|\^/| Maple 2019 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> 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," | \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, "");
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, " | \n")
end proc
# End Function number 7
# Begin Function number 8
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then
printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then
printf(" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then
printf(" = %d Hours %d Minutes %d Seconds\n", hours_int,
minutes_int, sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 8
# Begin Function number 9
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 9
# Begin Function number 10
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 10
# Begin Function number 11
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att := ret_att
+ c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 11
# Begin Function number 12
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 12
# Begin Function number 13
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 16
# Begin Function number 17
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 17
# Begin Function number 18
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> 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," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
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, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 19
# Begin Function number 20
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 20
# Begin Function number 21
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 21
# Begin Function number 22
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 22
# Begin Function number 23
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 23
# Begin Function number 24
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 24
# Begin Function number 25
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then
ret := glob__1 + float_abs(term2)*c(last_no)*
ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 26
# Begin Function number 27
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 30
# Begin Function number 31
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 31
# Begin Function number 32
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 32
# Begin Function number 33
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 35
# Begin Function number 36
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 36
# Begin Function number 37
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 37
# Begin Function number 38
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 38
# Begin Function number 39
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 39
# Begin Function number 40
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return((arcsin(c(0.1)) + arccos(c(0.1)) + arctan(c(0.1))) * c(x));
> end;
exact_soln_y := proc(x)
return (arcsin(c(0.1)) + arccos(c(0.1)) + arctan(c(0.1)))*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_0D1,
#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_a1,
> array_tmp1,
> array_tmp2,
> array_tmp3_a1,
> array_tmp3,
> array_tmp4,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
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_a1, array_tmp1,
array_tmp2, array_tmp3_a1, array_tmp3, array_tmp4, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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_0D1,
#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_a1,
> array_tmp1,
> array_tmp2,
> array_tmp3_a1,
> array_tmp3,
> array_tmp4,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
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_a1, array_tmp1,
array_tmp2, array_tmp3_a1, array_tmp3, array_tmp4, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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_0D1,
#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_a1,
> array_tmp1,
> array_tmp2,
> array_tmp3_a1,
> array_tmp3,
> array_tmp4,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
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_a1, array_tmp1,
array_tmp2, array_tmp3_a1, array_tmp3, array_tmp4, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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_0D1,
#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_a1,
> array_tmp1,
> array_tmp2,
> array_tmp3_a1,
> array_tmp3,
> array_tmp4,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
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_a1, array_tmp1,
array_tmp2, array_tmp3_a1, array_tmp3, array_tmp4, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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_0D1,
#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_a1,
> array_tmp1,
> array_tmp2,
> array_tmp3_a1,
> array_tmp3,
> array_tmp4,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := round(-log10(relerr));
> 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)*27*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 * c(100.0),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_0D1,
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_a1, array_tmp1,
array_tmp2, array_tmp3_a1, array_tmp3, array_tmp4, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := round(-log10(relerr))
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)*27*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*c(100.0), 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_0D1,
#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_a1,
> array_tmp1,
> array_tmp2,
> array_tmp3_a1,
> array_tmp3,
> array_tmp4,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
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_a1, array_tmp1,
array_tmp2, array_tmp3_a1, array_tmp3, array_tmp4, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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_0D1,
#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_a1,
> array_tmp1,
> array_tmp2,
> array_tmp3_a1,
> array_tmp3,
> array_tmp4,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_0D1,
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_a1, array_tmp1,
array_tmp2, array_tmp3_a1, array_tmp3, array_tmp4, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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_0D1,
#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_a1,
> array_tmp1,
> array_tmp2,
> array_tmp3_a1,
> array_tmp3,
> array_tmp4,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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 asin ID_CONST $eq_no = 1
> array_tmp1[1] := arcsin(array_const_0D1[1]);
> #emit pre add CONST CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre acos ID_CONST $eq_no = 1
> array_tmp3[1] := arccos(array_const_0D1[1]);
> #emit pre add CONST CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp2[1] + array_tmp3[1];
> #emit pre atan ID_CONST $eq_no = 1
> array_tmp5[1] := arctan(array_const_0D1[1]);
> #emit pre add CONST CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_tmp4[1] + array_tmp5[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_tmp6[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 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_tmp6[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 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_tmp6[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 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_tmp6[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 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_tmp6[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 (false) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #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_tmp6[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_0D1,
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_a1, array_tmp1,
array_tmp2, array_tmp3_a1, array_tmp3, array_tmp4, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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] := arcsin(array_const_0D1[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := arccos(array_const_0D1[1]);
array_tmp4[1] := array_tmp2[1] + array_tmp3[1];
array_tmp5[1] := arctan(array_const_0D1[1]);
array_tmp6[1] := array_tmp4[1] + array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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;
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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;
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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;
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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;
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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
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_0D1,
> #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_a1,
> array_tmp1,
> array_tmp2,
> array_tmp3_a1,
> array_tmp3,
> array_tmp4,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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_a1:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3_a1:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5_a1:= Array(0..(30),[]);
> array_tmp5_a2:= Array(0..(30),[]);
> array_tmp5:= Array(0..(30),[]);
> array_tmp6:= 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_a1[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_a1[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_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp6[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_a1);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3_a1);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5_a1);
> zero_ats_ar(array_tmp5_a2);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> 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_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_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,"##############R:\Temp/arcsin_c_arccos_c_arctan_cpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(-5.0);");
> 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:=12;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=2;");
> omniout_str(ALWAYS,"glob_max_iter:=1000000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"glob_h_reason:=1;");
> 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((arcsin(c(0.1)) + arccos(c(0.1)) + arctan(c(0.1))) * 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(-5.0);
> 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:=12;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=2;
> glob_max_iter:=1000000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> glob_h_reason:=1;
> #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 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; ");
> 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,"2020-05-25T23:33:25-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"arcsin_c_arccos_c_arctan_c")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; ")
> ;
> 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," 310 | ")
> ;
> logitem_str(html_log_file,"arcsin_c_arccos_c_arctan_c diffeq.mxt")
> ;
> logitem_str(html_log_file,"arcsin_c_arccos_c_arctan_c maple results")
> ;
> logitem_str(html_log_file,"Naturally has problem passing zero (RE)")
> ;
> 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_0D1,
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_a1, array_tmp1,
array_tmp2, array_tmp3_a1, array_tmp3, array_tmp4, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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_a1 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3_a1 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5_a1 := Array(0 .. 30, []);
array_tmp5_a2 := Array(0 .. 30, []);
array_tmp5 := Array(0 .. 30, []);
array_tmp6 := 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_a1[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_a1[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_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp5_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp5_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp6[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_a1);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3_a1);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5_a1);
zero_ats_ar(array_tmp5_a2);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
