            logitem_str(html_log_file, "Maple");
            logitem_str(html_log_file,
                "<a href=\"div_c_exp.ode.txt\">div_c_exp</a>");
            logitem_str(html_log_file,
                "diff  (  y  ,  x  ,  1  )   =   2.0  /  exp ( 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.div_c_exp.mxt.tx\
                t\">div_c_exp diffeq.mxt</a>");
            logitem_str(html_log_file, "<a href=\"results.div_c_exp.mxt.t\
                xt\">div_c_exp maple results</a>");
            logitem_str(html_log_file, "OK");
            logend(html_log_file)
        end if;
        if glob_html_log then fclose(html_log_file) end if
    end if
end proc

# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/div_c_exppostode.ode#################
diff  (  y  ,  x  ,  1  )   =   2.0  /  exp ( x )  ; 
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(1.0);

x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(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(0.005);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(-2.0)/exp(c(x)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                              = 1                                            
y[1] (closed_form)                = -0.73575888234288464319104754032291          
y[1] (numeric)                    = -0.73575888234288464319104754032291          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 14                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=4.2MB, alloc=40.3MB, time=0.11
x[1]                              = 1.01                                         
y[1] (closed_form)                = -0.72843795914304663951409259127469          
y[1] (numeric)                    = -0.72843795914304663951409259127468          
absolute error                    = 1e-32                                        
relative error                    = 1.3728005075084582469948881583302e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 14                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.02                                         
y[1] (closed_form)                = -0.72118988034615659656268326930804          
y[1] (numeric)                    = -0.72118988034615659656268326930802          
absolute error                    = 2e-32                                        
relative error                    = 2.7731947639642979167991997771454e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.03                                         
y[1] (closed_form)                = -0.71401392113829473953486123130269          
y[1] (numeric)                    = -0.71401392113829473953486123130269          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.04                                         
y[1] (closed_form)                = -0.70690936391756029630511653061792          
y[1] (numeric)                    = -0.7069093639175602963051165306179           
absolute error                    = 2e-32                                        
relative error                    = 2.8292170143515595195194860071813e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.05                                         
y[1] (closed_form)                = -0.69987549822231070934359774715362          
y[1] (numeric)                    = -0.69987549822231070934359774715362          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.06                                         
y[1] (closed_form)                = -0.69291162066011487940701669618026          
y[1] (numeric)                    = -0.69291162066011487940701669618025          
absolute error                    = 1e-32                                        
relative error                    = 1.4431854946339791231206876424608e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.07                                         
y[1] (closed_form)                = -0.68601703483741333626641097879752          
y[1] (numeric)                    = -0.6860170348374133362664109787975           
absolute error                    = 2e-32                                        
relative error                    = 2.9153794999769966738778707729755e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.08                                         
y[1] (closed_form)                = -0.67919105128987830243022043049529          
y[1] (numeric)                    = -0.67919105128987830243022043049529          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.09                                         
y[1] (closed_form)                = -0.67243298741346668581101630178611          
y[1] (numeric)                    = -0.6724329874134666858110163017861           
absolute error                    = 1e-32                                        
relative error                    = 1.4871370362815326581559532945679e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.1                                          
y[1] (closed_form)                = -0.66574216739615910657769381286262          
y[1] (numeric)                    = -0.66574216739615910657769381286262          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.11                                         
y[1] (closed_form)                = -0.65911792215037813203892896763225          
y[1] (numeric)                    = -0.65911792215037813203892896763225          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.12                                         
y[1] (closed_form)                = -0.65255958924607896132506964748516          
y[1] (numeric)                    = -0.65255958924607896132506964748514          
absolute error                    = 2e-32                                        
relative error                    = 3.0648542032930020449686230918988e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.13                                         
y[1] (closed_form)                = -0.64606651284450586888117122528068          
y[1] (numeric)                    = -0.64606651284450586888117122528067          
absolute error                    = 1e-32                                        
relative error                    = 1.5478282500623557451965061635118e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.14                                         
y[1] (closed_form)                = -0.63963804363260778236032285534765          
y[1] (numeric)                    = -0.63963804363260778236032285534764          
absolute error                    = 1e-32                                        
relative error                    = 1.5633841825930778780657781205898e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.15                                         
y[1] (closed_form)                = -0.63327353875810643642039990485905          
y[1] (numeric)                    = -0.63327353875810643642039990485905          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.16                                         
y[1] (closed_form)                = -0.62697236176521060918551214962199          
y[1] (numeric)                    = -0.62697236176521060918551214962199          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.17                                         
y[1] (closed_form)                = -0.62073388253097001274222223091491          
y[1] (numeric)                    = -0.62073388253097001274222223091491          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.18                                         
y[1] (closed_form)                = -0.61455747720226247300654539383636          
y[1] (numeric)                    = -0.61455747720226247300654539383636          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.19                                         
y[1] (closed_form)                = -0.60844252813340809762720634865897          
y[1] (numeric)                    = -0.60844252813340809762720634865894          
absolute error                    = 3e-32                                        
relative error                    = 4.9306218110746774164762468054117e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.2                                          
y[1] (closed_form)                = -0.60238842382440419328995521416645          
y[1] (numeric)                    = -0.60238842382440419328995521416642          
absolute error                    = 3e-32                                        
relative error                    = 4.9801753841048212342961511444024e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.21                                         
y[1] (closed_form)                = -0.59639455885977475586320190075193          
y[1] (numeric)                    = -0.5963945588597747558632019007519           
absolute error                    = 3e-32                                        
relative error                    = 5.0302269788235355215053841410635e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.22                                         
y[1] (closed_form)                = -0.59046033384802841828302456864059          
y[1] (numeric)                    = -0.59046033384802841828302456864057          
absolute error                    = 2e-32                                        
relative error                    = 3.3871877336213346338871451880633e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.23                                         
y[1] (closed_form)                = -0.58458515536171880192188878381439          
y[1] (numeric)                    = -0.58458515536171880192188878381436          
absolute error                    = 3e-32                                        
relative error                    = 5.1318443044345103606852285271783e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.24                                         
y[1] (closed_form)                = -0.57876843587810127742626436986212          
y[1] (numeric)                    = -0.57876843587810127742626436986211          
absolute error                    = 1e-32                                        
relative error                    = 1.7278067323813377990288077470610e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.25                                         
y[1] (closed_form)                = -0.57300959372038020064977085329567          
y[1] (numeric)                    = -0.57300959372038020064977085329567          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.26                                         
y[1] (closed_form)                = -0.56730805299954074835648401695181          
y[1] (numeric)                    = -0.56730805299954074835648401695181          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.27                                         
y[1] (closed_form)                = -0.56166324355675953682950026030951          
y[1] (numeric)                    = -0.5616632435567595368295002603095           
absolute error                    = 1e-32                                        
relative error                    = 1.7804262811777602621797356947760e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.28                                         
y[1] (closed_form)                = -0.55607460090638826439862831202818          
y[1] (numeric)                    = -0.55607460090638826439862831202817          
absolute error                    = 1e-32                                        
relative error                    = 1.7983198627846407311843592036204e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.29                                         
y[1] (closed_form)                = -0.55054156617950467620394727427232          
y[1] (numeric)                    = -0.55054156617950467620394727427231          
absolute error                    = 1e-32                                        
relative error                    = 1.8163932778764045452578408512557e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.3                                          
y[1] (closed_form)                = -0.5450635860680252062446663351267           
y[1] (numeric)                    = -0.54506358606802520624466633512669          
absolute error                    = 1e-32                                        
relative error                    = 1.8346483338096221102287449580057e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.31                                         
y[1] (closed_form)                = -0.53964011276937370793091808153778          
y[1] (numeric)                    = -0.53964011276937370793091808153777          
absolute error                    = 1e-32                                        
relative error                    = 1.8530868561050993451731625061123e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.32                                         
y[1] (closed_form)                = -0.5342706039317007399654310472076           
y[1] (numeric)                    = -0.53427060393170073996543104720759          
absolute error                    = 1e-32                                        
relative error                    = 1.8717106886304312842790279149130e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.33                                         
y[1] (closed_form)                = -0.52895452259964792943801891542745          
y[1] (numeric)                    = -0.52895452259964792943801891542745          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.34                                         
y[1] (closed_form)                = -0.52369133716065198852399931102871          
y[1] (numeric)                    = -0.5236913371606519885239993110287           
absolute error                    = 1e-32                                        
relative error                    = 1.9095217526831678968590932800393e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.35                                         
y[1] (closed_form)                = -0.51848052129178301514346522142309          
y[1] (numeric)                    = -0.51848052129178301514346522142309          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.36                                         
y[1] (closed_form)                = -0.51332155390711176136717341008552          
y[1] (numeric)                    = -0.51332155390711176136717341008551          
absolute error                    = 1e-32                                        
relative error                    = 1.9480966508976072853320848856501e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.37                                         
y[1] (closed_form)                = -0.50821391910560060625202965545668          
y[1] (numeric)                    = -0.50821391910560060625202965545668          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=44.7MB, alloc=44.3MB, time=0.56
x[1]                              = 1.38                                         
y[1] (closed_form)                = -0.50315710611951302216003002973818          
y[1] (numeric)                    = -0.50315710611951302216003002973818          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.39                                         
y[1] (closed_form)                = -0.49815060926333637546429785699966          
y[1] (numeric)                    = -0.49815060926333637546429785699964          
absolute error                    = 2e-32                                        
relative error                    = 4.0148500529942018780345658588566e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.4                                          
y[1] (closed_form)                = -0.49319392788321295387972247966754          
y[1] (numeric)                    = -0.49319392788321295387972247966752          
absolute error                    = 2e-32                                        
relative error                    = 4.0551999668446745872241088952286e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.41                                         
y[1] (closed_form)                = -0.48828656630687416347879194624471          
y[1] (numeric)                    = -0.4882865663068741634787919462447           
absolute error                    = 1e-32                                        
relative error                    = 2.0479777020355881670203686398563e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.42                                         
y[1] (closed_form)                = -0.48342803379407288877059956197097          
y[1] (numeric)                    = -0.48342803379407288877059956197095          
absolute error                    = 2e-32                                        
relative error                    = 4.1371204402513927462243008090194e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.43                                         
y[1] (closed_form)                = -0.4786178444875090590377256987904           
y[1] (numeric)                    = -0.47861784448750905903772569879038          
absolute error                    = 2e-32                                        
relative error                    = 4.1786991919232461565803917643529e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.44                                         
y[1] (closed_form)                = -0.4738555173642435134467330551028           
y[1] (numeric)                    = -0.47385551736424351344673305510279          
absolute error                    = 1e-32                                        
relative error                    = 2.1103479084982764128366644646454e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.45                                         
y[1] (closed_form)                = -0.46914057618759530627829783412195          
y[1] (numeric)                    = -0.46914057618759530627829783412194          
absolute error                    = 1e-32                                        
relative error                    = 2.1315572575844086941943053377905e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.46                                         
y[1] (closed_form)                = -0.4644725494595176419674141413649           
y[1] (numeric)                    = -0.46447254945951764196741414136489          
absolute error                    = 1e-32                                        
relative error                    = 2.1529797641726030520779949446413e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.47                                         
y[1] (closed_form)                = -0.45985097037344767750748876862291          
y[1] (numeric)                    = -0.4598509703734476775074887686229           
absolute error                    = 1e-32                                        
relative error                    = 2.1746175705313704542540859599310e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.48                                         
y[1] (closed_form)                = -0.45527537676762547715927481158951          
y[1] (numeric)                    = -0.4552753767676254771592748115895           
absolute error                    = 1e-32                                        
relative error                    = 2.1964728404593783428668938216586e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.49                                         
y[1] (closed_form)                = -0.45074531107887745132121401376173          
y[1] (numeric)                    = -0.45074531107887745132121401376173          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.5                                          
y[1] (closed_form)                = -0.44626032029685965786656094152802          
y[1] (numeric)                    = -0.44626032029685965786656094152802          
absolute error                    = 0                                            
relative error                    = 0                                          % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.51                                         
y[1] (closed_form)                = -0.44181995591875639023929199353893          
y[1] (numeric)                    = -0.44181995591875639023929199353892          
absolute error                    = 1e-32                                        
relative error                    = 2.2633653971571260920421698719058e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.52                                         
y[1] (closed_form)                = -0.43742377390442952212985753283752          
y[1] (numeric)                    = -0.43742377390442952212985753283751          
absolute error                    = 1e-32                                        