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_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_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, "##############R:Temp/arcsin_c_arccos_c_arctan_cp\
ostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin ( 0.1 ) \
+ arccos ( 0.1 ) + arctan ( 0.1 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(-5.0);");
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:=12;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=2;");
omniout_str(ALWAYS, "glob_max_iter:=1000000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "glob_h_reason:=1;");
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((arcsin(c(0.1)) + arccos(c(0.1)) + arctan\
(c(0.1))) * 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(-5.0);
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 := 12;
glob_max_minutes := 3.0;
glob_subiter_method := 2;
glob_max_iter := 1000000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_h_reason := 1;
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 ) = arcsin ( 0.1 ) \
+ arccos ( 0.1 ) + arctan ( 0.1 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2020-05-25T23:33:25-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "arcsin_c_arccos_c_arctan_c");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ar\
csin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; \
");
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, " 310 | ");
logitem_str(html_log_file, "arcsin_c_arccos_c_arctan_c diffeq.m\
xt");
logitem_str(html_log_file, "arcsin_c_arccos_c_arctan_c maple r\
esults");
logitem_str(html_log_file,
"Naturally has problem passing zero (RE)");
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#################
##############R:Temp/arcsin_c_arccos_c_arctan_cpostode.ode#################
diff ( y , x , 1 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-5.0);
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:=12;
glob_max_minutes:=(3.0);
glob_subiter_method:=2;
glob_max_iter:=1000000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
glob_h_reason:=1;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return((arcsin(c(0.1)) + arccos(c(0.1)) + arctan(c(0.1))) * c(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -5
y[1] (closed_form) = -8.352324896430293233048839057589
y[1] (numeric) = -8.352324896430293233048839057589
absolute error = 0
relative error = 0 %
Desired digits = 12
Estimated correct digits = 14
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=4.2MB, alloc=40.3MB, time=0.09
TOP MAIN SOLVE Loop
x[1] = -4.99
y[1] (closed_form) = -8.3356202466374326465827413794738
y[1] (numeric) = -8.335620246637432646582741379474
absolute error = 2e-31
relative error = 2.3993415496666786811223493189086e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.3189155968445720601166437013586
y[1] (numeric) = -8.318915596844572060116643701359
absolute error = 4e-31
relative error = 4.8083190091713761521287241370899e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.3022109470517114736505460232435
y[1] (numeric) = -8.302210947051711473650546023244
absolute error = 5e-31
relative error = 6.0224921191331622830988546787494e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.2855062972588508871844483451283
y[1] (numeric) = -8.285506297258850887184448345129
absolute error = 7e-31
relative error = 8.4484879364775288640729497691005e-30 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.2688016474659903007183506670131
y[1] (numeric) = -8.268801647465990300718350667014
absolute error = 9e-31
relative error = 1.0884285757124296926182293728504e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.2520969976731297142522529888979
y[1] (numeric) = -8.252096997673129714252252988899
absolute error = 1.1e-30
relative error = 1.3329945107409311012834590497459e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.2353923478802691277861553107828
y[1] (numeric) = -8.235392347880269127786155310784
absolute error = 1.2e-30
relative error = 1.4571254766129890408276498703473e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.2186876980874085413200576326676
y[1] (numeric) = -8.218687698087408541320057632669
absolute error = 1.4e-30
relative error = 1.7034349660540058197480419046642e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.2019830482945479548539599545524
y[1] (numeric) = -8.201983048294547954853959954554
absolute error = 1.6e-30
relative error = 1.9507477528043546425744233159029e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.1852783985016873683878622764372
y[1] (numeric) = -8.185278398501687368387862276439
absolute error = 1.8e-30
relative error = 2.1990699795006232565143817941262e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.168573748708826781921764598322
y[1] (numeric) = -8.168573748708826781921764598324
absolute error = 2.0e-30
relative error = 2.4484078390259154639673871372912e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.1518690989159661954556669202069
y[1] (numeric) = -8.151869098915966195455666920209
absolute error = 2.1e-30
relative error = 2.5760963216144596208484732082831e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.1351644491231056089895692420917
y[1] (numeric) = -8.135164449123105608989569242094
absolute error = 2.3e-30
relative error = 2.8272323373228409880124438535024e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.1184597993302450225234715639765
y[1] (numeric) = -8.118459799330245022523471563979
absolute error = 2.5e-30
relative error = 3.0794018345773473813787353655746e-29 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.1017551495373844360573738858613
y[1] (numeric) = -8.101755149537384436057373885864
absolute error = 2.7e-30
relative error = 3.3326112060473362753362280797583e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.0850504997445238495912762077462
y[1] (numeric) = -8.085050499744523849591276207749
absolute error = 2.8e-30
relative error = 3.4631818318122762946943661863420e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.068345849951663263125178529631
y[1] (numeric) = -8.068345849951663263125178529634
absolute error = 3.0e-30
relative error = 3.7182342648561262791305972364453e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.0516412001588026766590808515158
y[1] (numeric) = -8.051641200158802676659080851519
absolute error = 3.2e-30
relative error = 3.9743450067507806203487213614453e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.0349365503659420901929831734006
y[1] (numeric) = -8.034936550365942090192983173404
absolute error = 3.4e-30
relative error = 4.2315206581751424640251329048444e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.0182319005730815037268854952854
y[1] (numeric) = -8.018231900573081503726885495289
absolute error = 3.6e-30
relative error = 4.4897678748137724820501961630077e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -8.0015272507802209172607878171703
y[1] (numeric) = -8.001527250780220917260787817174
absolute error = 3.7e-30
relative error = 4.6241172266697169613321435777671e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.9848226009873603307946901390551
y[1] (numeric) = -7.984822600987360330794690139059
absolute error = 3.9e-30
relative error = 4.8842663073287901478370334827699e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.9681179511944997443285924609399
y[1] (numeric) = -7.968117951194499744328592460944
absolute error = 4.1e-30
relative error = 5.1455061598145261149981283768921e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.9514133014016391578624947828247
y[1] (numeric) = -7.951413301401639157862494782829
absolute error = 4.3e-30
relative error = 5.4078436587392777795002362747712e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.9347086516087785713963971047096
y[1] (numeric) = -7.934708651608778571396397104714
absolute error = 4.4e-30
relative error = 5.5452571646822733813391896469428e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.9180040018159179849302994265944
y[1] (numeric) = -7.918004001815917984930299426599
absolute error = 4.6e-30
relative error = 5.8095449294355424521605913782941e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=48.2MB, alloc=42.3MB, time=0.38
TOP MAIN SOLVE Loop
x[1] = -4.73
y[1] (closed_form) = -7.9012993520230573984642017484792
y[1] (numeric) = -7.901299352023057398464201748484
absolute error = 4.8e-30
relative error = 6.0749501900228634006598848717229e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.884594702230196811998104070364
y[1] (numeric) = -7.884594702230196811998104070369
absolute error = 5.0e-30
relative error = 6.3414800491719950311443448630052e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.8678900524373362255320063922488
y[1] (numeric) = -7.867890052437336225532006392254
absolute error = 5.2e-30
relative error = 6.6091416699311017428622845145478e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.7
y[1] (closed_form) = -7.8511854026444756390659087141337
y[1] (numeric) = -7.851185402644475639065908714139
absolute error = 5.3e-30
relative error = 6.7505729748973033063449757911889e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.8344807528516150525998110360185
y[1] (numeric) = -7.834480752851615052599811036024
absolute error = 5.5e-30
relative error = 7.0202482761835817061197097076169e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.8177761030587544661337133579033
y[1] (numeric) = -7.817776103058754466133713357909
absolute error = 5.7e-30
relative error = 7.2910760360223655691413441963373e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.8010714532658938796676156797881
y[1] (numeric) = -7.801071453265893879667615679794
absolute error = 5.9e-30
relative error = 7.5630636577876538598418721946454e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.7843668034730332932015180016729
y[1] (numeric) = -7.784366803473033293201518001679
absolute error = 6.1e-30
relative error = 7.8362186084017202118758788538905e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.7676621536801727067354203235578
y[1] (numeric) = -7.767662153680172706735420323564
absolute error = 6.2e-30
relative error = 7.9818095552244844125336820675692e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.7509575038873121202693226454426
y[1] (numeric) = -7.750957503887312120269322645449
absolute error = 6.4e-30
relative error = 8.2570443674736045646900159319682e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.7342528540944515338032249673274
y[1] (numeric) = -7.734252854094451533803224967334
absolute error = 6.6e-30
relative error = 8.5334680989980988859701352558246e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.7175482043015909473371272892122
y[1] (numeric) = -7.717548204301590947337127289219
absolute error = 6.8e-30
relative error = 8.8110884700530022735761425421219e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.7008435545087303608710296110971
y[1] (numeric) = -7.700843554508730360871029611104
absolute error = 6.9e-30
relative error = 8.9600573640535155823995237960240e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.6841389047158697744049319329819
y[1] (numeric) = -7.684138904715869774404931932989
absolute error = 7.1e-30
relative error = 9.2398121481674738036395341325666e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.6674342549230091879388342548667
y[1] (numeric) = -7.667434254923009187938834254874
absolute error = 7.3e-30
relative error = 9.5207859073756104920744900479176e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.6507296051301486014727365767515
y[1] (numeric) = -7.650729605130148601472736576759
absolute error = 7.5e-30
relative error = 9.8029866262309442839523933690125e-29 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.6340249553372880150066388986363
y[1] (numeric) = -7.634024955337288015006638898644
absolute error = 7.7e-30
relative error = 1.0086422359173172315619696704642e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.6173203055444274285405412205212
y[1] (numeric) = -7.617320305544427428540541220529
absolute error = 7.8e-30
relative error = 1.0239821468873516187132026336684e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.600615655751566842074443542406
y[1] (numeric) = -7.600615655751566842074443542414
absolute error = 8.0e-30
relative error = 1.0525463149746572851692767561630e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.5839110059587062556083458642908
y[1] (numeric) = -7.583911005958706255608345864299
absolute error = 8.2e-30
relative error = 1.0812363164015546065436595752324e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.5672063561658456691422481861756
y[1] (numeric) = -7.567206356165845669142248186184
absolute error = 8.4e-30
relative error = 1.1100529845014183620079955193308e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.5505017063729850826761505080605
y[1] (numeric) = -7.550501706372985082676150508069
absolute error = 8.5e-30
relative error = 1.1257530069592054895996067075388e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.5337970565801244962100528299453
y[1] (numeric) = -7.533797056580124496210052829954
absolute error = 8.7e-30
relative error = 1.1547961717924558933876336029022e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.5170924067872639097439551518301
y[1] (numeric) = -7.517092406787263909743955151839
absolute error = 8.9e-30
relative error = 1.1839684173582985211924961733561e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.5003877569944033232778574737149
y[1] (numeric) = -7.500387756994403323277857473724
absolute error = 9.1e-30
relative error = 1.2132706061115168399898080202931e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.4836831072015427368117597955997
y[1] (numeric) = -7.483683107201542736811759795609
absolute error = 9.3e-30
relative error = 1.2427036082073834548531792951182e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.4669784574086821503456621174846
y[1] (numeric) = -7.466978457408682150345662117494
absolute error = 9.4e-30
relative error = 1.2588760036763448570103458294488e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=89.2MB, alloc=42.3MB, time=0.64
TOP MAIN SOLVE Loop
x[1] = -4.46
y[1] (closed_form) = -7.4502738076158215638795644393694
y[1] (numeric) = -7.450273807615821563879564439379
absolute error = 9.6e-30
relative error = 1.2885432465833248378978141454372e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.4335691578229609774134667612542
y[1] (numeric) = -7.433569157822960977413466761264
absolute error = 9.8e-30
relative error = 1.3183438254134822569016306336322e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.416864508030100390947369083139
y[1] (numeric) = -7.416864508030100390947369083149
absolute error = 1.00e-29
relative error = 1.3482786410852169615766354843867e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.4001598582372398044812714050239
y[1] (numeric) = -7.400159858237239804481271405034
absolute error = 1.01e-29
relative error = 1.3648353810570083391634907824342e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.3834552084443792180151737269087
y[1] (numeric) = -7.383455208444379218015173726919
absolute error = 1.03e-29
relative error = 1.3950108328983968797923686418998e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.3667505586515186315490760487935
y[1] (numeric) = -7.366750558651518631549076048804
absolute error = 1.05e-29
relative error = 1.4253231348615150736667289406374e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.3500459088586580450829783706783
y[1] (numeric) = -7.350045908858658045082978370689
absolute error = 1.07e-29
relative error = 1.4557732200153747138768817861874e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.3333412590657974586168806925631
y[1] (numeric) = -7.333341259065797458616880692574
absolute error = 1.09e-29
relative error = 1.4863620299307553547258052597353e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.316636609272936872150783014448
y[1] (numeric) = -7.316636609272936872150783014459
absolute error = 1.10e-29
relative error = 1.5034230326621460366073716223161e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.2999319594800762856846853363328
y[1] (numeric) = -7.299931959480076285684685336344
absolute error = 1.12e-29
relative error = 1.5342608756037910541254674912490e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.2832273096872156992185876582176
y[1] (numeric) = -7.283227309687215699218587658229
absolute error = 1.14e-29
relative error = 1.5652401765405812322743803137091e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.2665226598943551127524899801024
y[1] (numeric) = -7.266522659894355112752489980114
absolute error = 1.16e-29
relative error = 1.5963619110448968825067364135139e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.2498180101014945262863923019873
y[1] (numeric) = -7.249818010101494526286392301999
absolute error = 1.17e-29
relative error = 1.6138336139883606156678124456894e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.2331133603086339398202946238721
y[1] (numeric) = -7.233113360308633939820294623884
absolute error = 1.19e-29
relative error = 1.6452113228724832189806723430267e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.2164087105157733533541969457569
y[1] (numeric) = -7.216408710515773353354196945769
absolute error = 1.21e-29
relative error = 1.6767342989273656491607214065553e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.1997040607229127668880992676417
y[1] (numeric) = -7.199704060722912766888099267654
absolute error = 1.23e-29
relative error = 1.7084035532934076265805850829078e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.1829994109300521804220015895265
y[1] (numeric) = -7.182999410930052180422001589539
absolute error = 1.25e-29
relative error = 1.7402201065169660783140295205456e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.29
y[1] (closed_form) = -7.1662947611371915939559039114114
y[1] (numeric) = -7.166294761137191593955903911424
absolute error = 1.26e-29
relative error = 1.7582307761508479649986782176813e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.1495901113443310074898062332962
y[1] (numeric) = -7.149590111344331007489806233309
absolute error = 1.28e-29
relative error = 1.7903124236017535130916670058099e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.132885461551470421023708555181
y[1] (numeric) = -7.132885461551470421023708555194
absolute error = 1.30e-29
relative error = 1.8225443363802979630492599568806e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.1161808117586098345576108770658
y[1] (numeric) = -7.116180811758609834557610877079
absolute error = 1.32e-29
relative error = 1.8549275726930139831944472410548e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.0994761619657492480915131989506
y[1] (numeric) = -7.099476161965749248091513198964
absolute error = 1.34e-29
relative error = 1.8874632007060251375520824653899e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.0827715121728886616254155208355
y[1] (numeric) = -7.082771512172888661625415520849
absolute error = 1.35e-29
relative error = 1.9060335317605637895496115786353e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.0660668623800280751593178427203
y[1] (numeric) = -7.066066862380028075159317842734
absolute error = 1.37e-29
relative error = 1.9388438104002736959523305731507e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.0493622125871674886932201646051
y[1] (numeric) = -7.049362212587167488693220164619
absolute error = 1.39e-29
relative error = 1.9718095879908827014375269088723e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -7.0326575627943069022271224864899
y[1] (numeric) = -7.032657562794306902227122486504
absolute error = 1.41e-29
relative error = 2.0049319726009245288015127758799e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=130.2MB, alloc=42.3MB, time=0.92
TOP MAIN SOLVE Loop
x[1] = -4.2
y[1] (closed_form) = -7.0159529130014463157610248083748
y[1] (numeric) = -7.015952913001446315761024808389
absolute error = 1.42e-29
relative error = 2.0239588515033514046067550957050e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.9992482632085857292949271302596
y[1] (numeric) = -6.999248263208585729294927130274
absolute error = 1.44e-29
relative error = 2.0573637994373372710110684088245e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.9825436134157251428288294521444
y[1] (numeric) = -6.982543613415725142828829452159
absolute error = 1.46e-29
relative error = 2.0909285796580886200297564267915e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.9658389636228645563627317740292
y[1] (numeric) = -6.965838963622864556362731774044
absolute error = 1.48e-29
relative error = 2.1246543420381721098111240035976e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.949134313830003969896634095914
y[1] (numeric) = -6.949134313830003969896634095929
absolute error = 1.50e-29
relative error = 2.1585422475066213856010558475999e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.9324296640371433834305364177989
y[1] (numeric) = -6.932429664037143383430536417814
absolute error = 1.51e-29
relative error = 2.1781685111546333969143120341017e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.9157250142442827969644387396837
y[1] (numeric) = -6.915725014244282796964438739699
absolute error = 1.53e-29
relative error = 2.2123493875893951360827053556850e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.8990203644514222104983410615685
y[1] (numeric) = -6.899020364451422210498341061584
absolute error = 1.55e-29
relative error = 2.2466957888495068110339964657504e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.8823157146585616240322433834533
y[1] (numeric) = -6.882315714658561624032243383469
absolute error = 1.57e-29
relative error = 2.2812089202128229115918472413987e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.8656110648657010375661457053382
y[1] (numeric) = -6.865611064865701037566145705354
absolute error = 1.58e-29
relative error = 2.3013246527837017101830689172918e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.848906415072840451100048027223
y[1] (numeric) = -6.848906415072840451100048027239
absolute error = 1.60e-29
relative error = 2.3361393820169222670830288978251e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.8322017652799798646339503491078
y[1] (numeric) = -6.832201765279979864633950349124
absolute error = 1.62e-29
relative error = 2.3711243544248773988333554308305e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.8154971154871192781678526709926
y[1] (numeric) = -6.815497115487119278167852671009
absolute error = 1.64e-29
relative error = 2.4062808217956166243667717997819e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.7987924656942586917017549928774
y[1] (numeric) = -6.798792465694258691701754992894
absolute error = 1.66e-29
relative error = 2.4416100482197747158733253499076e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.7820878159013981052356573147623
y[1] (numeric) = -6.782087815901398105235657314779
absolute error = 1.67e-29
relative error = 2.4623685881573070755414868939976e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.7653831661085375187695596366471
y[1] (numeric) = -6.765383166108537518769559636664
absolute error = 1.69e-29
relative error = 2.4980107682091441957744301285541e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.7486785163156769323034619585319
y[1] (numeric) = -6.748678516315676932303461958549
absolute error = 1.71e-29
relative error = 2.5338293946968814997709027850638e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.7319738665228163458373642804167
y[1] (numeric) = -6.731973866522816345837364280434
absolute error = 1.73e-29
relative error = 2.5698257811175604281048269187770e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.7152692167299557593712666023016
y[1] (numeric) = -6.715269216729955759371266602319
absolute error = 1.74e-29
relative error = 2.5911098183004856115314564920840e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.6985645669370951729051689241864
y[1] (numeric) = -6.698564566937095172905168924204
absolute error = 1.76e-29
relative error = 2.6274285817696557168440050696238e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.6818599171442345864390712460712
y[1] (numeric) = -6.681859917144234586439071246089
absolute error = 1.78e-29
relative error = 2.6639289390561716726831163900512e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.665155267351373999972973567956
y[1] (numeric) = -6.665155267351373999972973567974
absolute error = 1.80e-29
relative error = 2.7006122555270811922106443085761e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.6484506175585134135068758898408
y[1] (numeric) = -6.648450617558513413506875889859
absolute error = 1.82e-29
relative error = 2.7374799102717138751528834226714e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.6317459677656528270407782117257
y[1] (numeric) = -6.631745967765652827040778211744
absolute error = 1.83e-29
relative error = 2.7594543109686662106303472639140e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.6150413179727922405746805336105
y[1] (numeric) = -6.615041317972792240574680533629
absolute error = 1.85e-29
relative error = 2.7966567570388818490885060274627e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.5983366681799316541085828554953
y[1] (numeric) = -6.598336668179931654108582855514