relative error                    = 2.2861125975710796034941182117199e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 13                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.53                                         
y[1] (closed_form)                = -0.43307133463201412362786904627373          
y[1] (numeric)                    = -0.43307133463201412362786904627371          
absolute error                    = 2e-32                                        
relative error                    = 4.6181768222997808090795197077546e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.54                                         
y[1] (closed_form)                = -0.42876220285395590837633282336661          
y[1] (numeric)                    = -0.4287622028539559083763328233666           
absolute error                    = 1e-32                                        
relative error                    = 2.3322951354940629513966933831219e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.55                                         
y[1] (closed_form)                = -0.42449594765348611543550999515945          
y[1] (numeric)                    = -0.42449594765348611543550999515943          
absolute error                    = 2e-32                                        
relative error                    = 4.7114701825907413254726398125845e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.56                                         
y[1] (closed_form)                = -0.42027214240152947330831826638783          
y[1] (numeric)                    = -0.42027214240152947330831826638782          
absolute error                    = 1e-32                                        
relative error                    = 2.3794106225689270309419677522075e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.57                                         
y[1] (closed_form)                = -0.41609036471404093688776773145513          
y[1] (numeric)                    = -0.41609036471404093688776773145512          
absolute error                    = 1e-32                                        
relative error                    = 2.4033240968875890868105698795396e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.58                                         
y[1] (closed_form)                = -0.41195019640976693096457268007686          
y[1] (numeric)                    = -0.41195019640976693096457268007684          
absolute error                    = 2e-32                                        
relative error                    = 4.8549558112374333164794020642401e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.59                                         
y[1] (closed_form)                = -0.40785122346842687638409107270102          
y[1] (numeric)                    = -0.40785122346842687638409107270101          
absolute error                    = 1e-32                                        
relative error                    = 2.4518744641633110990231433853019e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.6                                          
y[1] (closed_form)                = -0.4037930359893108169703585352867           
y[1] (numeric)                    = -0.40379303598931081697035853528668          
absolute error                    = 2e-32                                        
relative error                    = 4.9530324243951148036542863564240e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.61                                         
y[1] (closed_form)                = -0.39977522815028900694540718427019          
y[1] (numeric)                    = -0.39977522815028900694540718427016          
absolute error                    = 3e-32                                        
relative error                    = 7.5042168417503815492798251679712e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.62                                         
y[1] (closed_form)                = -0.39579739816722935976845242258825          
y[1] (numeric)                    = -0.39579739816722935976845242258823          
absolute error                    = 2e-32                                        
relative error                    = 5.0530903165638672074060929249050e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.63                                         
y[1] (closed_form)                = -0.39185914825381870010601272007459          
y[1] (numeric)                    = -0.39185914825381870010601272007457          
absolute error                    = 2e-32                                        
relative error                    = 5.1038747185367257355366544351225e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.64                                         
y[1] (closed_form)                = -0.38796008458178380102467698857468          
y[1] (numeric)                    = -0.38796008458178380102467698857466          
absolute error                    = 2e-32                                        
relative error                    = 5.1551695122346810458097983038692e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.65                                         
y[1] (closed_form)                = -0.38409981724150822847708958234667          
y[1] (numeric)                    = -0.38409981724150822847708958234664          
absolute error                    = 3e-32                                        
relative error                    = 7.8104697407697731064859606390684e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.66                                         
y[1] (closed_form)                = -0.38027796020304105473278211658868          
y[1] (numeric)                    = -0.38027796020304105473278211658865          
absolute error                    = 3e-32                                        
relative error                    = 7.8889662666703481013307057089807e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.67                                         
y[1] (closed_form)                = -0.37649413127749354159270234015759          
y[1] (numeric)                    = -0.37649413127749354159270234015756          
absolute error                    = 3e-32                                        
relative error                    = 7.9682516957717506003785242832470e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.68                                         
y[1] (closed_form)                = -0.37274795207881993302359197748017          
y[1] (numeric)                    = -0.37274795207881993302359197748014          
absolute error                    = 3e-32                                        
relative error                    = 8.0483339566829621550348529003847e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.69                                         
y[1] (closed_form)                = -0.3690390479859785352596275318049           
y[1] (numeric)                    = -0.36903904798597853525962753180488          
absolute error                    = 2e-32                                        
relative error                    = 5.4194807051312062175548592062532e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.7                                          
y[1] (closed_form)                = -0.36536704810546930044780167551788          
y[1] (numeric)                    = -0.36536704810546930044780167551785          
absolute error                    = 3e-32                                        
relative error                    = 8.2109210875907996411862939945136e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.71                                         
y[1] (closed_form)                = -0.36173158523424416756419098130371          
y[1] (numeric)                    = -0.36173158523424416756419098130367          
absolute error                    = 4e-32                                        
relative error                    = 1.1057922955248008111757704702922e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.72                                         
y[1] (closed_form)                = -0.35813229582298645160429346866125          
y[1] (numeric)                    = -0.35813229582298645160429346866122          
absolute error                    = 3e-32                                        
relative error                    = 8.3767926964140810114692782095290e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.73                                         
y[1] (closed_form)                = -0.35456881993975560895575438851885          
y[1] (numeric)                    = -0.35456881993975560895575438851882          
absolute error                    = 3e-32                                        
relative error                    = 8.4609808626424811964766450767121e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.74                                         
y[1] (closed_form)                = -0.35104080123399374339972138868441          
y[1] (numeric)                    = -0.35104080123399374339972138868439          
absolute error                    = 2e-32                                        
relative error                    = 5.6973434226719910119370988363602e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.75                                         
y[1] (closed_form)                = -0.34754788690089025336143451733274          
y[1] (numeric)                    = -0.34754788690089025336143451733272          
absolute error                    = 2e-32                                        
relative error                    = 5.7546026760057304368664997048427e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.76                                         
y[1] (closed_form)                = -0.34408972764610105684507989725189          
y[1] (numeric)                    = -0.34408972764610105684507989725187          
absolute error                    = 2e-32                                        
relative error                    = 5.8124373944025886498803406244497e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.77                                         
y[1] (closed_form)                = -0.34066597765081886594599981232611          
y[1] (numeric)                    = -0.34066597765081886594599981232609          
absolute error                    = 2e-32                                        
relative error                    = 5.8708533613826010961162539158286e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.78                                         
y[1] (closed_form)                = -0.33727629453719101793860222566362          
y[1] (numeric)                    = -0.3372762945371910179386022256636           
absolute error                    = 2e-32                                        
relative error                    = 5.9298564185911459115690715820468e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.79                                         
y[1] (closed_form)                = -0.33392033933408140469425995016587          
y[1] (numeric)                    = -0.33392033933408140469425995016586          
absolute error                    = 1e-32                                        
relative error                    = 2.9947262331915566644792333634078e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=90.0MB, alloc=52.3MB, time=1.09
 
TOP MAIN SOLVE Loop
x[1]                              = 1.8                                          
y[1] (closed_form)                = -0.33059777644317307659360944086443          
y[1] (numeric)                    = -0.33059777644317307659360944086442          
absolute error                    = 1e-32                                        
relative error                    = 3.0248237322064730418655119765138e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.81                                         
y[1] (closed_form)                = -0.32730827360540813116539251467187          
y[1] (numeric)                    = -0.32730827360540813116539251467186          
absolute error                    = 1e-32                                        
relative error                    = 3.0552237161153049123645204629974e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.82                                         
y[1] (closed_form)                = -0.3240515018677615304127380290285           
y[1] (numeric)                    = -0.32405150186776153041273802902849          
absolute error                    = 1e-32                                        
relative error                    = 3.0859292249417765635318858229498e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.83                                         
y[1] (closed_form)                = -0.32082713555034552418092756975611          
y[1] (numeric)                    = -0.3208271355503455241809275697561           
absolute error                    = 1e-32                                        
relative error                    = 3.1169433292623586518480168849864e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.84                                         
y[1] (closed_form)                = -0.31763485221384138998156885278391          
y[1] (numeric)                    = -0.3176348522138413899815688527839           
absolute error                    = 1e-32                                        
relative error                    = 3.1482691305133284086060072885124e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.85                                         
y[1] (closed_form)                = -0.31447433262725523242001894980624          
y[1] (numeric)                    = -0.31447433262725523242001894980622          
absolute error                    = 2e-32                                        
relative error                    = 6.3598195226018317043472218706368e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.86                                         
y[1] (closed_form)                = -0.31134526073599461777912982348316          
y[1] (numeric)                    = -0.31134526073599461777912982348313          
absolute error                    = 3e-32                                        
relative error                    = 9.6356051571437010645269164393645e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.87                                         
y[1] (closed_form)                = -0.30824732363026285139617165354796          
y[1] (numeric)                    = -0.30824732363026285139617165354792          
absolute error                    = 4e-32                                        
relative error                    = 1.2976592798573422230058062648698e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.88                                         
y[1] (closed_form)                = -0.30518021151376773723433345617434          
y[1] (numeric)                    = -0.3051802115137677372343334561743           
absolute error                    = 4e-32                                        
relative error                    = 1.3107009724382297094603236282640e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.89                                         
y[1] (closed_form)                = -0.3021436176727416904986820260546           
y[1] (numeric)                    = -0.30214361767274169049868202605456          
absolute error                    = 4e-32                                        
relative error                    = 1.3238737362086154700935144993520e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.9                                          
y[1] (closed_form)                = -0.29913723844527010528202413820747          
y[1] (numeric)                    = -0.29913723844527010528202413820743          
absolute error                    = 4e-32                                        
relative error                    = 1.3371788884558538832145061455386e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.91                                         
y[1] (closed_form)                = -0.29616077319092491005187681690838          
y[1] (numeric)                    = -0.29616077319092491005187681690835          
absolute error                    = 3e-32                                        
relative error                    = 1.0129633197796930023720986878278e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.92                                         
y[1] (closed_form)                = -0.29321392426070027430878891399001          
y[1] (numeric)                    = -0.29321392426070027430878891398998          
absolute error                    = 3e-32                                        
relative error                    = 1.0231437703936124752419898249413e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.93                                         
y[1] (closed_form)                = -0.29029639696724745996162616737418          
y[1] (numeric)                    = -0.29029639696724745996162616737414          
absolute error                    = 4e-32                                        
relative error                    = 1.3779020483162586134558038467988e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.94                                         
y[1] (closed_form)                = -0.28740789955540584088015289513921          
y[1] (numeric)                    = -0.28740789955540584088015289513917          
absolute error                    = 4e-32                                        
relative error                    = 1.3917501941274544202263736251752e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.95                                         
y[1] (closed_form)                = -0.28454814317302714370230801772766          
y[1] (numeric)                    = -0.28454814317302714370230801772762          
absolute error                    = 4e-32                                        
relative error                    = 1.4057375161178586668581763867129e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.96                                         
y[1] (closed_form)                = -0.28171684184208999229594292219192          
y[1] (numeric)                    = -0.28171684184208999229594292219189          
absolute error                    = 3e-32                                        
relative error                    = 1.0648990597734949007162153208123e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.97                                         
y[1] (closed_form)                = -0.27891371243010186730539604907824          
y[1] (numeric)                    = -0.27891371243010186730539604907821          
absolute error                    = 3e-32                                        
relative error                    = 1.0756014732519919919816751155846e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.98                                         
y[1] (closed_form)                = -0.27613847462178562095502707959073          
y[1] (numeric)                    = -0.2761384746217856209550270795907           
absolute error                    = 3e-32                                        
relative error                    = 1.0864114477741518312768652129717e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 1.99                                         
y[1] (closed_form)                = -0.27339085089104771573759642680838          
y[1] (numeric)                    = -0.27339085089104771573759642680834          
absolute error                    = 4e-32                                        
relative error                    = 1.4631067524619133022870341667028e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2                                            
y[1] (closed_form)                = -0.27067056647322538378799898994497          
y[1] (numeric)                    = -0.27067056647322538378799898994493          
absolute error                    = 4e-32                                        
relative error                    = 1.4778112197861300454460854921150e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.01                                         
y[1] (closed_form)                = -0.26797734933760993163516210074751          
y[1] (numeric)                    = -0.26797734933760993163516210074747          
absolute error                    = 4e-32                                        
relative error                    = 1.4926634694638388564699529574731e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.02                                         
y[1] (closed_form)                = -0.2653109301602434426396855294633           
y[1] (numeric)                    = -0.26531093016024344263968552946325          
absolute error                    = 5e-32                                        