absolute error = 1.87e-29
relative error = 2.8340475699246428831844276201939e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.5816320183870710676424851773801
y[1] (numeric) = -6.581632018387071067642485177399
absolute error = 1.89e-29
relative error = 2.8716281838910422981640848555278e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=171.3MB, alloc=42.3MB, time=1.19
TOP MAIN SOLVE Loop
x[1] = -3.93
y[1] (closed_form) = -6.564927368594210481176387499265
y[1] (numeric) = -6.564927368594210481176387499284
absolute error = 1.90e-29
relative error = 2.8941675868180382411858770855690e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.5482227188013498947102898211498
y[1] (numeric) = -6.548222718801349894710289821169
absolute error = 1.92e-29
relative error = 2.9320933060008310086858423921683e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.5315180690084893082441921430346
y[1] (numeric) = -6.531518069008489308244192143054
absolute error = 1.94e-29
relative error = 2.9702130186321291100349123806428e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.5148134192156287217780944649194
y[1] (numeric) = -6.514813419215628721778094464939
absolute error = 1.96e-29
relative error = 3.0085282169692287401088493946992e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.4981087694227681353119967868042
y[1] (numeric) = -6.498108769422768135311996786824
absolute error = 1.98e-29
relative error = 3.0470404086139741266356087070284e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.4814041196299075488458991086891
y[1] (numeric) = -6.481404119629907548845899108709
absolute error = 1.99e-29
relative error = 3.0703223611269440684810619808884e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.87
y[1] (closed_form) = -6.4646994698370469623798014305739
y[1] (numeric) = -6.464699469837046962379801430594
absolute error = 2.01e-29
relative error = 3.1091932569769793932543994100415e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.4479948200441863759137037524587
y[1] (numeric) = -6.447994820044186375913703752479
absolute error = 2.03e-29
relative error = 3.1482655564324553155654225253560e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.4312901702513257894476060743435
y[1] (numeric) = -6.431290170251325789447606074364
absolute error = 2.05e-29
relative error = 3.1875408288721155283819574490618e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.4145855204584652029815083962284
y[1] (numeric) = -6.414585520458465202981508396249
absolute error = 2.06e-29
relative error = 3.2114311882348511503553486443735e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.3978808706656046165154107181132
y[1] (numeric) = -6.397880870665604616515410718134
absolute error = 2.08e-29
relative error = 3.2510764768016176719458339491927e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.381176220872744030049313039998
y[1] (numeric) = -6.381176220872744030049313040019
absolute error = 2.10e-29
relative error = 3.2909293323242311386755364545606e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.3644715710798834435832153618828
y[1] (numeric) = -6.364471571079883443583215361904
absolute error = 2.12e-29
relative error = 3.3309913891881706603487019652061e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.3477669212870228571171176837676
y[1] (numeric) = -6.347766921287022857117117683789
absolute error = 2.14e-29
relative error = 3.3712642989829730216096209785391e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.3310622714941622706510200056525
y[1] (numeric) = -6.331062271494162270651020005674
absolute error = 2.15e-29
relative error = 3.3959545930869343311901219878510e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.3143576217013016841849223275373
y[1] (numeric) = -6.314357621701301684184922327559
absolute error = 2.17e-29
relative error = 3.4366124473883196776186686679812e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.2976529719084410977188246494221
y[1] (numeric) = -6.297652971908441097718824649444
absolute error = 2.19e-29
relative error = 3.4774859932244603839752182482712e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.2809483221155805112527269713069
y[1] (numeric) = -6.280948322115580511252726971329
absolute error = 2.21e-29
relative error = 3.5185769515384529025996218156904e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.2642436723227199247866292931918
y[1] (numeric) = -6.264243672322719924786629293214
absolute error = 2.22e-29
relative error = 3.5439234425196710791649548380007e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.2475390225298593383205316150766
y[1] (numeric) = -6.247539022529859338320531615099
absolute error = 2.24e-29
relative error = 3.5854117788174154580365202870364e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.2308343727369987518544339369614
y[1] (numeric) = -6.230834372736998751854433936984
absolute error = 2.26e-29
relative error = 3.6271225726824399676258957384799e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.2141297229441381653883362588462
y[1] (numeric) = -6.214129722944138165388336258869
absolute error = 2.28e-29
relative error = 3.6690576181273839638259667568665e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.197425073151277578922238580731
y[1] (numeric) = -6.197425073151277578922238580754
absolute error = 2.30e-29
relative error = 3.7112187285073411352077093171313e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.1807204233584169924561409026159
y[1] (numeric) = -6.180720423358416992456140902639
absolute error = 2.31e-29
relative error = 3.7374283930882214174904335627199e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.1640157735655564059900432245007
y[1] (numeric) = -6.164015773565556405990043224524
absolute error = 2.33e-29
relative error = 3.7800033056246033904885120360643e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.1473111237726958195239455463855
y[1] (numeric) = -6.147311123772695819523945546409
absolute error = 2.35e-29
relative error = 3.8228096035552048307311452837203e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=212.3MB, alloc=42.3MB, time=1.47
TOP MAIN SOLVE Loop
x[1] = -3.67
y[1] (closed_form) = -6.1306064739798352330578478682703
y[1] (numeric) = -6.130606473979835233057847868294
absolute error = 2.37e-29
relative error = 3.8658491783137659518470353883118e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.1139018241869746465917501901551
y[1] (numeric) = -6.113901824186974646591750190179
absolute error = 2.39e-29
relative error = 3.9091239420054339643351434716169e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.09719717439411406012565251204
y[1] (numeric) = -6.097197174394114060125652512064
absolute error = 2.40e-29
relative error = 3.9362348491518005322083911566095e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.0804925246012534736595548339248
y[1] (numeric) = -6.080492524601253473659554833949
absolute error = 2.42e-29
relative error = 3.9799407534979228595463277342413e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.0637878748083928871934571558096
y[1] (numeric) = -6.063787874808392887193457155834
absolute error = 2.44e-29
relative error = 4.0238874617247400757401207117498e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.0470832250155323007273594776944
y[1] (numeric) = -6.047083225015532300727359477719
absolute error = 2.46e-29
relative error = 4.0680769694445231329073600592998e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.0303785752226717142612617995793
y[1] (numeric) = -6.030378575222671714261261799604
absolute error = 2.47e-29
relative error = 4.0959285875494064748528105346737e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -6.0136739254298111277951641214641
y[1] (numeric) = -6.013673925429811127795164121489
absolute error = 2.49e-29
relative error = 4.1405637067727012890018475725515e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.9969692756369505413290664433489
y[1] (numeric) = -5.996969275636950541329066443374
absolute error = 2.51e-29
relative error = 4.1854474896128389711962831454594e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.9802646258440899548629687652337
y[1] (numeric) = -5.980264625844089954862968765259
absolute error = 2.53e-29
relative error = 4.2305820198431450203303524366516e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.9635599760512293683968710871185
y[1] (numeric) = -5.963559976051229368396871087144
absolute error = 2.55e-29
relative error = 4.2759694045845452210001868219121e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.9468553262583687819307734090034
y[1] (numeric) = -5.946855326258368781930773409029
absolute error = 2.56e-29
relative error = 4.3047961646154522674338959465542e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.9301506764655081954646757308882
y[1] (numeric) = -5.930150676465508195464675730914
absolute error = 2.58e-29
relative error = 4.3506483068617964333106126199286e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.913446026672647608998578052773
y[1] (numeric) = -5.913446026672647608998578052799
absolute error = 2.60e-29
relative error = 4.3967595007592498882600791050170e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.8967413768797870225324803746578
y[1] (numeric) = -5.896741376879787022532480374684
absolute error = 2.62e-29
relative error = 4.4431319478799183769486360517772e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.8800367270869264360663826965427
y[1] (numeric) = -5.880036727086926436066382696569
absolute error = 2.63e-29
relative error = 4.4727611783182657681030363290569e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.8633320772940658496002850184275
y[1] (numeric) = -5.863332077294065849600285018454
absolute error = 2.65e-29
relative error = 4.5196143849027529259004823673202e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.8466274275012052631341873403123
y[1] (numeric) = -5.846627427501205263134187340339
absolute error = 2.67e-29
relative error = 4.5667353240962942960281995258021e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.8299227777083446766680896621971
y[1] (numeric) = -5.829922777708344676668089662224
absolute error = 2.69e-29
relative error = 4.6141262973253287399102302496622e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.8132181279154840902019919840819
y[1] (numeric) = -5.813218127915484090201991984109
absolute error = 2.71e-29
relative error = 4.6617896324694725771479048282571e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.7965134781226235037358943059668
y[1] (numeric) = -5.796513478122623503735894305994
absolute error = 2.72e-29
relative error = 4.6924759344835585595298880166689e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.46
y[1] (closed_form) = -5.7798088283297629172697966278516
y[1] (numeric) = -5.779808828329762917269796627879
absolute error = 2.74e-29
relative error = 4.7406412242735015802765077019811e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.7631041785369023308036989497364
y[1] (numeric) = -5.763104178536902330803698949764
absolute error = 2.76e-29
relative error = 4.7890857331346906475202092405416e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.7463995287440417443376012716212
y[1] (numeric) = -5.746399528744041744337601271649
absolute error = 2.78e-29
relative error = 4.8378118961171656977130020671169e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.7296948789511811578715035935061
y[1] (numeric) = -5.729694878951181157871503593534
absolute error = 2.79e-29
relative error = 4.8693692403228086394247025441366e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.7129902291583205714054059153909
y[1] (numeric) = -5.712990229158320571405405915419
absolute error = 2.81e-29
relative error = 4.9186150987238599121095716249714e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.6962855793654599849393082372757
y[1] (numeric) = -5.696285579365459984939308237304
absolute error = 2.83e-29
relative error = 4.9681497891389935969509502018814e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=253.2MB, alloc=42.3MB, time=1.72
TOP MAIN SOLVE Loop
x[1] = -3.4
y[1] (closed_form) = -5.6795809295725993984732105591605
y[1] (numeric) = -5.679580929572599398473210559189
absolute error = 2.85e-29
relative error = 5.0179758600859810093502192410086e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.6628762797797388120071128810453
y[1] (numeric) = -5.662876279779738812007112881074
absolute error = 2.87e-29
relative error = 5.0680958901535996159229352951159e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.6461716299868782255410152029302
y[1] (numeric) = -5.646171629986878225541015202959
absolute error = 2.88e-29
relative error = 5.1008013725694929973588027414052e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.629466980194017639074917524815
y[1] (numeric) = -5.629466980194017639074917524844
absolute error = 2.90e-29
relative error = 5.1514646239208467647658037082976e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.6127623304011570526088198466998
y[1] (numeric) = -5.612762330401157052608819846729
absolute error = 2.92e-29
relative error = 5.2024294422445300188835606333264e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.5960576806082964661427221685846
y[1] (numeric) = -5.596057680608296466142722168614
absolute error = 2.94e-29
relative error = 5.2536985281402949640706773011911e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.5793530308154358796766244904695
y[1] (numeric) = -5.579353030815435879676624490499
absolute error = 2.95e-29
relative error = 5.2873513895012490307577160402685e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.5626483810225752932105268123543
y[1] (numeric) = -5.562648381022575293210526812384
absolute error = 2.97e-29
relative error = 5.3391834186974591678434765181713e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.5459437312297147067444291342391
y[1] (numeric) = -5.545943731229714706744429134269
absolute error = 2.99e-29
relative error = 5.3913276890334055105743319387121e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.5292390814368541202783314561239
y[1] (numeric) = -5.529239081436854120278331456154
absolute error = 3.01e-29
relative error = 5.4437870304892065139863405642108e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.5125344316439935338122337780087
y[1] (numeric) = -5.512534431643993533812233778039
absolute error = 3.03e-29
relative error = 5.4965643073477699477220583328943e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.4958297818511329473461360998936
y[1] (numeric) = -5.495829781851132947346136099924
absolute error = 3.04e-29
relative error = 5.5314668042285180731236459313245e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.4791251320582723608800384217784
y[1] (numeric) = -5.479125132058272360880038421809
absolute error = 3.06e-29
relative error = 5.5848332101342047947453659588632e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.4624204822654117744139407436632
y[1] (numeric) = -5.462420482265411774413940743694
absolute error = 3.08e-29
relative error = 5.6385260160760119244503992587416e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.445715832472551187947843065548
y[1] (numeric) = -5.445715832472551187947843065579
absolute error = 3.10e-29
relative error = 5.6925482257352534537241750942020e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.4290111826796906014817453874328
y[1] (numeric) = -5.429011182679690601481745387464
absolute error = 3.12e-29
relative error = 5.7469028797616287770242510886499e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.4123065328868300150156477093177
y[1] (numeric) = -5.412306532886830015015647709349
absolute error = 3.13e-29
relative error = 5.7831166453362583822292650165490e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.3956018830939694285495500312025
y[1] (numeric) = -5.395601883093969428549550031234
absolute error = 3.15e-29
relative error = 5.8380882582717784596318340200100e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.3788972333011088420834523530873
y[1] (numeric) = -5.378897233301108842083452353119
absolute error = 3.17e-29
relative error = 5.8934013097969601524219966197658e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.3621925835082482556173546749721
y[1] (numeric) = -5.362192583508248255617354675004
absolute error = 3.19e-29
relative error = 5.9490589909266601112108518213893e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.345487933715387669151256996857
y[1] (numeric) = -5.345487933715387669151256996889
absolute error = 3.20e-29
relative error = 5.9863571664183633094002615506769e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.3287832839225270826851593187418
y[1] (numeric) = -5.328783283922527082685159318774
absolute error = 3.22e-29
relative error = 6.0426551961965924314322389320312e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.3120786341296664962190616406266
y[1] (numeric) = -5.312078634129666496219061640659
absolute error = 3.24e-29
relative error = 6.0993073016338041265587570516331e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.2953739843368059097529639625114
y[1] (numeric) = -5.295373984336805909752963962544
absolute error = 3.26e-29
relative error = 6.1563168336037427093516885347656e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.2786693345439453232868662843962
y[1] (numeric) = -5.278669334543945323286866284429
absolute error = 3.28e-29
relative error = 6.2136871853962758401369803437407e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.2619646847510847368207686062811
y[1] (numeric) = -5.261964684751084736820768606314
absolute error = 3.29e-29
relative error = 6.2524174849258461231513842862625e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=294.2MB, alloc=42.3MB, time=2.00
TOP MAIN SOLVE Loop
x[1] = -3.14
y[1] (closed_form) = -5.2452600349582241503546709281659
y[1] (numeric) = -5.245260034958224150354670928199
absolute error = 3.31e-29
relative error = 6.3104593060015231064060081951403e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.2285553851653635638885732500507
y[1] (numeric) = -5.228555385165363563888573250084
absolute error = 3.33e-29
relative error = 6.3688720013332747029721632472058e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.2118507353725029774224755719355
y[1] (numeric) = -5.211850735372502977422475571969
absolute error = 3.35e-29
relative error = 6.4276591370197170149009218572974e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.1951460855796423909563778938204
y[1] (numeric) = -5.195146085579642390956377893854
absolute error = 3.36e-29
relative error = 6.4675755881561738648182890065191e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.1784414357867818044902802157052
y[1] (numeric) = -5.178441435786781804490280215739
absolute error = 3.38e-29
relative error = 6.5270603943529251567009303358993e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.16173678599392121802418253759
y[1] (numeric) = -5.161736785993921218024182537624
absolute error = 3.40e-29
relative error = 6.5869302154765162627705143276057e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.1450321362010606315580848594748
y[1] (numeric) = -5.145032136201060631558084859509
absolute error = 3.42e-29
relative error = 6.6471888016723384799184722413361e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.1283274864082000450919871813596
y[1] (numeric) = -5.128327486408200045091987181394
absolute error = 3.44e-29
relative error = 6.7078399519476123076015960046674e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.1116228366153394586258895032445
y[1] (numeric) = -5.111622836615339458625889503279
absolute error = 3.45e-29
relative error = 6.7493242562559978488336282189004e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.0949181868224788721597918251293
y[1] (numeric) = -5.094918186822478872159791825164
absolute error = 3.47e-29
relative error = 6.8107079893349903880717729773275e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.0782135370296182856936941470141
y[1] (numeric) = -5.078213537029618285693694147049
absolute error = 3.49e-29
relative error = 6.8724955627631868255943792144285e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.0615088872367576992275964688989
y[1] (numeric) = -5.061508887236757699227596468934
absolute error = 3.51e-29
relative error = 6.9346909749598862098993128854377e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.0448042374438971127614987907838
y[1] (numeric) = -5.044804237443897112761498790819
absolute error = 3.52e-29
relative error = 6.9774759025803439897645432643651e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.0280995876510365262954011126686
y[1] (numeric) = -5.028099587651036526295401112704
absolute error = 3.54e-29
relative error = 7.0404333452229256196933308602645e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -5.0113949378581759398293034345534
y[1] (numeric) = -5.011394937858175939829303434589
absolute error = 3.56e-29
relative error = 7.1038105041497911271549770401366e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.9946902880653153533632057564382
y[1] (numeric) = -4.994690288065315353363205756474
absolute error = 3.58e-29
relative error = 7.1676115905611172734625205188707e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.977985638272454766897108078323
y[1] (numeric) = -4.977985638272454766897108078359
absolute error = 3.60e-29
relative error = 7.2318408721832576892083696585360e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.9612809884795941804310104002079
y[1] (numeric) = -4.961280988479594180431010400244
absolute error = 3.61e-29
relative error = 7.2763465894849466487996445110921e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.9445763386867335939649127220927
y[1] (numeric) = -4.944576338686733593964912722129
absolute error = 3.63e-29
relative error = 7.3413772007090063557847802124856e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.9278716888938730074988150439775
y[1] (numeric) = -4.927871688893873007498815044014
absolute error = 3.65e-29
relative error = 7.4068486974328901963765947999901e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.9111670391010124210327173658623
y[1] (numeric) = -4.911167039101012421032717365899
absolute error = 3.67e-29
relative error = 7.4727655784882290290812788744845e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.8944623893081518345666196877472
y[1] (numeric) = -4.894462389308151834566619687784
absolute error = 3.68e-29
relative error = 7.5187011509964426548098848145020e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.877757739515291248100522009632
y[1] (numeric) = -4.877757739515291248100522009669
absolute error = 3.70e-29
relative error = 7.5854525738862822756099204580495e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.8610530897224306616344243315168
y[1] (numeric) = -4.861053089722430661634424331554
absolute error = 3.72e-29
relative error = 7.6526627694420314470683755905561e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.8443484399295700751683266534016
y[1] (numeric) = -4.844348439929570075168326653439
absolute error = 3.74e-29
relative error = 7.7203364835878202679851648963903e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.8276437901367094887022289752864
y[1] (numeric) = -4.827643790136709488702228975324
absolute error = 3.76e-29
relative error = 7.7884785279353100496003402873860e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.8109391403438489022361312971713
y[1] (numeric) = -4.810939140343848902236131297209
absolute error = 3.77e-29
relative error = 7.8363078185407047487635368215458e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=335.2MB, alloc=42.3MB, time=2.26
TOP MAIN SOLVE Loop
x[1] = -2.87
y[1] (closed_form) = -4.7942344905509883157700336190561
y[1] (numeric) = -4.794234490550988315770033619094
absolute error = 3.79e-29
relative error = 7.9053288016465494573613210024619e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.7775298407581277293039359409409
y[1] (numeric) = -4.777529840758127729303935940979
absolute error = 3.81e-29
relative error = 7.9748324489699175555297190587689e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.7608251909652671428378382628257
y[1] (numeric) = -4.760825190965267142837838262864
absolute error = 3.83e-29
relative error = 8.0448238411867829736852637681027e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.7441205411724065563717405847106
y[1] (numeric) = -4.744120541172406556371740584749
absolute error = 3.84e-29
relative error = 8.0942294081149701084848606882392e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.7274158913795459699056429065954
y[1] (numeric) = -4.727415891379545969905642906634
absolute error = 3.86e-29
relative error = 8.1651373365282269873798620443862e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.7107112415866853834395452284802
y[1] (numeric) = -4.710711241586685383439545228519
absolute error = 3.88e-29
relative error = 8.2365481580507977448485868144066e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.694006591793824796973447550365
y[1] (numeric) = -4.694006591793824796973447550404
absolute error = 3.90e-29
relative error = 8.3084672416482622443633523301210e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.6773019420009642105073498722498
y[1] (numeric) = -4.677301942000964210507349872289
absolute error = 3.92e-29