relative error                    = 1.8845812334154805277843571692650e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.03                                         
y[1] (closed_form)                = -0.2626710422969861567647978241762           
y[1] (numeric)                    = -0.26267104229698615676479782417615          
absolute error                    = 5e-32                                        
relative error                    = 1.9035215896949936291708374140341e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.04                                         
y[1] (closed_form)                = -0.2600574217568518343961621541422           
y[1] (numeric)                    = -0.26005742175685183439616215414215          
absolute error                    = 5e-32                                        
relative error                    = 1.9226522997197495089021428903711e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.05                                         
y[1] (closed_form)                = -0.25746980717560843772469303348974          
y[1] (numeric)                    = -0.25746980717560843772469303348969          
absolute error                    = 5e-32                                        
relative error                    = 1.9419752765766929540611660363111e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.06                                         
y[1] (closed_form)                = -0.25490793978964148973852270144483          
y[1] (numeric)                    = -0.25490793978964148973852270144478          
absolute error                    = 5e-32                                        
relative error                    = 1.9614924525796121933815738537389e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.07                                         
y[1] (closed_form)                = -0.25237156341007749713823574894352          
y[1] (numeric)                    = -0.25237156341007749713823574894347          
absolute error                    = 5e-32                                        
relative error                    = 1.9812057794623718863375390135866e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.08                                         
y[1] (closed_form)                = -0.24986042439716484949609962897764          
y[1] (numeric)                    = -0.24986042439716484949609962897759          
absolute error                    = 5e-32                                        
relative error                    = 2.0011172285740881360599959819674e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.09                                         
y[1] (closed_form)                = -0.24737427163490963272785765185998          
y[1] (numeric)                    = -0.24737427163490963272785765185993          
absolute error                    = 5e-32                                        
relative error                    = 2.0212287910762650437433601791105e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.1                                          
y[1] (closed_form)                = -0.24491285650596382043729475214525          
y[1] (numeric)                    = -0.2449128565059638204372947521452           
absolute error                    = 5e-32                                        
relative error                    = 2.0415424781419125183624318526197e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.11                                         
y[1] (closed_form)                = -0.24247593286676333193178390681564          
y[1] (numeric)                    = -0.2424759328667633319317839068156           
absolute error                    = 4e-32                                        
relative error                    = 1.6496482569253322029171107333181e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.12                                         
y[1] (closed_form)                = -0.24006325702291347069389640532458          
y[1] (numeric)                    = -0.24006325702291347069389640532454          
absolute error                    = 4e-32                                        
relative error                    = 1.6662274975375383875001298898894e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.13                                         
y[1] (closed_form)                = -0.23767458770481928183241092954488          
y[1] (numeric)                    = -0.23767458770481928183241092954484          
absolute error                    = 4e-32                                        
relative error                    = 1.6829733622880258689544947909498e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.14                                         
y[1] (closed_form)                = -0.23530968604355839152815844137813          
y[1] (numeric)                    = -0.23530968604355839152815844137808          
absolute error                    = 5e-32                                        
relative error                    = 2.1248594072215307872959972658441e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.15                                         
y[1] (closed_form)                = -0.23296831554699391573854142836567          
y[1] (numeric)                    = -0.23296831554699391573854142836563          
absolute error                    = 4e-32                                        
relative error                    = 1.7169716794355787732479975224804e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.16                                         
y[1] (closed_form)                = -0.23065024207612504943169198345969          
y[1] (numeric)                    = -0.23065024207612504943169198345965          
absolute error                    = 4e-32                                        
relative error                    = 1.7342275316926909767737972870820e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.17                                         
y[1] (closed_form)                = -0.22835523382167297138948422676448          
y[1] (numeric)                    = -0.22835523382167297138948422676444          
absolute error                    = 4e-32                                        
relative error                    = 1.7516568081481668764484850537516e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.18                                         
y[1] (closed_form)                = -0.2260830612808997231503695594535           
y[1] (numeric)                    = -0.22608306128089972315036955945346          
absolute error                    = 4e-32                                        
relative error                    = 1.7692612517441764653230014832678e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.19                                         
y[1] (closed_form)                = -0.22383349723465774396061136811429          
y[1] (numeric)                    = -0.22383349723465774396061136811426          
absolute error                    = 3e-32                                        
relative error                    = 1.3402819672048123221906711646498e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.2                                          
y[1] (closed_form)                = -0.22160631672466776666828885169988          
y[1] (numeric)                    = -0.22160631672466776666828885169985          
absolute error                    = 3e-32                                        
relative error                    = 1.3537520249151181389707665750333e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.21                                         
y[1] (closed_form)                = -0.21940129703102280233072422159711          
y[1] (numeric)                    = -0.21940129703102280233072422159708          
absolute error                    = 3e-32                                        
relative error                    = 1.3673574589560459154230306560343e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=135.4MB, alloc=52.3MB, time=1.59
 
TOP MAIN SOLVE Loop
x[1]                              = 2.22                                         
y[1] (closed_form)                = -0.21721821764991596391504727554914          
y[1] (numeric)                    = -0.21721821764991596391504727554912          
absolute error                    = 2e-32                                        
relative error                    = 9.2073308658822509587921440290796e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.23                                         
y[1] (closed_form)                = -0.21505686027158990185570719310607          
y[1] (numeric)                    = -0.21505686027158990185570719310604          
absolute error                    = 3e-32                                        
relative error                    = 1.3949799119225378006089872891907e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.24                                         
y[1] (closed_form)                = -0.2129170087585056463941117721627           
y[1] (numeric)                    = -0.21291700875850564639411177216268          
absolute error                    = 2e-32                                        
relative error                    = 9.3933312874427823071052091710136e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.25                                         
y[1] (closed_form)                = -0.2107984491237286735664353784814           
y[1] (numeric)                    = -0.21079844912372867356643537848138          
absolute error                    = 2e-32                                        
relative error                    = 9.4877358363585257205503690445116e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.26                                         
y[1] (closed_form)                = -0.20870096950953003342818271727923          
y[1] (numeric)                    = -0.20870096950953003342818271727921          
absolute error                    = 2e-32                                        
relative error                    = 9.5830891667643778717351852852968e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.27                                         
y[1] (closed_form)                = -0.20662436016620040061049843066899          
y[1] (numeric)                    = -0.20662436016620040061049843066897          
absolute error                    = 2e-32                                        
relative error                    = 9.6794008140728407194171550561075e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.28                                         
y[1] (closed_form)                = -0.20456841343107492859562313519417          
y[1] (numeric)                    = -0.20456841343107492859562313519415          
absolute error                    = 2e-32                                        
relative error                    = 9.7766804095289050835042636318176e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.29                                         
y[1] (closed_form)                = -0.20253292370776681017944409869335          
y[1] (numeric)                    = -0.20253292370776681017944409869333          
absolute error                    = 2e-32                                        
relative error                    = 9.8749376811731831702012210539709e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.3                                          
y[1] (closed_form)                = -0.20051768744560746745988138759597          
y[1] (numeric)                    = -0.20051768744560746745988138759596          
absolute error                    = 1e-32                                        
relative error                    = 4.9870912274073603699788075784545e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.31                                         
y[1] (closed_form)                = -0.19852250311929131535297509114374          
y[1] (numeric)                    = -0.19852250311929131535297509114372          
absolute error                    = 2e-32                                        
relative error                    = 1.0074424655013586200245455289684e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.32                                         
y[1] (closed_form)                = -0.19654717120872306309606247764772          
y[1] (numeric)                    = -0.1965471712087230630960624776477           
absolute error                    = 2e-32                                        
relative error                    = 1.0175674306073334882894211461532e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.33                                         
y[1] (closed_form)                = -0.19459149417906553845140142910307          
y[1] (numeric)                    = -0.19459149417906553845140142910306          
absolute error                    = 1e-32                                        
relative error                    = 5.1389707665217238766190693680524e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.34                                         
y[1] (closed_form)                = -0.19265527646098603937603364791825          
y[1] (numeric)                    = -0.19265527646098603937603364791823          
absolute error                    = 2e-32                                        
relative error                    = 1.0381236562731844795782169982426e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.35                                         
y[1] (closed_form)                = -0.1907383244310992377765931935996           
y[1] (numeric)                    = -0.19073832443109923777659319359958          
absolute error                    = 2e-32                                        
relative error                    = 1.0485569724727574328568707539109e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.36                                         
y[1] (closed_form)                = -0.18884044639260467962313819571542          
y[1] (numeric)                    = -0.18884044639260467962313819571539          
absolute error                    = 3e-32                                        
relative error                    = 1.5886427178650670774043491610654e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.37                                         
y[1] (closed_form)                = -0.18696145255611694515588165595398          
y[1] (numeric)                    = -0.18696145255611694515588165595396          
absolute error                    = 2e-32                                        
relative error                    = 1.0697392284111052377931159238180e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.38                                         
y[1] (closed_form)                = -0.18510115502068655218486709261196          
y[1] (numeric)                    = -0.18510115502068655218486709261194          
absolute error                    = 2e-32                                        
relative error                    = 1.0804902863931258630195290329287e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.39                                         
y[1] (closed_form)                = -0.18325936775500970455710302844059          
y[1] (numeric)                    = -0.18325936775500970455710302844057          
absolute error                    = 2e-32                                        
relative error                    = 1.0913493943041973741937818758192e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.4                                          
y[1] (closed_form)                = -0.18143590657882500675034444015938          
y[1] (numeric)                    = -0.18143590657882500675034444015937          
absolute error                    = 1e-32                                        
relative error                    = 5.5115881903208008261189698848340e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.41                                         
y[1] (closed_form)                = -0.17963058914449528424947775826781          
y[1] (numeric)                    = -0.17963058914449528424947775826779          
absolute error                    = 2e-32                                        
relative error                    = 1.1133961145065304659893688471457e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.42                                         
y[1] (closed_form)                = -0.17784323491877266787219852147351          
y[1] (numeric)                    = -0.1778432349187726678721985214735           
absolute error                    = 1e-32                                        
relative error                    = 5.6229296574409230399807946027656e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.43                                         
y[1] (closed_form)                = -0.17607366516474511853721843978805          
y[1] (numeric)                    = -0.17607366516474511853721843978804          
absolute error                    = 1e-32                                        
relative error                    = 5.6794410400007281761297855767367e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.44                                         
y[1] (closed_form)                = -0.1743217029239625871124340741545           
y[1] (numeric)                    = -0.17432170292396258711243407415449          
absolute error                    = 1e-32                                        
relative error                    = 5.7365203713974166946836126510321e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.45                                         
y[1] (closed_form)                = -0.17258717299874102194414703303231          
y[1] (numeric)                    = -0.17258717299874102194414703303229          
absolute error                    = 2e-32                                        
relative error                    = 1.1588346719223389065090706193080e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.46                                         
y[1] (closed_form)                = -0.17086990193464245445334189841079          
y[1] (numeric)                    = -0.17086990193464245445334189841078          
absolute error                    = 1e-32                                        
relative error                    = 5.8524057699904274344915000804046e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.47                                         
y[1] (closed_form)                = -0.16916971800312941079298153170792          
y[1] (numeric)                    = -0.1691697180031294107929815317079           
absolute error                    = 2e-32                                        
relative error                    = 1.1822446851646360888436353300643e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.48                                         
y[1] (closed_form)                = -0.16748645118439191499303078395017          
y[1] (numeric)                    = -0.16748645118439191499303078395016          
absolute error                    = 1e-32                                        
relative error                    = 5.9706322089245517136029853831596e-30      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.49                                         
y[1] (closed_form)                = -0.1658199331503453662792122341894           
y[1] (numeric)                    = -0.16581993315034536627921223418938          
absolute error                    = 2e-32                                        
relative error                    = 1.2061276120444717728097399349678e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.5                                          
y[1] (closed_form)                = -0.16416999724779759033905734893432          
y[1] (numeric)                    = -0.1641699972477975903390573489343           
absolute error                    = 2e-32                                        
relative error                    = 1.2182493960703473438070175951168e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.51                                         
y[1] (closed_form)                = -0.16253647848178338122635216367639          
y[1] (numeric)                    = -0.16253647848178338122635216367637          
absolute error                    = 2e-32                                        
relative error                    = 1.2304930060510411636294418494051e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.52                                         
y[1] (closed_form)                = -0.16091921349906486734428000303859          
y[1] (numeric)                    = -0.16091921349906486734428000303857          