relative error = 8.3809000329857086331603661709478e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.6605972922081036240412521941347
y[1] (numeric) = -4.660597292208103624041252194174
absolute error = 3.93e-29
relative error = 8.4323955785032859519509060552545e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.6438926424152430375751545160195
y[1] (numeric) = -4.643892642415243037575154516059
absolute error = 3.95e-29
relative error = 8.5057952544433579396154795414294e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.6271879926223824511090568379043
y[1] (numeric) = -4.627187992622382451109056837944
absolute error = 3.97e-29
relative error = 8.5797248919425640210538044607175e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.6104833428295218646429591597891
y[1] (numeric) = -4.610483342829521864642959159829
absolute error = 3.99e-29
relative error = 8.6541902514526339146764650678265e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.593778693036661278176861481674
y[1] (numeric) = -4.593778693036661278176861481714
absolute error = 4.00e-29
relative error = 8.7074286056994375409458349828027e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.5770740432438006917107638035588
y[1] (numeric) = -4.577074043243800691710763803599
absolute error = 4.02e-29
relative error = 8.7829035799276717167113326400442e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.5603693934509401052446661254436
y[1] (numeric) = -4.560369393450940105244666125484
absolute error = 4.04e-29
relative error = 8.8589314843700321501747460310384e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.5436647436580795187785684473284
y[1] (numeric) = -4.543664743658079518778568447369
absolute error = 4.06e-29
relative error = 8.9355184175215275868253904028487e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.5269600938652189323124707692132
y[1] (numeric) = -4.526960093865218932312470769254
absolute error = 4.08e-29
relative error = 9.0126705678918532481007627774030e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.5102554440723583458463730910981
y[1] (numeric) = -4.510255444072358345846373091139
absolute error = 4.09e-29
relative error = 9.0682225224633725686840999045439e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.4935507942794977593802754129829
y[1] (numeric) = -4.493550794279497759380275413024
absolute error = 4.11e-29
relative error = 9.1464416185797298147342286146030e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.4768461444866371729141777348677
y[1] (numeric) = -4.476846144486637172914177734909
absolute error = 4.13e-29
relative error = 9.2252444392939703238145821657820e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.4601414946937765864480800567525
y[1] (numeric) = -4.460141494693776586448080056794
absolute error = 4.15e-29
relative error = 9.3046375433094410988805563428125e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.4434368449009159999819823786373
y[1] (numeric) = -4.443436844900915999981982378679
absolute error = 4.17e-29
relative error = 9.3846275879566071429319889723019e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.4267321951080554135158847005222
y[1] (numeric) = -4.426732195108055413515884700564
absolute error = 4.18e-29
relative error = 9.4426313040108523144502238799356e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.410027545315194827049787022407
y[1] (numeric) = -4.410027545315194827049787022449
absolute error = 4.20e-29
relative error = 9.5237500374837598104095070124406e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.63
y[1] (closed_form) = -4.3933228955223342405836893442918
y[1] (numeric) = -4.393322895522334240583689344334
absolute error = 4.22e-29
relative error = 9.6054856434545601390376820318847e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.3766182457294736541175916661766
y[1] (numeric) = -4.376618245729473654117591666219
absolute error = 4.24e-29
relative error = 9.6878451853488016915485148759047e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.3599135959366130676514939880615
y[1] (numeric) = -4.359913595936613067651493988104
absolute error = 4.25e-29
relative error = 9.7478996004896720555368243641290e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=376.2MB, alloc=42.3MB, time=2.55
TOP MAIN SOLVE Loop
x[1] = -2.6
y[1] (closed_form) = -4.3432089461437524811853963099463
y[1] (numeric) = -4.343208946143752481185396309989
absolute error = 4.27e-29
relative error = 9.8314404233101582042842757005348e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.3265042963508918947192986318311
y[1] (numeric) = -4.326504296350891894719298631874
absolute error = 4.29e-29
relative error = 9.9156263490095670259950278194610e-28 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.3097996465580313082532009537159
y[1] (numeric) = -4.309799646558031308253200953759
absolute error = 4.31e-29
relative error = 1.0000464878784165063377956311402e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.2930949967651707217871032756007
y[1] (numeric) = -4.293094996765170721787103275644
absolute error = 4.33e-29
relative error = 1.0085963630580355303386432884993e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.2763903469723101353210055974856
y[1] (numeric) = -4.276390346972310135321005597529
absolute error = 4.34e-29
relative error = 1.0148746133693631547967630910132e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.2596856971794495488549079193704
y[1] (numeric) = -4.259685697179449548854907919414
absolute error = 4.36e-29
relative error = 1.0235496959052574129013780533706e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.2429810473865889623888102412552
y[1] (numeric) = -4.242981047386588962388810241299
absolute error = 4.38e-29
relative error = 1.0322930861776547754005175429908e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.22627639759372837592271256314
y[1] (numeric) = -4.226276397593728375922712563184
absolute error = 4.40e-29
relative error = 1.0411055941597153581565672262047e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.2095717478008677894566148850249
y[1] (numeric) = -4.209571747800867789456614885069
absolute error = 4.41e-29
relative error = 1.0476125041232135791450457713685e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.1928670980080072029905172069097
y[1] (numeric) = -4.192867098008007202990517206954
absolute error = 4.43e-29
relative error = 1.0565562648300139227347871979880e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.1761624482151466165244195287945
y[1] (numeric) = -4.176162448215146616524419528839
absolute error = 4.45e-29
relative error = 1.0655715756224686690732465560205e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.1594577984222860300583218506793
y[1] (numeric) = -4.159457798422286030058321850724
absolute error = 4.47e-29
relative error = 1.0746592985498025700007698446396e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.1427531486294254435922241725641
y[1] (numeric) = -4.142753148629425443592224172609
absolute error = 4.49e-29
relative error = 1.0838203095652601314196441275218e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.126048498836564857126126494449
y[1] (numeric) = -4.126048498836564857126126494494
absolute error = 4.50e-29
relative error = 1.0906318724243981737773755861557e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.1093438490437042706600288163338
y[1] (numeric) = -4.109343849043704270660028816379
absolute error = 4.52e-29
relative error = 1.0999322923663009007515927727260e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.0926391992508436841939311382186
y[1] (numeric) = -4.092639199250843684193931138264
absolute error = 4.54e-29
relative error = 1.1093086341036477316194770383703e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.0759345494579830977278334601034
y[1] (numeric) = -4.075934549457983097727833460149
absolute error = 4.56e-29
relative error = 1.1187618311011367496256226504544e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.0592298996651225112617357819883
y[1] (numeric) = -4.059229899665122511261735782034
absolute error = 4.57e-29
relative error = 1.1258293107214782026320656496540e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.0425252498722619247956381038731
y[1] (numeric) = -4.042525249872261924795638103919
absolute error = 4.59e-29
relative error = 1.1354289005727391566176529139507e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.0258206000794013383295404257579
y[1] (numeric) = -4.025820600079401338329540425804
absolute error = 4.61e-29
relative error = 1.1451081550700686662379753422664e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -4.0091159502865407518634427476427
y[1] (numeric) = -4.009115950286540751863442747689
absolute error = 4.63e-29
relative error = 1.1548680700215425884384671241514e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.9924113004936801653973450695275
y[1] (numeric) = -3.992411300493680165397345069574
absolute error = 4.65e-29
relative error = 1.1647096579014807275611387535836e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.9757066507008195789312473914124
y[1] (numeric) = -3.975706650700819578931247391459
absolute error = 4.66e-29
relative error = 1.1721186720802341605800512111830e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.9590020009079589924651497132972
y[1] (numeric) = -3.959002000907958992465149713344
absolute error = 4.68e-29
relative error = 1.1821160986851451598309377239311e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.942297351115098405999052035182
y[1] (numeric) = -3.942297351115098405999052035229
absolute error = 4.70e-29
relative error = 1.1921982492443350658551368342450e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.9255927013222378195329543570668
y[1] (numeric) = -3.925592701322237819532954357114
absolute error = 4.72e-29
relative error = 1.2023662053401989285263504050721e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=417.3MB, alloc=42.3MB, time=2.81
TOP MAIN SOLVE Loop
x[1] = -2.34
y[1] (closed_form) = -3.9088880515293772330668566789517
y[1] (numeric) = -3.908888051529377233066856678999
absolute error = 4.73e-29
relative error = 1.2100627947503785663873178262693e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.8921834017365166466007590008365
y[1] (numeric) = -3.892183401736516646600759000884
absolute error = 4.75e-29
relative error = 1.2203947013084646231609975264255e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.8754787519436560601346613227213
y[1] (numeric) = -3.875478751943656060134661322769
absolute error = 4.77e-29
relative error = 1.2308156760265341804241054998590e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.8587741021507954736685636446061
y[1] (numeric) = -3.858774102150795473668563644654
absolute error = 4.79e-29
relative error = 1.2413268756339376732479330228460e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.8420694523579348872024659664909
y[1] (numeric) = -3.842069452357934887202465966539
absolute error = 4.81e-29
relative error = 1.2519294769770577181832720895111e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.8253648025650743007363682883758
y[1] (numeric) = -3.825364802565074300736368288424
absolute error = 4.82e-29
relative error = 1.2600105476915507052973476276971e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.8086601527722137142702706102606
y[1] (numeric) = -3.808660152772213714270270610309
absolute error = 4.84e-29
relative error = 1.2707881002396876498902309607577e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.7919555029793531278041729321454
y[1] (numeric) = -3.791955502979353127804172932194
absolute error = 4.86e-29
relative error = 1.2816606091979403384883379355194e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.7752508531864925413380752540302
y[1] (numeric) = -3.775250853186492541338075254079
absolute error = 4.88e-29
relative error = 1.2926293350496288915873131135975e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.758546203393631954871977575915
y[1] (numeric) = -3.758546203393631954871977575964
absolute error = 4.90e-29
relative error = 1.3036955606866657873805014043697e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.7418415536007713684058798977999
y[1] (numeric) = -3.741841553600771368405879897849
absolute error = 4.91e-29
relative error = 1.3121881110318823146944323309743e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.7251369038079107819397822196847
y[1] (numeric) = -3.725136903807910781939782219734
absolute error = 4.93e-29
relative error = 1.3234412928449565522575466118761e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.22
y[1] (closed_form) = -3.7084322540150501954736845415695
y[1] (numeric) = -3.708432254015050195473684541619
absolute error = 4.95e-29
relative error = 1.3347958546743647919608691295428e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.6917276042221896090075868634543
y[1] (numeric) = -3.691727604222189609007586863504
absolute error = 4.97e-29
relative error = 1.3462531727194237849646742039305e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.6750229544293290225414891853392
y[1] (numeric) = -3.675022954429329022541489185389
absolute error = 4.98e-29
relative error = 1.3550935767619749673096955691987e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.658318304636468436075391507224
y[1] (numeric) = -3.658318304636468436075391507274
absolute error = 5.00e-29
relative error = 1.3667482115110418514612469293783e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.6416136548436078496092938291088
y[1] (numeric) = -3.641613654843607849609293829159
absolute error = 5.02e-29
relative error = 1.3785097695146873308802437148807e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.6249090050507472631431961509936
y[1] (numeric) = -3.624909005050747263143196151044
absolute error = 5.04e-29
relative error = 1.3903797289745876073445768762863e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.6082043552578866766770984728784
y[1] (numeric) = -3.608204355257886676677098472929
absolute error = 5.06e-29
relative error = 1.4023595954665239974798760854827e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.5914997054650260902110007947633
y[1] (numeric) = -3.591499705465026090211000794814
absolute error = 5.07e-29
relative error = 1.4116665504065628827283407470666e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.5747950556721655037449031166481
y[1] (numeric) = -3.574795055672165503744903116699
absolute error = 5.09e-29
relative error = 1.4238578493957695908807164155582e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.5580904058793049172788054385329
y[1] (numeric) = -3.558090405879304917278805438584
absolute error = 5.11e-29
relative error = 1.4361636206759547657763068790591e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.5413857560864443308127077604177
y[1] (numeric) = -3.541385756086444330812707760469
absolute error = 5.13e-29
relative error = 1.4485854841380284800577047997629e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.5246811062935837443466100823026
y[1] (numeric) = -3.524681106293583744346610082354
absolute error = 5.14e-29
relative error = 1.4582879542839046166027177426767e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.5079764565007231578805124041874
y[1] (numeric) = -3.507976456500723157880512404239
absolute error = 5.16e-29
relative error = 1.4709334751770835560240642667378e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.4912718067078625714144147260722
y[1] (numeric) = -3.491271806707862571414414726124
absolute error = 5.18e-29
relative error = 1.4837000058395752125690600398328e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.474567156915001984948317047957
y[1] (numeric) = -3.474567156915001984948317048009
absolute error = 5.20e-29
relative error = 1.4965892916045908273500653876692e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=458.3MB, alloc=42.3MB, time=3.09
TOP MAIN SOLVE Loop
x[1] = -2.07
y[1] (closed_form) = -3.4578625071221413984822193698418
y[1] (numeric) = -3.457862507122141398482219369894
absolute error = 5.22e-29
relative error = 1.5096031115315872693270224779968e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.4411578573292808120161216917267
y[1] (numeric) = -3.441157857329280812016121691779
absolute error = 5.23e-29
relative error = 1.5198372806003902965127848500019e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.4244532075364202255500240136115
y[1] (numeric) = -3.424453207536420225550024013664
absolute error = 5.25e-29
relative error = 1.5330914694486052377732377141977e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.4077485577435596390839263354963
y[1] (numeric) = -3.407748557743559639083926335549
absolute error = 5.27e-29
relative error = 1.5464756013247438549284009005915e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.3910439079506990526178286573811
y[1] (numeric) = -3.391043907950699052617828657434
absolute error = 5.29e-29
relative error = 1.5599915965691202909717922957183e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.374339258157838466151730979266
y[1] (numeric) = -3.374339258157838466151730979319
absolute error = 5.30e-29
relative error = 1.5706778703968973039515537731974e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.3576346083649778796856333011508
y[1] (numeric) = -3.357634608364977879685633301204
absolute error = 5.32e-29
relative error = 1.5844487624550095923387756940100e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.3409299585721172932195356230356
y[1] (numeric) = -3.340929958572117293219535623089
absolute error = 5.34e-29
relative error = 1.5983573634337030036098698340307e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.3242253087792567067534379449204
y[1] (numeric) = -3.324225308779256706753437944974
absolute error = 5.36e-29
relative error = 1.6124057493468556451449950709361e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.3075206589863961202873402668052
y[1] (numeric) = -3.307520658986396120287340266859
absolute error = 5.38e-29
relative error = 1.6265960381480199295239094516486e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.2908160091935355338212425886901
y[1] (numeric) = -3.290816009193535533821242588744
absolute error = 5.39e-29
relative error = 1.6378916308119278293232187694492e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.2741113594006749473551449105749
y[1] (numeric) = -3.274111359400674947355144910629
absolute error = 5.41e-29
relative error = 1.6523567484858849746865007647532e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.2574067096078143608890472324597
y[1] (numeric) = -3.257406709607814360889047232514
absolute error = 5.43e-29
relative error = 1.6669702263411134753868420625731e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.2407020598149537744229495543445
y[1] (numeric) = -3.240702059814953774422949554399
absolute error = 5.45e-29
relative error = 1.6817343586072206204243002809892e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.2239974100220931879568518762294
y[1] (numeric) = -3.223997410022093187956851876284
absolute error = 5.46e-29
relative error = 1.6935497475981483766489859101915e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.2072927602292326014907541981142
y[1] (numeric) = -3.207292760229232601490754198169
absolute error = 5.48e-29
relative error = 1.7086061079152411945579913175890e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.190588110436372015024656519999
y[1] (numeric) = -3.190588110436372015024656520054
absolute error = 5.50e-29
relative error = 1.7238201264555496440681381428651e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.1738834606435114285585588418838
y[1] (numeric) = -3.173883460643511428558558841939
absolute error = 5.52e-29
relative error = 1.7391942925594402877836549347230e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.1571788108506508420924611637686
y[1] (numeric) = -3.157178810850650842092461163824
absolute error = 5.54e-29
relative error = 1.7547311482517318906919285180291e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.1404741610577902556263634856535
y[1] (numeric) = -3.140474161057790255626363485709
absolute error = 5.55e-29
relative error = 1.7672490571075487429346516811839e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.1237695112649296691602658075383
y[1] (numeric) = -3.123769511264929669160265807594
absolute error = 5.57e-29
relative error = 1.7831021078583039376128051784637e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.1070648614720690826941681294231
y[1] (numeric) = -3.107064861472069082694168129479
absolute error = 5.59e-29
relative error = 1.7991256215203575752444872079723e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.0903602116792084962280704513079
y[1] (numeric) = -3.090360211679208496228070451364
absolute error = 5.61e-29
relative error = 1.8153223623571361170667820161783e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.0736555618863479097619727731928
y[1] (numeric) = -3.073655561886347909761972773249
absolute error = 5.62e-29
relative error = 1.8284416997430000977624711910219e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.0569509120934873232958750950776
y[1] (numeric) = -3.056950912093487323295875095134
absolute error = 5.64e-29
relative error = 1.8449756512895939379790970025037e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -3.0402462623006267368297774169624
y[1] (numeric) = -3.040246262300626736829777417019
absolute error = 5.66e-29
relative error = 1.8616912946114250731431582624633e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=499.2MB, alloc=42.3MB, time=3.36
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (closed_form) = -3.0235416125077661503636797388472
y[1] (numeric) = -3.023541612507766150363679738904
absolute error = 5.68e-29
relative error = 1.8785916411743814142206345639693e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.8
y[1] (closed_form) = -3.006836962714905563897582060732
y[1] (numeric) = -3.006836962714905563897582060789
absolute error = 5.70e-29
relative error = 1.8956797693658150479767494910477e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.9901323129220449774314843826169
y[1] (numeric) = -2.990132312922044977431484382674
absolute error = 5.71e-29
relative error = 1.9096144927513326534455582935399e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.9734276631291843909653867045017
y[1] (numeric) = -2.973427663129184390965386704559
absolute error = 5.73e-29
relative error = 1.9270689080661360540934549823246e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.9567230133363238044992890263865
y[1] (numeric) = -2.956723013336323804499289026444
absolute error = 5.75e-29
relative error = 1.9447205484127451428842657579883e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.9400183635434632180331913482713
y[1] (numeric) = -2.940018363543463218033191348329
absolute error = 5.77e-29
relative error = 1.9625727755814747895022448379208e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.9233137137506026315670936701562
y[1] (numeric) = -2.923313713750602631567093670214
absolute error = 5.78e-29
relative error = 1.9772082526798937101904863864521e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.906609063957742045100995992041
y[1] (numeric) = -2.906609063957742045100995992099
absolute error = 5.80e-29
relative error = 1.9954523888061211031334205168923e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.8899044141648814586348983139258
y[1] (numeric) = -2.889904414164881458634898313984
absolute error = 5.82e-29
relative error = 2.0139074398008597954167353887248e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.8731997643720208721688006358106
y[1] (numeric) = -2.873199764372020872168800635869
absolute error = 5.84e-29
relative error = 2.0325770844118163794707864799973e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.8564951145791602857027029576954
y[1] (numeric) = -2.856495114579160285702702957754
absolute error = 5.86e-29
relative error = 2.0514650874392753797126042506998e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.8397904647862996992366052795803
y[1] (numeric) = -2.839790464786299699236605279639
absolute error = 5.87e-29
relative error = 2.0670539156985760368340903119102e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.8230858149934391127705076014651
y[1] (numeric) = -2.823085814993439112770507601524
absolute error = 5.89e-29
relative error = 2.0863694503079384551696769546442e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.8063811652005785263044099233499
y[1] (numeric) = -2.806381165200578526304409923409
absolute error = 5.91e-29
relative error = 2.1059149317578885213425920097917e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.7896765154077179398383122452347
y[1] (numeric) = -2.789676515407717939838312245294
absolute error = 5.93e-29
relative error = 2.1256944908299936781283563470368e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.7729718656148573533722145671195
y[1] (numeric) = -2.772971865614857353372214567179
absolute error = 5.95e-29
relative error = 2.1457123578427266078874431461764e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.7562672158219967669061168890044
y[1] (numeric) = -2.756267215821996766906116889064
absolute error = 5.96e-29