absolute error                    = 2e-32                                        
relative error                    = 1.2428596663577543439863282465196e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.53                                         
y[1] (closed_form)                = -0.15931804057179605153010981297284          
y[1] (numeric)                    = -0.15931804057179605153010981297281          
absolute error                    = 3e-32                                        
relative error                    = 1.8830259205002347112048034800113e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.54                                         
y[1] (closed_form)                = -0.15773279958134989168182564520009          
y[1] (numeric)                    = -0.15773279958134989168182564520006          
absolute error                    = 3e-32                                        
relative error                    = 1.9019506456250814276216613584216e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.55                                         
y[1] (closed_form)                = -0.15616333200230630462128247910557          
y[1] (numeric)                    = -0.15616333200230630462128247910555          
absolute error                    = 2e-32                                        
relative error                    = 1.2807103782663032044941253752753e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.56                                         
y[1] (closed_form)                = -0.15460948088659949198093132207952          
y[1] (numeric)                    = -0.1546094808865994919809313220795           
absolute error                    = 2e-32                                        
relative error                    = 1.2935817315543076269846931825039e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.57                                         
y[1] (closed_form)                = -0.15307109084782300283349165501697          
y[1] (numeric)                    = -0.15307109084782300283349165501694          
absolute error                    = 3e-32                                        
relative error                    = 1.9598736661401837747333300733570e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.58                                         
y[1] (closed_form)                = -0.15154800804569096355775503214886          
y[1] (numeric)                    = -0.15154800804569096355775503214883          
absolute error                    = 3e-32                                        
relative error                    = 1.9795707239487536265871521806774e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.59                                         
y[1] (closed_form)                = -0.15004008017065392105055739728929          
y[1] (numeric)                    = -0.15004008017065392105055739728927          
absolute error                    = 2e-32                                        
relative error                    = 1.3329771603195774150522090176603e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.6                                          
y[1] (closed_form)                = -0.14854715642866776085642114033995          
y[1] (numeric)                    = -0.14854715642866776085642114033993          
absolute error                    = 2e-32                                        
relative error                    = 1.3463738035001690397750825332584e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.61                                         
y[1] (closed_form)                = -0.14706908752611417709398724772342          
y[1] (numeric)                    = -0.1470690875261141770939872477234           
absolute error                    = 2e-32                                        
relative error                    = 1.3599050851830925909193181507426e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.62                                         
y[1] (closed_form)                = -0.14560572565487118621366387301155          
y[1] (numeric)                    = -0.14560572565487118621366387301153          
absolute error                    = 2e-32                                        
relative error                    = 1.3735723585077924664960939361653e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=180.8MB, alloc=52.3MB, time=2.11
 
TOP MAIN SOLVE Loop
x[1]                              = 2.63                                         
y[1] (closed_form)                = -0.14415692447753219162542581259969          
y[1] (numeric)                    = -0.14415692447753219162542581259965          
absolute error                    = 4e-32                                        
relative error                    = 2.7747539804259811377898667633501e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.64                                         
y[1] (closed_form)                = -0.14272253911277212109091017917259          
y[1] (numeric)                    = -0.14272253911277212109091017917256          
absolute error                    = 3e-32                                        
relative error                    = 2.1019805411600419740400136696302e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.65                                         
y[1] (closed_form)                = -0.14130242612085917348135255637331          
y[1] (numeric)                    = -0.14130242612085917348135255637328          
absolute error                    = 3e-32                                        
relative error                    = 2.1231057968063703887469959711846e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.66                                         
y[1] (closed_form)                = -0.13989644348931072606396584367654          
y[1] (numeric)                    = -0.1398964434893107260639658436765           
absolute error                    = 4e-32                                        
relative error                    = 2.8592578197355202249219491022201e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.67                                         
y[1] (closed_form)                = -0.13850445061869196789553697891176          
y[1] (numeric)                    = -0.13850445061869196789553697891172          
absolute error                    = 4e-32                                        
relative error                    = 2.8879938385605762757136780661188e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.68                                         
y[1] (closed_form)                = -0.13712630830855583917474638648806          
y[1] (numeric)                    = -0.13712630830855583917474638648801          
absolute error                    = 5e-32                                        
relative error                    = 3.6462733239701974231077805697630e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.69                                         
y[1] (closed_form)                = -0.13576187874352287053542862700309          
y[1] (numeric)                    = -0.13576187874352287053542862700304          
absolute error                    = 5e-32                                        
relative error                    = 3.6829189801106427531793699091811e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.7                                          
y[1] (closed_form)                = -0.13441102547949953025310340171193          
y[1] (numeric)                    = -0.13441102547949953025310340171188          
absolute error                    = 5e-32                                        
relative error                    = 3.7199329312182085279672482548671e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.71                                         
y[1] (closed_form)                = -0.13307361343003370118801281601234          
y[1] (numeric)                    = -0.13307361343003370118801281601229          
absolute error                    = 5e-32                                        
relative error                    = 3.7573188787188505661219136624809e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.72                                         
y[1] (closed_form)                = -0.13174950885280592300098873189073          
y[1] (numeric)                    = -0.13174950885280592300098873189067          
absolute error                    = 6e-32                                        
relative error                    = 4.5540966734861687903373074942189e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.73                                         
y[1] (closed_form)                = -0.13043857933625504875511446038598          
y[1] (numeric)                    = -0.13043857933625504875511446038591          
absolute error                    = 7e-32                                        
relative error                    = 5.3665104569675185180264458294304e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.74                                         
y[1] (closed_form)                = -0.12914069378633697845769563692426          
y[1] (numeric)                    = -0.12914069378633697845769563692419          
absolute error                    = 7e-32                                        
relative error                    = 5.4204447837189771536508788600824e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.75                                         
y[1] (closed_form)                = -0.1278557224134151454048600511159           
y[1] (numeric)                    = -0.12785572241341514540486005111583          
absolute error                    = 7e-32                                        
relative error                    = 5.4749211594658600635744443161550e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.76                                         
y[1] (closed_form)                = -0.12658353671928144436649625986908          
y[1] (numeric)                    = -0.126583536719281444366496259869            
absolute error                    = 8e-32                                        
relative error                    = 6.3199371793041589339437026626034e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.77                                         
y[1] (closed_form)                = -0.12532400948430630369353354844936          
y[1] (numeric)                    = -0.12532400948430630369353354844929          
absolute error                    = 7e-32                                        
relative error                    = 5.5855219034279100722955568732572e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.78                                         
y[1] (closed_form)                = -0.12407701475471661634406565854311          
y[1] (numeric)                    = -0.12407701475471661634406565854303          
absolute error                    = 8e-32                                        
relative error                    = 6.4476083792110182513758344666973e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.79                                         
y[1] (closed_form)                = -0.12284242783000025761081913621326          
y[1] (numeric)                    = -0.12284242783000025761081913621318          
absolute error                    = 8e-32                                        
relative error                    = 6.5124079207153709861129907249074e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.8                                          
y[1] (closed_form)                = -0.12162012525043592999124277636788          
y[1] (numeric)                    = -0.1216201252504359299912427763678           
absolute error                    = 8e-32                                        
relative error                    = 6.5778587084388199485992064043701e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.81                                         
y[1] (closed_form)                = -0.12040998478474708817431334210487          
y[1] (numeric)                    = -0.12040998478474708817431334210479          
absolute error                    = 8e-32                                        
relative error                    = 6.6439672875146799886416725953511e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.82                                         
y[1] (closed_form)                = -0.11921188541787870952626780936569          
y[1] (numeric)                    = -0.11921188541787870952626780936562          
absolute error                    = 7e-32                                        
relative error                    = 5.8718977352489556886375200365729e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.83                                         
y[1] (closed_form)                = -0.11802570733889568774212465157395          
y[1] (numeric)                    = -0.11802570733889568774212465157387          
absolute error                    = 8e-32                                        
relative error                    = 6.7781843298164065215383682805896e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.84                                         
y[1] (closed_form)                = -0.11685133192900163949227461081453          
y[1] (numeric)                    = -0.11685133192900163949227461081445          
absolute error                    = 8e-32                                        
relative error                    = 6.8463062148583510951231094865038e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.85                                         
y[1] (closed_form)                = -0.1156886417496769259348212535548           
y[1] (numeric)                    = -0.11568864174967692593482125355472          
absolute error                    = 8e-32                                        
relative error                    = 6.9151127362270557004172123013785e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.86                                         
y[1] (closed_form)                = -0.11453752053093470288593752994038          
y[1] (numeric)                    = -0.1145375205309347028859375299403           
absolute error                    = 8e-32                                        
relative error                    = 6.9846107746319961668180272999878e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.87                                         
y[1] (closed_form)                = -0.11339785315969382524346871484118          
y[1] (numeric)                    = -0.1133978531596938252434687148411           
absolute error                    = 8e-32                                        
relative error                    = 7.0548072799349282134267630322728e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.88                                         
y[1] (closed_form)                = -0.11226952566826744294453481233074          
y[1] (numeric)                    = -0.11226952566826744294453481233066          
absolute error                    = 8e-32                                        
relative error                    = 7.1257092718448794161911644494627e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.89                                         
y[1] (closed_form)                = -0.11115242522296613730713531516097          
y[1] (numeric)                    = -0.11115242522296613730713531516089          
absolute error                    = 8e-32                                        
relative error                    = 7.1973238406201259604401298850909e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.9                                          
y[1] (closed_form)                = -0.11004644011281445805989306166835          
y[1] (numeric)                    = -0.11004644011281445805989306166828          
absolute error                    = 7e-32                                        
relative error                    = 6.3609508793050713299366898009448e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.91                                         
y[1] (closed_form)                = -0.10895145973837973270423724734572          
y[1] (numeric)                    = -0.10895145973837973270423724734565          
absolute error                    = 7e-32                                        
relative error                    = 6.4248794984562730203817028367737e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.92                                         
y[1] (closed_form)                = -0.10786737460071203108065245281805          
y[1] (numeric)                    = -0.10786737460071203108065245281798          
absolute error                    = 7e-32                                        
relative error                    = 6.4894506109114044337616800824410e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.93                                         
y[1] (closed_form)                = -0.10679407629039417912623358620798          
y[1] (numeric)                    = -0.10679407629039417912623358620792          
absolute error                    = 6e-32                                        
relative error                    = 5.6182891490018747339672205182697e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.94                                         
y[1] (closed_form)                = -0.10573145747670072681579747643322          
y[1] (numeric)                    = -0.10573145747670072681579747643315          
absolute error                    = 7e-32                                        
relative error                    = 6.6205462092892639331947827872336e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.95                                         
y[1] (closed_form)                = -0.10467941189686478617431100509864          
y[1] (numeric)                    = -0.10467941189686478617431100509857          
absolute error                    = 7e-32                                        
relative error                    = 6.6870838048810765013344913544972e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.96                                         
y[1] (closed_form)                = -0.10363783434545166603549268832574          
y[1] (numeric)                    = -0.10363783434545166603549268832568          
absolute error                    = 6e-32                                        
relative error                    = 5.7893915266508276483924501889230e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.97                                         
y[1] (closed_form)                = -0.10260662066383824090120823479189          
y[1] (numeric)                    = -0.10260662066383824090120823479182          
absolute error                    = 7e-32                                        
relative error                    = 6.8221718586108911321123308406545e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.98                                         
y[1] (closed_form)                = -0.10158566772979700182977879769406          
y[1] (numeric)                    = -0.10158566772979700182977879769399          
absolute error                    = 7e-32                                        
relative error                    = 6.8907358256668399295669821767843e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 2.99                                         
y[1] (closed_form)                = -0.10057487344718374774961076493595          
y[1] (numeric)                    = -0.10057487344718374774961076493588          
absolute error                    = 7e-32                                        
relative error                    = 6.9599888720476544067039861688685e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3                                            
y[1] (closed_form)                = -0.099574136735727885958684831300122         
y[1] (numeric)                    = -0.099574136735727885958684831300058         
absolute error                    = 6.4e-32                                      
relative error                    = 6.4273718154200536770971294894662e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.01                                         
y[1] (closed_form)                = -0.098583357520924320831446190234969         
y[1] (numeric)                    = -0.098583357520924320831446190234905         
absolute error                    = 6.4e-32                                      
relative error                    = 6.4919679760770977925060872498848e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.02                                         
y[1] (closed_form)                = -0.097602436724025919913543080119995         
y[1] (numeric)                    = -0.09760243672402591991354308011993          
absolute error                    = 6.5e-32                                      
relative error                    = 6.6596697973627056669367145088962e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.03                                         
y[1] (closed_form)                = -0.096631276252135556642683519477524         
y[1] (numeric)                    = -0.096631276252135556642683519477459         
absolute error                    = 6.5e-32                                      
relative error                    = 6.7266005915515884891775204469002e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.04                                         
y[1] (closed_form)                = -0.095669778988396738891625658216285         
memory used=226.1MB, alloc=52.3MB, time=2.61
y[1] (numeric)                    = -0.095669778988396738891625658216216         
absolute error                    = 6.9e-32                                      
relative error                    = 7.2123089161070007650780280921138e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.05                                         
y[1] (closed_form)                = -0.094717848782281842387981540479467         
y[1] (numeric)                    = -0.094717848782281842387981540479401         
absolute error                    = 6.6e-32                                      
relative error                    = 6.9680636594384019643033502311038e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.06                                         
y[1] (closed_form)                = -0.093775390439976977826083093679625         
y[1] (numeric)                    = -0.093775390439976977826083093679557         
absolute error                    = 6.8e-32                                      
relative error                    = 7.2513694350891464258271379484735e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.07                                         
y[1] (closed_form)                = -0.092842309714862530149608892870319         
y[1] (numeric)                    = -0.092842309714862530149608892870254         
absolute error                    = 6.5e-32                                      
relative error                    = 7.0011183693757854362618440930884e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.08                                         
y[1] (closed_form)                = -0.091918513298088418050967052756972         
y[1] (numeric)                    = -0.091918513298088418050967052756906         
absolute error                    = 6.6e-32                                      
relative error                    = 7.1802727907450356886475081258350e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.09                                         
y[1] (closed_form)                = -0.091003908809243131205530209038912         
y[1] (numeric)                    = -0.091003908809243131205530209038845         
absolute error                    = 6.7e-32                                      
relative error                    = 7.3623211218807460706919645906365e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.1                                          
y[1] (closed_form)                = -0.090098404787115612136670184356672         
y[1] (numeric)                    = -0.090098404787115612136670184356605         
absolute error                    = 6.7e-32                                      
relative error                    = 7.4363136792829471906173714177211e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.11                                         
y[1] (closed_form)                = -0.089201910680549058892080384870443         
y[1] (numeric)                    = -0.08920191068054905889208038487038          
absolute error                    = 6.3e-32                                      
relative error                    = 7.0626289862350984425532592760106e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.12                                         
y[1] (closed_form)                = -0.088314336839385733904031703200168         
y[1] (numeric)                    = -0.088314336839385733904031703200104         
absolute error                    = 6.4e-32                                      
relative error                    = 7.2468414858161266245838840792377e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.13                                         
y[1] (closed_form)                = -0.087435594505501873506901935547708         
y[1] (numeric)                    = -0.087435594505501873506901935547642         
absolute error                    = 6.6e-32                                      
relative error                    = 7.5484132490054675058696976692055e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 12                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.14                                         
y[1] (closed_form)                = -0.086565595803931801595459532304399         
y[1] (numeric)                    = -0.086565595803931801595459532304335         
absolute error                    = 6.4e-32                                      
relative error                    = 7.3932373947910984910653070656048e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.15                                         
y[1] (closed_form)                = -0.085704253734080359827870913912309         
y[1] (numeric)                    = -0.085704253734080359827870913912245         
absolute error                    = 6.4e-32                                      
relative error                    = 7.4675406659016683914816280205472e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.16                                         
y[1] (closed_form)                = -0.08485148216102277560912865346997          
y[1] (numeric)                    = -0.084851482161022775609128653469904         
absolute error                    = 6.6e-32                                      
relative error                    = 7.7782966565924809992626091862935e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.17                                         
y[1] (closed_form)                = -0.084007195806891097834448734719998         
y[1] (numeric)                    = -0.084007195806891097834448734719935         
absolute error                    = 6.3e-32                                      
relative error                    = 7.4993575722750311500570146667031e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.18                                         
y[1] (closed_form)                = -0.083171310242346339029033231003973         
y[1] (numeric)                    = -0.083171310242346339029033231003907         
absolute error                    = 6.6e-32                                      
relative error                    = 7.9354286721812835780853234940656e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.19                                         
y[1] (closed_form)                = -0.082343741878135471091305809546969         
y[1] (numeric)                    = -0.082343741878135471091305809546905         
absolute error                    = 6.4e-32                                      
relative error                    = 7.7722967817902577933782714547750e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.2                                          
y[1] (closed_form)                = -0.081524407956732430332158524288851         
y[1] (numeric)                    = -0.081524407956732430332158524288786         
absolute error                    = 6.5e-32                                      
relative error                    = 7.9730723140605383091570857115883e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.21                                         
y[1] (closed_form)                = -0.080713226544062295903747969588037         
y[1] (numeric)                    = -0.080713226544062295903747969587973         
absolute error                    = 6.4e-32                                      
relative error                    = 7.9293075918680626969518333402103e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.22                                         
y[1] (closed_form)                = -0.079910116521307814028787133448768         
y[1] (numeric)                    = -0.079910116521307814028787133448706         
absolute error                    = 6.2e-32                                      
relative error                    = 7.7587172562147208933506579745339e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.23                                         
y[1] (closed_form)                = -0.079114997576797448675927960221868         
y[1] (numeric)                    = -0.079114997576797448675927960221803         
absolute error                    = 6.5e-32                                      
relative error                    = 8.2158885155629401795646791886461e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.24                                         
y[1] (closed_form)                = -0.078327790197974147479542180731511         
y[1] (numeric)                    = -0.078327790197974147479542180731447         
absolute error                    = 6.4e-32                                      
relative error                    = 8.1707909591524875861841054412976e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.25                                         
y[1] (closed_form)                = -0.077548415663444019773799670535193         
y[1] (numeric)                    = -0.077548415663444019773799670535129         
absolute error                    = 6.4e-32                                      
relative error                    = 8.2529087735017798685056344542006e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.26                                         
y[1] (closed_form)                = -0.076776796035104131602221620427345         
y[1] (numeric)                    = -0.076776796035104131602221620427282         
absolute error                    = 6.3e-32                                      
relative error                    = 8.2056041998932775247771988545303e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.27                                         
y[1] (closed_form)                = -0.076012854150348630475649281811054         
y[1] (numeric)                    = -0.07601285415034863047564928181099          
absolute error                    = 6.4e-32                                      
relative error                    = 8.4196285898450855746472718909277e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.28                                         
y[1] (closed_form)                = -0.075256513614352420484609166127661         
y[1] (numeric)                    = -0.075256513614352420484609166127598         
absolute error                    = 6.3e-32                                      
relative error                    = 8.3713684004602971759912056530725e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.29                                         
y[1] (closed_form)                = -0.07450769879243161612715564269026          
y[1] (numeric)                    = -0.074507698792431616127155642690196         
absolute error                    = 6.4e-32                                      
relative error                    = 8.5897163698875406798386321809276e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.3                                          
y[1] (closed_form)                = -0.073766334802480010891207409483032         
y[1] (numeric)                    = -0.073766334802480010891207409482966         
absolute error                    = 6.6e-32                                      
relative error                    = 8.9471708438171028508500627963762e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.31                                         
y[1] (closed_form)                = -0.073032347507480804231933106715629         
y[1] (numeric)                    = -0.073032347507480804231933106715564         
absolute error                    = 6.5e-32                                      
relative error                    = 8.9001657783685455568886700740751e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.32                                         
y[1] (closed_form)                = -0.072305663508092838110643563374324         
y[1] (numeric)                    = -0.072305663508092838110643563374259         
absolute error                    = 6.5e-32                                      
relative error                    = 8.9896139315179440926510447639071e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.33                                         
y[1] (closed_form)                = -0.071586210135310601712666409183133         
y[1] (numeric)                    = -0.071586210135310601712666409183067         
absolute error                    = 6.6e-32                                      
relative error                    = 9.2196527620680468652094551159218e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.34                                         
y[1] (closed_form)                = -0.070873915443197270338558156312127         
y[1] (numeric)                    = -0.070873915443197270338558156312062         
absolute error                    = 6.5e-32                                      
relative error                    = 9.1712161792577992011323591628949e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.35                                         
y[1] (closed_form)                = -0.070168708201690051766487050931066         
y[1] (numeric)                    = -0.070168708201690051766487050931            
absolute error                    = 6.6e-32                                      
relative error                    = 9.4059021024432018621138246977408e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.36                                         
y[1] (closed_form)                = -0.069470517889477120614427368210285         
y[1] (numeric)                    = -0.069470517889477120614427368210218         
absolute error                    = 6.7e-32                                      
relative error                    = 9.6443789445462970469983636806838e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.37                                         
y[1] (closed_form)                = -0.068779274686945428389665462380541         
y[1] (numeric)                    = -0.068779274686945428389665462380476         
absolute error                    = 6.5e-32                                      
relative error                    = 9.4505212937840489757984503742750e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.38                                         
y[1] (closed_form)                = -0.068094909469198684000745677908606         
y[1] (numeric)                    = -0.068094909469198684000745677908539         
absolute error                    = 6.7e-32                                      
relative error                    = 9.8392083229519611115385435196388e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.39                                         
y[1] (closed_form)                = -0.067417353799144806524088947411793         
y[1] (numeric)                    = -0.067417353799144806524088947411728         
absolute error                    = 6.5e-32                                      
relative error                    = 9.6414344878698767893860903677821e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.4                                          
y[1] (closed_form)                = -0.066746539920652158964800262941896         
y[1] (numeric)                    = -0.06674653992065215896480026294183          
absolute error                    = 6.6e-32                                      
relative error                    = 9.8881530156410144048937085011310e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.41                                         
y[1] (closed_form)                = -0.066082400751773878629337943842434         
y[1] (numeric)                    = -0.066082400751773878629337943842369         
absolute error                    = 6.5e-32                                      
relative error                    = 9.8362043843050264369954980166415e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.42                                         
y[1] (closed_form)                = -0.065424869878039626537435557928615         
y[1] (numeric)                    = -0.06542486987803962653743555792855          
absolute error                    = 6.5e-32                                      
relative error                    = 9.9350598818413183482414033646990e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.43                                         
y[1] (closed_form)                = -0.064773881545814085042627460724618         
y[1] (numeric)                    = -0.064773881545814085042627460724553         
absolute error                    = 6.5e-32                                      
relative error                    = 1.0034908893645038556961073252714e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.44                                         
y[1] (closed_form)                = -0.064129370655721539505605401547277         
y[1] (numeric)                    = -0.064129370655721539505605401547213         
absolute error                    = 6.4e-32                                      
relative error                    = 9.9798266138590279112572795665079e-29      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.45                                         
y[1] (closed_form)                = -0.06349127275613588647309399855947          
y[1] (numeric)                    = -0.063491272756135886473093998559405         
absolute error                    = 6.5e-32                                      
relative error                    = 1.0237627500343077937496059771250e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=271.5MB, alloc=52.3MB, time=3.11
 
TOP MAIN SOLVE Loop
x[1]                              = 3.46                                         
y[1] (closed_form)                = -0.062859524036735417357637959073097         
y[1] (numeric)                    = -0.062859524036735417357637959073032         
absolute error                    = 6.5e-32                                      
relative error                    = 1.0340517367266999648606042428516e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.47                                         
y[1] (closed_form)                = -0.062234061322121733091297992320118         
y[1] (numeric)                    = -0.062234061322121733091297992320054         
absolute error                    = 6.4e-32                                      
relative error                    = 1.0283757582321008826532789716491e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.48                                         
y[1] (closed_form)                = -0.061614822065502151639403195435717         
y[1] (numeric)                    = -0.061614822065502151639403195435652         
absolute error                    = 6.5e-32                                      
relative error                    = 1.0549409674655734098923680670555e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.49                                         
y[1] (closed_form)                = -0.061001744342434976609846609938077         
y[1] (numeric)                    = -0.061001744342434976609846609938012         
absolute error                    = 6.5e-32                                      
relative error                    = 1.0655433004525363214657758980879e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.5                                          
y[1] (closed_form)                = -0.060394766844637001479572584727239         
y[1] (numeric)                    = -0.060394766844637001479572584727176         
absolute error                    = 6.3e-32                                      
relative error                    = 1.0431367366988078831455773545373e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.51                                         
y[1] (closed_form)                = -0.059793828873852630183518163993323         
y[1] (numeric)                    = -0.059793828873852630183518163993259         
absolute error                    = 6.4e-32                                      
relative error                    = 1.0703445690862371798866477221251e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.52                                         
y[1] (closed_form)                = -0.059198870335784000972958310966756         
y[1] (numeric)                    = -0.059198870335784000972958310966692         
absolute error                    = 6.4e-32                                      
relative error                    = 1.0811017108431857242269122740170e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.53                                         
y[1] (closed_form)                = -0.058609831734081506550582555054073         
y[1] (numeric)                    = -0.058609831734081506550582555054008         
absolute error                    = 6.5e-32                                      
relative error                    = 1.1090289474795168651148194570278e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.54                                         
y[1] (closed_form)                = -0.05802665416439410952930865344351          
y[1] (numeric)                    = -0.058026654164394109529308653443445         
absolute error                    = 6.5e-32                                      
relative error                    = 1.1201748737028650509559230346100e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.55                                         
y[1] (closed_form)                = -0.057449279308478858241421061568647         
y[1] (numeric)                    = -0.057449279308478858241421061568582         
absolute error                    = 6.5e-32                                      
relative error                    = 1.1314328183470656963236042396314e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.56                                         
y[1] (closed_form)                = -0.056877649428369013844706373088932         
y[1] (numeric)                    = -0.056877649428369013844706373088867         
absolute error                    = 6.5e-32                                      
relative error                    = 1.1428039072159648730913580105065e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.57                                         
y[1] (closed_form)                = -0.056311707360600205533436432653193         
y[1] (numeric)                    = -0.056311707360600205533436432653128         
absolute error                    = 6.5e-32                                      
relative error                    = 1.1542892774279254101540248100233e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.58                                         
y[1] (closed_form)                = -0.055751396510494036464908666394755         
y[1] (numeric)                    = -0.05575139651049403646490866639469          
absolute error                    = 6.5e-32                                      
relative error                    = 1.1658900775295396773124744678946e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.59                                         
y[1] (closed_form)                = -0.055196660846498568757372606584414         
y[1] (numeric)                    = -0.055196660846498568757372606584348         
absolute error                    = 6.6e-32                                      
relative error                    = 1.1957245055737234355072590963264e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.6                                          
y[1] (closed_form)                = -0.054647444894585121603126124871106         
y[1] (numeric)                    = -0.054647444894585121603126124871041         
absolute error                    = 6.5e-32                                      
relative error                    = 1.1894426194195346019593298917235e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.61                                         
y[1] (closed_form)                = -0.054103693732700822171923333263377         
y[1] (numeric)                    = -0.054103693732700822171923333263312         
absolute error                    = 6.5e-32                                      
relative error                    = 1.2013967164817314426057070808519e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.62                                         
y[1] (closed_form)                = -0.053565352985276354555161603984964         
y[1] (numeric)                    = -0.053565352985276354555161603984899         
absolute error                    = 6.5e-32                                      
relative error                    = 1.2134709542167437240168483634004e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.63                                         
y[1] (closed_form)                = -0.053032368817788357521165235770362         
y[1] (numeric)                    = -0.053032368817788357521165235770298         
absolute error                    = 6.4e-32                                      
relative error                    = 1.2068101317498159711898396659347e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.64                                         
y[1] (closed_form)                = -0.052504687931375927316809944658597         
y[1] (numeric)                    = -0.052504687931375927316809944658533         
absolute error                    = 6.4e-32                                      
relative error                    = 1.2189387752127684885311515301583e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.65                                         
y[1] (closed_form)                = -0.051982257557510687161282079114776         
y[1] (numeric)                    = -0.051982257557510687161282079114713         
absolute error                    = 6.3e-32                                      
relative error                    = 1.2119519805445119191371854183371e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.66                                         
y[1] (closed_form)                = -0.051465025452719890434480311840354         
y[1] (numeric)                    = -0.051465025452719890434480311840291         
absolute error                    = 6.3e-32                                      
relative error                    = 1.2241323004469726588948164972247e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.67                                         
y[1] (closed_form)                = -0.050952939893362029865981219773543         
y[1] (numeric)                    = -0.050952939893362029865981219773479         
absolute error                    = 6.4e-32                                      
relative error                    = 1.2560609875297439966114413782032e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.68                                         
y[1] (closed_form)                = -0.050445949670454430281133975316452         
y[1] (numeric)                    = -0.050445949670454430281133975316389         
absolute error                    = 6.3e-32                                      
relative error                    = 1.2488614132860367569895141708430e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.69                                         
y[1] (closed_form)                = -0.049944004084552307659248404512019         
y[1] (numeric)                    = -0.049944004084552307659248404511954         
absolute error                    = 6.5e-32                                      
relative error                    = 1.3014575261118184046026669446929e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.7                                          
y[1] (closed_form)                = -0.049447052940678782405514765966805         
y[1] (numeric)                    = -0.049447052940678782405514765966741         
absolute error                    = 6.4e-32                                      
relative error                    = 1.2943137395221564969246140556493e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.71                                         
y[1] (closed_form)                = -0.048955046543305339833757439474213         
y[1] (numeric)                    = -0.048955046543305339833757439474149         
absolute error                    = 6.4e-32                                      
relative error                    = 1.3073218088636885432245576340788e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.72                                         
y[1] (closed_form)                = -0.048467935691382235901887836166041         
y[1] (numeric)                    = -0.048467935691382235901887836165977         
absolute error                    = 6.4e-32                                      
relative error                    = 1.3204606114755454305545179251605e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.73                                         
y[1] (closed_form)                = -0.047985671673418351236488733125186         
y[1] (numeric)                    = -0.047985671673418351236488733125122         
absolute error                    = 6.4e-32                                      
relative error                    = 1.3337314612489373832765144255607e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.74                                         
y[1] (closed_form)                = -0.047508206262610001427832355579656         
y[1] (numeric)                    = -0.047508206262610001427832355579592         
absolute error                    = 6.4e-32                                      
relative error                    = 1.3471356852799008189271833826543e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.75                                         
y[1] (closed_form)                = -0.047035491712018216472302370200866         
y[1] (numeric)                    = -0.047035491712018216472302370200801         
absolute error                    = 6.5e-32                                      
relative error                    = 1.3819351650020404493043406102021e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.76                                         
y[1] (closed_form)                = -0.046567480749794007086145084511088         
y[1] (numeric)                    = -0.046567480749794007086145084511023         
absolute error                    = 6.5e-32                                      
relative error                    = 1.3958238443097983096480379229564e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.77                                         
y[1] (closed_form)                = -0.046104126574451140413202269518292         
y[1] (numeric)                    = -0.046104126574451140413202269518227         
absolute error                    = 6.5e-32                                      
relative error                    = 1.4098521071651775640429121173955e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.78                                         
y[1] (closed_form)                = -0.045645382850185952400257012152537         
y[1] (numeric)                    = -0.045645382850185952400257012152472         
absolute error                    = 6.5e-32                                      
relative error                    = 1.4240213564061540084280184648138e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.79                                         
y[1] (closed_form)                = -0.045191203702243728817329962734743         
y[1] (numeric)                    = -0.045191203702243728817329962734677         
absolute error                    = 6.6e-32                                      
relative error                    = 1.4604612091074511719309005965153e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.8                                          
y[1] (closed_form)                = -0.044741543712331191557166645081646         
y[1] (numeric)                    = -0.04474154371233119155716664508158          
absolute error                    = 6.6e-32                                      
relative error                    = 1.4751390882789271602394083480591e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.81                                         
y[1] (closed_form)                = -0.044296357914074631458722837151075         
y[1] (numeric)                    = -0.044296357914074631458722837151009         
absolute error                    = 6.6e-32                                      
relative error                    = 1.4899644825885177124456083928522e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.82                                         
y[1] (closed_form)                = -0.043855601788523233464145468835525         
y[1] (numeric)                    = -0.04385560178852323346414546883546          
absolute error                    = 6.5e-32                                      
relative error                    = 1.4821367704275839554983100298423e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.83                                         
y[1] (closed_form)                = -0.043419231259697144438017493467177         
y[1] (numeric)                    = -0.043419231259697144438017493467112         
absolute error                    = 6.5e-32                                      
relative error                    = 1.4970324926119704086362967739301e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.84                                         
y[1] (closed_form)                = -0.04298720269017983845193870167105          
y[1] (numeric)                    = -0.042987202690179838451938701670984         
absolute error                    = 6.6e-32                                      
relative error                    = 1.5353406565130438989523871315670e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.85                                         
y[1] (closed_form)                = -0.042559472876754338767297894474697         
y[1] (numeric)                    = -0.042559472876754338767297894474631         
absolute error                    = 6.6e-32                                      
relative error                    = 1.5507710866421162685394057159584e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.86                                         
y[1] (closed_form)                = -0.042135999046082860134798199089125         
y[1] (numeric)                    = -0.04213599904608286013479819908906          
absolute error                    = 6.5e-32                                      
relative error                    = 1.5426239194877396327461536290845e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
memory used=316.7MB, alloc=52.3MB, time=3.61
x[1]                              = 3.87                                         
y[1] (closed_form)                = -0.041716738850429439371365169807746         
y[1] (numeric)                    = -0.041716738850429439371365169807681         
absolute error                    = 6.5e-32                                      
relative error                    = 1.5581275476266256293291360240130e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.88                                         
y[1] (closed_form)                = -0.041301650363425126473930878432624         
y[1] (numeric)                    = -0.041301650363425126473930878432558         
absolute error                    = 6.6e-32                                      
relative error                    = 1.5979990973543908279391532967633e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.89                                         
y[1] (closed_form)                = -0.040890692075875312785676353468485         
y[1] (numeric)                    = -0.04089069207587531278567635346842          
absolute error                    = 6.5e-32                                      
relative error                    = 1.5896038120212862515895164731095e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.9                                          
y[1] (closed_form)                = -0.040483822891608776944055087487307         
y[1] (numeric)                    = -0.040483822891608776944055087487242         
absolute error                    = 6.5e-32                                      
relative error                    = 1.6055795959297306510922483125897e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.91                                         
y[1] (closed_form)                = -0.04008100212336803351173327510709          
y[1] (numeric)                    = -0.040081002123368033511733275107025         
absolute error                    = 6.5e-32                                      
relative error                    = 1.6217159391357554802194844731936e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.92                                         
y[1] (closed_form)                = -0.039682189488740573321885154718708         
y[1] (numeric)                    = -0.039682189488740573321885154718644         
absolute error                    = 6.4e-32                                      
relative error                    = 1.6128142328980955952729409476022e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.93                                         
y[1] (closed_form)                = -0.039287345106130588658487339147276         
y[1] (numeric)                    = -0.039287345106130588658487339147211         
absolute error                    = 6.5e-32                                      
relative error                    = 1.6544767742490465066334573398997e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.94                                         
y[1] (closed_form)                = -0.038896429490770780440773257808341         
y[1] (numeric)                    = -0.038896429490770780440773257808276         
absolute error                    = 6.5e-32                                      
relative error                    = 1.6711045422671248199530602287650e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.95                                         
y[1] (closed_form)                = -0.038509403550773848589242650711833         
y[1] (numeric)                    = -0.038509403550773848589242650711769         
absolute error                    = 6.4e-32                                      
relative error                    = 1.6619317387146058892563168935264e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.96                                         
y[1] (closed_form)                = -0.038126228583223270718972279600075         
y[1] (numeric)                    = -0.038126228583223270718972279600011         
absolute error                    = 6.4e-32                                      
relative error                    = 1.6786344303711696099978084197923e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.97                                         
y[1] (closed_form)                = -0.037746866270302978234839492009752         
y[1] (numeric)                    = -0.037746866270302978234839492009688         
absolute error                    = 6.4e-32                                      
relative error                    = 1.6955049868696371358913520018512e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.98                                         
y[1] (closed_form)                = -0.037371278675465542793042879942699         
y[1] (numeric)                    = -0.037371278675465542793042879942634         
absolute error                    = 6.5e-32                                      
relative error                    = 1.7393036123934627382223703562552e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 3.99                                         
y[1] (closed_form)                = -0.03699942823963848994437299661867          
y[1] (numeric)                    = -0.036999428239638489944372996618606         
absolute error                    = 6.4e-32                                      
relative error                    = 1.7297564596264508209043807284732e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4                                            
y[1] (closed_form)                = -0.036631277777468360587436042546482         
y[1] (numeric)                    = -0.036631277777468360587436042546418         
absolute error                    = 6.4e-32                                      
relative error                    = 1.7471408010606156504995283584916e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.01                                         
y[1] (closed_form)                = -0.036266790473602144634845884059948         
y[1] (numeric)                    = -0.036266790473602144634845884059884         
absolute error                    = 6.4e-32                                      
relative error                    = 1.7646998580308420623877972011226e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.02                                         
y[1] (closed_form)                = -0.035905929879005715032652207912938         
y[1] (numeric)                    = -0.035905929879005715032652207912873         
absolute error                    = 6.5e-32                                      
relative error                    = 1.8102859393708574828898852670006e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.03                                         
y[1] (closed_form)                = -0.035548659907318893973338772871938         
y[1] (numeric)                    = -0.035548659907318893973338772871874         
absolute error                    = 6.4e-32                                      
relative error                    = 1.8003491599080908077675004423360e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.04                                         
y[1] (closed_form)                = -0.035194944831246786805975603183958         
y[1] (numeric)                    = -0.035194944831246786805975603183893         
absolute error                    = 6.5e-32                                      
relative error                    = 1.8468561411777432279226724917160e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.05                                         
y[1] (closed_form)                = -0.034844749278987022773908907373465         
y[1] (numeric)                    = -0.0348447492789870227739089073734           
absolute error                    = 6.5e-32                                      
relative error                    = 1.8654173539770014180091643560987e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.06                                         
y[1] (closed_form)                = -0.034498038230692545301085182050658         
y[1] (numeric)                    = -0.034498038230692545301085182050593         
absolute error                    = 6.5e-32                                      
relative error                    = 1.8841651100661769516090835494814e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.07                                         
y[1] (closed_form)                = -0.034154777014969598103090448554437         
y[1] (numeric)                    = -0.034154777014969598103090448554372         
absolute error                    = 6.5e-32                                      
relative error                    = 1.9031012842365019284272962510852e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.08                                         
y[1] (closed_form)                = -0.033814931305410556918597371718443         
y[1] (numeric)                    = -0.033814931305410556918597371718377         
absolute error                    = 6.6e-32                                      
relative error                    = 1.9518005050461147106840610296118e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.09                                         
y[1] (closed_form)                = -0.033478467117161260141504088950542         
y[1] (numeric)                    = -0.033478467117161260141504088950476         
absolute error                    = 6.6e-32                                      
relative error                    = 1.9714164262367917634471415103965e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.1                                          
y[1] (closed_form)                = -0.033145350803522495083967396166902         
y[1] (numeric)                    = -0.033145350803522495083967396166837         
absolute error                    = 6.5e-32                                      
relative error                    = 1.9610593469142640086683346405140e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.11                                         
y[1] (closed_form)                = -0.032815549052585300016124489678115         
y[1] (numeric)                    = -0.03281554905258530001612448967805          
absolute error                    = 6.5e-32                                      
relative error                    = 1.9807683210127218525922220352911e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.12                                         
y[1] (closed_form)                = -0.032489028883899745509903311888252         
y[1] (numeric)                    = -0.032489028883899745509903311888187         
absolute error                    = 6.5e-32                                      
relative error                    = 2.0006753735939267383560204820416e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.13                                         
y[1] (closed_form)                = -0.032165757645176861962279857041206         
y[1] (numeric)                    = -0.03216575764517686196227985704114          
absolute error                    = 6.6e-32                                      
relative error                    = 2.0518714568471064530336509579781e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.14                                         
y[1] (closed_form)                = -0.031845703009023383487986359852932         
y[1] (numeric)                    = -0.031845703009023383487986359852866         
absolute error                    = 6.6e-32                                      
relative error                    = 2.0724931078236552012024509288570e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.15                                         
y[1] (closed_form)                = -0.031528832969708981653338582022219         
y[1] (numeric)                    = -0.031528832969708981653338582022153         
absolute error                    = 6.6e-32                                      
relative error                    = 2.0933220098380696616799968911557e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.16                                         
y[1] (closed_form)                = -0.031215115839965665771861598480226         
y[1] (numeric)                    = -0.03121511583996566577186159848016          
absolute error                    = 6.6e-32                                      
relative error                    = 2.1143602457979087521158464524342e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.17                                         
y[1] (closed_form)                = -0.030904520247819029699076470646538         
y[1] (numeric)                    = -0.030904520247819029699076470646472         
absolute error                    = 6.6e-32                                      
relative error                    = 2.1356099195443003781585577956767e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.18                                         
y[1] (closed_form)                = -0.030597015133451028248486648885946         
y[1] (numeric)                    = -0.03059701513345102824848664888588          
absolute error                    = 6.6e-32                                      
relative error                    = 2.1570731560623272994530384700524e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.19                                         
y[1] (closed_form)                = -0.030292569746093969503791341104983         
y[1] (numeric)                    = -0.030292569746093969503791341104917         
absolute error                    = 6.6e-32                                      
relative error                    = 2.1787521016935274087433149282562e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.2                                          
y[1] (closed_form)                = -0.029991153640955412423968720457457         
y[1] (numeric)                    = -0.029991153640955412423968720457392         
absolute error                    = 6.5e-32                                      
relative error                    = 2.1673057588300671034632063762548e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.21                                         
y[1] (closed_form)                = -0.029692736676173662228426886608675         
y[1] (numeric)                    = -0.02969273667617366222842688660861          
absolute error                    = 6.5e-32                                      
relative error                    = 2.1890875438287889182948935369540e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.22                                         
y[1] (closed_form)                = -0.029397289009803559109224000018468         
y[1] (numeric)                    = -0.029397289009803559109224000018403         
absolute error                    = 6.5e-32                                      
relative error                    = 2.2110882394061393126853257245639e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.23                                         
y[1] (closed_form)                = -0.029104781096832258846716960143819         
y[1] (numeric)                    = -0.029104781096832258846716960143754         
absolute error                    = 6.5e-32                                      
relative error                    = 2.2333100456500099957682197119354e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.24                                         
y[1] (closed_form)                = -0.028815183686224706904213334652431         
y[1] (numeric)                    = -0.028815183686224706904213334652366         
absolute error                    = 6.5e-32                                      
relative error                    = 2.2557551847595435882091258180130e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.25                                         
y[1] (closed_form)                = -0.028528467817998510546573891712003         
y[1] (numeric)                    = -0.028528467817998510546573891711938         
absolute error                    = 6.5e-32                                      
relative error                    = 2.2784259012673553883062860998406e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.26                                         
y[1] (closed_form)                = -0.028244604820327916467539980915243         
y[1] (numeric)                    = -0.028244604820327916467539980915178         
absolute error                    = 6.5e-32                                      
relative error                    = 2.3013244622639885039705450826359e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.27                                         
y[1] (closed_form)                = -0.027963566306676604321135135556967         
y[1] (numeric)                    = -0.027963566306676604321135135556902         
absolute error                    = 6.5e-32                                      
relative error                    = 2.3244531576246247962845575858121e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.28                                         
y[1] (closed_form)                = -0.027685324172959009434104689735196         
y[1] (numeric)                    = -0.027685324172959009434104689735131         
absolute error                    = 6.5e-32                                      
relative error                    = 2.3478143002380743059245759817807e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=362.0MB, alloc=52.3MB, time=4.11
 
TOP MAIN SOLVE Loop
x[1]                              = 4.29                                         
y[1] (closed_form)                = -0.027409850594729890829299081946433         
y[1] (numeric)                    = -0.027409850594729890829299081946367         
absolute error                    = 6.6e-32                                      
relative error                    = 2.4078934604878824625256424432011e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.3                                          
y[1] (closed_form)                = -0.027137118024401863514461149051535         
y[1] (numeric)                    = -0.027137118024401863514461149051469         
absolute error                    = 6.6e-32                                      
relative error                    = 2.4320931920866612980881443886315e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.31                                         
y[1] (closed_form)                = -0.026867099188490616787327558519805         
y[1] (numeric)                    = -0.02686709918849061678732755851974          
absolute error                    = 6.5e-32                                      
relative error                    = 2.4193158905612271568557377216124e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.32                                         
y[1] (closed_form)                = -0.026599767084887543076579230029926         
y[1] (numeric)                    = -0.026599767084887543076579230029861         
absolute error                    = 6.5e-32                                      
relative error                    = 2.4436304194907503325965057151494e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.33                                         
y[1] (closed_form)                = -0.026335094980159504579252024594645         
y[1] (numeric)                    = -0.02633509498015950457925202459458          
absolute error                    = 6.5e-32                                      
relative error                    = 2.4681893134985880541538895290548e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.34                                         
y[1] (closed_form)                = -0.02607305640687546766902124030864          
y[1] (numeric)                    = -0.026073056406875467669021240308575         
absolute error                    = 6.5e-32                                      
relative error                    = 2.4929950284946069185258481781587e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.35                                         
y[1] (closed_form)                = -0.025813625160959737736572931083345         
y[1] (numeric)                    = -0.02581362516095973773657293108328          
absolute error                    = 6.5e-32                                      
relative error                    = 2.5180500450709780256670548341572e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.36                                         
y[1] (closed_form)                = -0.025556775299071529783340440515445         
y[1] (numeric)                    = -0.02555677529907152978334044051538          
absolute error                    = 6.5e-32                                      
relative error                    = 2.5433568687502382627659254223389e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.37                                         
y[1] (closed_form)                = -0.025302481136010612723481826091564         
y[1] (numeric)                    = -0.025302481136010612723481826091499         
absolute error                    = 6.5e-32                                      
relative error                    = 2.5689180302358446458757446664200e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.38                                         
y[1] (closed_form)                = -0.025050717242148767956366401183318         
y[1] (numeric)                    = -0.025050717242148767956366401183252         
absolute error                    = 6.6e-32                                      
relative error                    = 2.6346551023677890326127386543848e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.39                                         
y[1] (closed_form)                = -0.024801458440886805353287185162491         
y[1] (numeric)                    = -0.024801458440886805353287185162425         
absolute error                    = 6.6e-32                                      
relative error                    = 2.6611338263557412100711170138063e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.4                                          
y[1] (closed_form)                = -0.024554679806136882357878772473083         
y[1] (numeric)                    = -0.024554679806136882357878772473017         
absolute error                    = 6.6e-32                                      
relative error                    = 2.6878786659439478756652267869640e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.41                                         
y[1] (closed_form)                = -0.024310356659829874430052588037247         
y[1] (numeric)                    = -0.02431035665982987443005258803718          
absolute error                    = 6.7e-32                                      
relative error                    = 2.7560270273907561284140092063589e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.42                                         
y[1] (closed_form)                = -0.024068464569447547568416724299946         
y[1] (numeric)                    = -0.024068464569447547568416724299879         
absolute error                    = 6.7e-32                                      
relative error                    = 2.7837255595045162431900318196537e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.43                                         
y[1] (closed_form)                = -0.023828979345579286126376072142976         
y[1] (numeric)                    = -0.023828979345579286126376072142909         
absolute error                    = 6.7e-32                                      
relative error                    = 2.8117024664940058417622771069517e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.44                                         
y[1] (closed_form)                = -0.023591877039503131592658288741304         
y[1] (numeric)                    = -0.023591877039503131592658288741237         
absolute error                    = 6.7e-32                                      
relative error                    = 2.8399605460732380399622795924463e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.45                                         
y[1] (closed_form)                = -0.023357133940790890438127847222936         
y[1] (numeric)                    = -0.023357133940790890438127847222869         
absolute error                    = 6.7e-32                                      
relative error                    = 2.8685026240737192391540251086210e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.46                                         
y[1] (closed_form)                = -0.0231247265749370715376770994238           
y[1] (numeric)                    = -0.023124726574937071537677099423733         
absolute error                    = 6.7e-32                                      
relative error                    = 2.8973315547270346317415254086160e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.47                                         
y[1] (closed_form)                = -0.022894631701011416058960648775872         
y[1] (numeric)                    = -0.022894631701011416058960648775804         
absolute error                    = 6.8e-32                                      
relative error                    = 2.9701285824569942417778648320660e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.48                                         
y[1] (closed_form)                = -0.022666826309334785069005675152334         
y[1] (numeric)                    = -0.022666826309334785069005675152266         
absolute error                    = 6.8e-32                                      
relative error                    = 2.9999788709721502576616413618904e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.49                                         
y[1] (closed_form)                = -0.02244128761917817244552210591857          
y[1] (numeric)                    = -0.022441287619178172445522105918502         
absolute error                    = 6.8e-32                                      
relative error                    = 3.0301291598743942143374983906504e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.5                                          
y[1] (closed_form)                = -0.022217993076484612992286268573861         
y[1] (numeric)                    = -0.022217993076484612992286268573793         
absolute error                    = 6.8e-32                                      
relative error                    = 3.0605824642177416607039255293495e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.51                                         
y[1] (closed_form)                = -0.021996920351613757947511147117173         
y[1] (numeric)                    = -0.021996920351613757947511147117105         
absolute error                    = 6.8e-32                                      
relative error                    = 3.0913418293580047697176787490860e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.52                                         
y[1] (closed_form)                = -0.02177804733710889234087455248789          
y[1] (numeric)                    = -0.021778047337108892340874552487822         
absolute error                    = 6.8e-32                                      
relative error                    = 3.1224103312573304574160455375873e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.53                                         
y[1] (closed_form)                = -0.021561352145486170899080084826662         
y[1] (numeric)                    = -0.021561352145486170899080084826593         
absolute error                    = 6.9e-32                                      
relative error                    = 3.2001703573328550309322935803764e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.54                                         
y[1] (closed_form)                = -0.021346813107045851421699134099529         
y[1] (numeric)                    = -0.021346813107045851421699134099461         
absolute error                    = 6.8e-32                                      
relative error                    = 3.1854872040621150355438558215781e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.55                                         
y[1] (closed_form)                = -0.021134408767705306748807525018684         
y[1] (numeric)                    = -0.021134408767705306748807525018616         
absolute error                    = 6.8e-32                                      
relative error                    = 3.2175018827074186403156143637096e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.56                                         
y[1] (closed_form)                = -0.020924117886853598619807740544615         
y[1] (numeric)                    = -0.020924117886853598619807740544548         
absolute error                    = 6.7e-32                                      
relative error                    = 3.2020465743072203537866864119265e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.57                                         
y[1] (closed_form)                = -0.020715919435227398879034745114834         
y[1] (numeric)                    = -0.020715919435227398879034745114766         
absolute error                    = 6.8e-32                                      
relative error                    = 3.2824997322767181943545931411692e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.58                                         
y[1] (closed_form)                = -0.020509792592808045618495896619257         
y[1] (numeric)                    = -0.020509792592808045618495896619189         
absolute error                    = 6.8e-32                                      
relative error                    = 3.3154894030398361287682047833437e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.59                                         
y[1] (closed_form)                = -0.02030571674673952396160676205756          
y[1] (numeric)                    = -0.020305716746739523961606762057491         
absolute error                    = 6.9e-32                                      
relative error                    = 3.3980578405871482554935504067501e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.6                                          
y[1] (closed_form)                = -0.0201036714892671632842661886631           
y[1] (numeric)                    = -0.020103671489267163284266188663031         
absolute error                    = 6.9e-32                                      
relative error                    = 3.4322088896467164013731648453210e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.61                                         
y[1] (closed_form)                = -0.01990363661569684474127497995891          
y[1] (numeric)                    = -0.01990363661569684474127497995884          
absolute error                    = 7.0e-32                                      
relative error                    = 3.5169452372736275061889631488072e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.62                                         
y[1] (closed_form)                = -0.019705592122374515017150152549829         
y[1] (numeric)                    = -0.019705592122374515017150152549759         
absolute error                    = 7.0e-32                                      
relative error                    = 3.5522911245340965364254471880161e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.63                                         
y[1] (closed_form)                = -0.019509518204685804251026110923004         
y[1] (numeric)                    = -0.019509518204685804251026110922933         
absolute error                    = 7.1e-32                                      
relative error                    = 3.6392492759225181825524819057774e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.64                                         
y[1] (closed_form)                = -0.019315395255075548095768239755011         
y[1] (numeric)                    = -0.019315395255075548095768239754941         
absolute error                    = 7.0e-32                                      
relative error                    = 3.6240521654148365891121984841439e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.65                                         
y[1] (closed_form)                = -0.019123203861087015861854421299449         
y[1] (numeric)                    = -0.01912320386108701586185442129938          
absolute error                    = 6.9e-32                                      
relative error                    = 3.6081820024104396558434327283779e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.66                                         
y[1] (closed_form)                = -0.018932924803420648667204884013348         
y[1] (numeric)                    = -0.018932924803420648667204884013278         
absolute error                    = 7.0e-32                                      
relative error                    = 3.6972628754830823958415921646338e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.67                                         
y[1] (closed_form)                = -0.018744539054012113465157641806389         
y[1] (numeric)                    = -0.01874453905401211346515764180632          
absolute error                    = 6.9e-32                                      
relative error                    = 3.6810721139195535995603505768219e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.68                                         
y[1] (closed_form)                = -0.01855802777412948075439069447478          
y[1] (numeric)                    = -0.01855802777412948075439069447471          
absolute error                    = 7.0e-32                                      
relative error                    = 3.7719525399990170711765759368270e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.69                                         
y[1] (closed_form)                = -0.018373372312489335686976291012424         
y[1] (numeric)                    = -0.018373372312489335686976291012354         
absolute error                    = 7.0e-32                                      
relative error                    = 3.8098612932595592910107058325355e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=407.3MB, alloc=52.3MB, time=4.63
 
TOP MAIN SOLVE Loop
x[1]                              = 4.7                                          
y[1] (closed_form)                = -0.018190554203391634184108148582775         
y[1] (numeric)                    = -0.018190554203391634184108148582707         
absolute error                    = 6.8e-32                                      
relative error                    = 3.7382038633721989619107758154827e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.71                                         
y[1] (closed_form)                = -0.018009555164873117543558908122057         
y[1] (numeric)                    = -0.018009555164873117543558908121988         
absolute error                    = 6.9e-32                                      
relative error                    = 3.8312995167466216922546837146613e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.72                                         
y[1] (closed_form)                = -0.017830357096879100878789746029528         
y[1] (numeric)                    = -0.017830357096879100878789746029458         
absolute error                    = 7.0e-32                                      
relative error                    = 3.9258888433733221776726469250635e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.73                                         
y[1] (closed_form)                = -0.017652942079453452567032538193552         
y[1] (numeric)                    = -0.017652942079453452567032538193483         
absolute error                    = 6.9e-32                                      
relative error                    = 3.9086969010287654134480197002707e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.74                                         
y[1] (closed_form)                = -0.017477292370946583702781029082076         
y[1] (numeric)                    = -0.017477292370946583702781029082007         
absolute error                    = 6.9e-32                                      
relative error                    = 3.9479799579654744033376692712773e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.75                                         
y[1] (closed_form)                = -0.017303390406241268354143007914501         
y[1] (numeric)                    = -0.017303390406241268354143007914431         
absolute error                    = 7.0e-32                                      
relative error                    = 4.0454499584515680346694993497785e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.76                                         
y[1] (closed_form)                = -0.017131218794996117202600639084614         
y[1] (numeric)                    = -0.017131218794996117202600639084544         
absolute error                    = 7.0e-32                                      
relative error                    = 4.0861074064646470197166920432333e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.77                                         
y[1] (closed_form)                = -0.016960760319906528912079146021476         
y[1] (numeric)                    = -0.016960760319906528912079146021405         
absolute error                    = 7.1e-32                                      
relative error                    = 4.1861330896038086583884202724723e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.78                                         
y[1] (closed_form)                = -0.016791997934982945321011543333507         
y[1] (numeric)                    = -0.016791997934982945321011543333437         
absolute error                    = 7.0e-32                                      
relative error                    = 4.1686522515684846662033017698370e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.79                                         
y[1] (closed_form)                = -0.016624914763846238281483831586441         
y[1] (numeric)                    = -0.01662491476384623828148383158637          
absolute error                    = 7.1e-32                                      
relative error                    = 4.2706985875441490446420048468330e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.8                                          
y[1] (closed_form)                = -0.016459494098040057682724053532149         
y[1] (numeric)                    = -0.016459494098040057682724053532079         
absolute error                    = 7.0e-32                                      
relative error                    = 4.2528646131557208264966840704258e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.81                                         
y[1] (closed_form)                = -0.016295719395359971892331179358986         
y[1] (numeric)                    = -0.016295719395359971892331179358916         
absolute error                    = 7.0e-32                                      
relative error                    = 4.2956066131042815712874837168181e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.82                                         
y[1] (closed_form)                = -0.016133574278199233527895556245215         
y[1] (numeric)                    = -0.016133574278199233527895556245145         
absolute error                    = 7.0e-32                                      
relative error                    = 4.3387781772938368540842129734868e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.83                                         
y[1] (closed_form)                = -0.01597304253191100513420955114174          
y[1] (numeric)                    = -0.01597304253191100513420955114167          
absolute error                    = 7.0e-32                                      
relative error                    = 4.3823836229167820538276733649097e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.84                                         
y[1] (closed_form)                = -0.015814108103186880987271291363368         
y[1] (numeric)                    = -0.015814108103186880987271291363298         
absolute error                    = 7.0e-32                                      
relative error                    = 4.4264273105540174575167477088540e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.85                                         
y[1] (closed_form)                = -0.015656755098451542875910667028563         
y[1] (numeric)                    = -0.015656755098451542875910667028494         
absolute error                    = 6.9e-32                                      
relative error                    = 4.4070434496879955557228206617444e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.86                                         
y[1] (closed_form)                = -0.015500967782273389325277966639986         
y[1] (numeric)                    = -0.015500967782273389325277966639916         
absolute error                    = 7.0e-32                                      
relative error                    = 4.5158470737582374013508387940904e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.87                                         
y[1] (closed_form)                = -0.015346730575790979323793014607349         
y[1] (numeric)                    = -0.015346730575790979323793014607279         
absolute error                    = 7.0e-32                                      
relative error                    = 4.5612320913760590812157635714252e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.88                                         
y[1] (closed_form)                = -0.015194028055155133196616204361159         
y[1] (numeric)                    = -0.01519402805515513319661620436109          
absolute error                    = 6.9e-32                                      
relative error                    = 4.5412579040611426687723323828463e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.89                                         
y[1] (closed_form)                = -0.015042844949986534834430520561019         
y[1] (numeric)                    = -0.01504284494998653483443052056095          
absolute error                    = 6.9e-32                                      
relative error                    = 4.5868983047692559873871519623727e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.9                                          
y[1] (closed_form)                = -0.014893166141848681036472092840257         
y[1] (numeric)                    = -0.014893166141848681036472092840188         
absolute error                    = 6.9e-32                                      
relative error                    = 4.6329973991302742269820226582150e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.91                                         
y[1] (closed_form)                = -0.014744976662736025261471037686311         
y[1] (numeric)                    = -0.014744976662736025261471037686242         
absolute error                    = 6.9e-32                                      
relative error                    = 4.6795597970920495294016877152193e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.92                                         
y[1] (closed_form)                = -0.014598261693577164599617798133888         
y[1] (numeric)                    = -0.01459826169357716459961779813382          
absolute error                    = 6.8e-32                                      
relative error                    = 4.6580888483399457041685562297573e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.93                                         
y[1] (closed_form)                = -0.014453006562752920283004829557022         
y[1] (numeric)                    = -0.014453006562752920283004829556954         
absolute error                    = 6.8e-32                                      
relative error                    = 4.7049034195586621214899785901750e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.94                                         
y[1] (closed_form)                = -0.014309196744629163541359738704192         
y[1] (numeric)                    = -0.014309196744629163541359738704124         
absolute error                    = 6.8e-32                                      
relative error                    = 4.7521884850401003238552716642669e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.95                                         
y[1] (closed_form)                = -0.014166817858104240084432800094696         
y[1] (numeric)                    = -0.014166817858104240084432800094628         
absolute error                    = 6.8e-32                                      
relative error                    = 4.7999487733302128076668424809473e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.96                                         
y[1] (closed_form)                = -0.014025855665170847952276604894962         
y[1] (numeric)                    = -0.014025855665170847952276604894894         
absolute error                    = 6.8e-32                                      
relative error                    = 4.8481890604976289570825369794643e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.97                                         
y[1] (closed_form)                = -0.013886296069492224920004431120137         
y[1] (numeric)                    = -0.013886296069492224920004431120069         
absolute error                    = 6.8e-32                                      
relative error                    = 4.8969141706112658870245138284521e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.98                                         
y[1] (closed_form)                = -0.013748125114992503074581296546882         
y[1] (numeric)                    = -0.013748125114992503074581296546815         
absolute error                    = 6.7e-32                                      
relative error                    = 4.8733917853959343644474270835276e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                              = 4.99                                         
y[1] (closed_form)                = -0.013611328984461089597930665007658         
y[1] (numeric)                    = -0.013611328984461089597930665007591         
absolute error                    = 6.7e-32                                      
relative error                    = 4.9223701871057755861498840435882e-28      % 
Desired digits                    = 8                                   
Estimated correct digits          = 11                                  
Correct digits                    = 32                                  
h                                 = 0.005                                        
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =   2.0  /  exp ( x )  ; 
Iterations                       = 800                                 
Total Elapsed Time               = 4 Seconds
Elapsed Time(since restart)      = 4 Seconds
Time to Timeout                  = 2 Minutes 55 Seconds
Percent Done                     = 100.1                                      % 
> quit
memory used=440.5MB, alloc=52.3MB, time=4.98