relative error = 2.1623447704153603226682156873960e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.7395625660291361804400192108892
y[1] (numeric) = -2.739562566029136180440019210949
absolute error = 5.98e-29
relative error = 2.1828302350720617433057051264054e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.722857916236275593973921532774
y[1] (numeric) = -2.722857916236275593973921532834
absolute error = 6.00e-29
relative error = 2.2035670551233239175706484235621e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.7061532664434150075078238546588
y[1] (numeric) = -2.706153266443415007507823854719
absolute error = 6.02e-29
relative error = 2.2245598852986757483079984280911e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.6894486166505544210417261765437
y[1] (numeric) = -2.689448616650554421041726176604
absolute error = 6.03e-29
relative error = 2.2420952617082441463157501335765e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.6727439668576938345756284984285
y[1] (numeric) = -2.672743966857693834575628498489
absolute error = 6.05e-29
relative error = 2.2635913035519436263669738988497e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.6560393170648332481095308203133
y[1] (numeric) = -2.656039317064833248109530820374
absolute error = 6.07e-29
relative error = 2.2853577358590858671735589693465e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.6393346672719726616434331421981
y[1] (numeric) = -2.639334667271972661643433142259
absolute error = 6.09e-29
relative error = 2.3073996926258121869776957495964e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.6226300174791120751773354640829
y[1] (numeric) = -2.622630017479112075177335464144
absolute error = 6.11e-29
relative error = 2.3297224386507133643589552913781e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.6059253676862514887112377859678
y[1] (numeric) = -2.605925367686251488711237786029
absolute error = 6.12e-29
relative error = 2.3484939652872040675339487621886e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.5892207178933909022451401078526
y[1] (numeric) = -2.589220717893390902245140107914
absolute error = 6.14e-29
relative error = 2.3713698710844355303043616723327e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=540.3MB, alloc=42.3MB, time=3.62
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (closed_form) = -2.5725160681005303157790424297374
y[1] (numeric) = -2.572516068100530315779042429799
absolute error = 6.16e-29
relative error = 2.3945428665673453237601046202708e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.5558114183076697293129447516222
y[1] (numeric) = -2.555811418307669729312944751684
absolute error = 6.18e-29
relative error = 2.4180187770238879249734389792931e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.5391067685148091428468470735071
y[1] (numeric) = -2.539106768514809142846847073569
absolute error = 6.19e-29
relative error = 2.4378651881664255845518170393875e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.5224021187219485563807493953919
y[1] (numeric) = -2.522402118721948556380749395454
absolute error = 6.21e-29
relative error = 2.4619389406263600100248757768016e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.5056974689290879699146517172767
y[1] (numeric) = -2.505697468929087969914651717339
absolute error = 6.23e-29
relative error = 2.4863336764524268945042419640478e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.4889928191362273834485540391615
y[1] (numeric) = -2.488992819136227383448554039224
absolute error = 6.25e-29
relative error = 2.5110558583969644754195727981028e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.4722881693433667969824563610463
y[1] (numeric) = -2.472288169343366796982456361109
absolute error = 6.27e-29
relative error = 2.5361121238812931047256513461314e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.4555835195505062105163586829312
y[1] (numeric) = -2.455583519550506210516358682994
absolute error = 6.28e-29
relative error = 2.5574369391229470464648736420579e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.438878869757645624050261004816
y[1] (numeric) = -2.438878869757645624050261004879
absolute error = 6.30e-29
relative error = 2.5831541197558690992617566965250e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.4221742199647850375841633267008
y[1] (numeric) = -2.422174219964785037584163326764
absolute error = 6.32e-29
relative error = 2.6092260201216590424420450345020e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.4054695701719244511180656485856
y[1] (numeric) = -2.405469570171924451118065648649
absolute error = 6.34e-29
relative error = 2.6356600302147516237220595993953e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.3887649203790638646519679704705
y[1] (numeric) = -2.388764920379063864651967970534
absolute error = 6.35e-29
relative error = 2.6582774829899725185099063529229e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.3720602705862032781858702923553
y[1] (numeric) = -2.372060270586203278185870292419
absolute error = 6.37e-29
relative error = 2.6854292359214770620337793012543e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.3553556207933426917197726142401
y[1] (numeric) = -2.355355620793342691719772614304
absolute error = 6.39e-29
relative error = 2.7129661201002369891537355538174e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.3386509710004821052536749361249
y[1] (numeric) = -2.338650971000482105253674936189
absolute error = 6.41e-29
relative error = 2.7408963883386934866611197528457e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.3219463212076215187875772580097
y[1] (numeric) = -2.321946321207621518787577258074
absolute error = 6.43e-29
relative error = 2.7692285309402932431254447317161e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.38
y[1] (closed_form) = -2.3052416714147609323214795798946
y[1] (numeric) = -2.305241671414760932321479579959
absolute error = 6.44e-29
relative error = 2.7936333443285695443867887236492e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.2885370216219003458553819017794
y[1] (numeric) = -2.288537021621900345855381901844
absolute error = 6.46e-29
relative error = 2.8227640361359581736296123808301e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.2718323718290397593892842236642
y[1] (numeric) = -2.271832371829039759389284223729
absolute error = 6.48e-29
relative error = 2.8523231204699260474201246212049e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.255127722036179172923186545549
y[1] (numeric) = -2.255127722036179172923186545614
absolute error = 6.50e-29
relative error = 2.8823201171643971489704963021778e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.2384230722433185864570888674339
y[1] (numeric) = -2.238423072243318586457088867499
absolute error = 6.51e-29
relative error = 2.9082973995062347122534106488736e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.2217184224504579999909911893187
y[1] (numeric) = -2.221718422450457999990991189384
absolute error = 6.53e-29
relative error = 2.9391663380986400308559178891669e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.2050137726575974135248935112035
y[1] (numeric) = -2.205013772657597413524893511269
absolute error = 6.55e-29
relative error = 2.9705029878818393694372509967374e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.1883091228647368270587958330883
y[1] (numeric) = -2.188309122864736827058795833154
absolute error = 6.57e-29
relative error = 3.0023180597991333544091388082403e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.1716044730718762405926981549731
y[1] (numeric) = -2.171604473071876240592698155039
absolute error = 6.59e-29
relative error = 3.0346225943613087853036710476124e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.154899823279015654126600476858
y[1] (numeric) = -2.154899823279015654126600476924
absolute error = 6.60e-29
relative error = 3.0627873874698602978326919561602e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=581.3MB, alloc=42.3MB, time=3.91
TOP MAIN SOLVE Loop
x[1] = -1.28
y[1] (closed_form) = -2.1381951734861550676605027987428
y[1] (numeric) = -2.138195173486155067660502798809
absolute error = 6.62e-29
relative error = 3.0960690970069972740804477707407e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.1214905236932944811944051206276
y[1] (numeric) = -2.121490523693294481194405120694
absolute error = 6.64e-29
relative error = 3.1298749279541679034974595824012e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.1047858739004338947283074425124
y[1] (numeric) = -2.104785873900433894728307442579
absolute error = 6.66e-29
relative error = 3.1642173593925634635401382482150e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.0880812241075733082622097643972
y[1] (numeric) = -2.088081224107573308262209764464
absolute error = 6.68e-29
relative error = 3.1991092697339733525434997726818e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.0713765743147127217961120862821
y[1] (numeric) = -2.071376574314712721796112086349
absolute error = 6.69e-29
relative error = 3.2297362454305524628941733688732e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.0546719245218521353300144081669
y[1] (numeric) = -2.054671924521852135330014408234
absolute error = 6.71e-29
relative error = 3.2657281777778225858598174800847e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.0379672747289915488639167300517
y[1] (numeric) = -2.037967274728991548863916730119
absolute error = 6.73e-29
relative error = 3.3023101418029168092019475603325e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.0212626249361309623978190519365
y[1] (numeric) = -2.021262624936130962397819052004
absolute error = 6.75e-29
relative error = 3.3394967663904092841695673939727e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -2.0045579751432703759317213738214
y[1] (numeric) = -2.004557975143270375931721373889
absolute error = 6.76e-29
relative error = 3.3723145370823446642954806735479e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.9878533253504097894656236957062
y[1] (numeric) = -1.987853325350409789465623695774
absolute error = 6.78e-29
relative error = 3.4107144191862607762801490179487e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.971148675557549202999526017591
y[1] (numeric) = -1.971148675557549202999526017659
absolute error = 6.80e-29
relative error = 3.4497651467495652969425236054749e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.9544440257646886165334283394758
y[1] (numeric) = -1.954444025764688616533428339544
absolute error = 6.82e-29
relative error = 3.4894834081173707495820328013348e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.9377393759718280300673306613606
y[1] (numeric) = -1.937739375971828030067330661429
absolute error = 6.84e-29
relative error = 3.5298864670949659514049818109165e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.9210347261789674436012329832455
y[1] (numeric) = -1.921034726178967443601232983314
absolute error = 6.85e-29
relative error = 3.5657866599970251016862427497510e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.9043300763861068571351353051303
y[1] (numeric) = -1.904330076386106857135135305199
absolute error = 6.87e-29
relative error = 3.6075678713415926259280523555395e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.8876254265932462706690376270151
y[1] (numeric) = -1.887625426593246270669037627084
absolute error = 6.89e-29
relative error = 3.6500885731524356815723718658553e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.8709207768003856842029399488999
y[1] (numeric) = -1.870920776800385684202939948969
absolute error = 6.91e-29
relative error = 3.6933685732099009346389113674266e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.8542161270075250977368422707848
y[1] (numeric) = -1.854216127007525097736842270854
absolute error = 6.92e-29
relative error = 3.7320352785238805496441270207823e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.8375114772146645112707445926696
y[1] (numeric) = -1.837511477214664511270744592739
absolute error = 6.94e-29
relative error = 3.7768471577221310333852559237907e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.8208068274218039248046469145544
y[1] (numeric) = -1.820806827421803924804646914624
absolute error = 6.96e-29
relative error = 3.8224812732359457461858550819001e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.8041021776289433383385492364392
y[1] (numeric) = -1.804102177628943338338549236509
absolute error = 6.98e-29
relative error = 3.8689604649629792499642431133079e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.787397527836082751872451558324
y[1] (numeric) = -1.787397527836082751872451558394
absolute error = 7.00e-29
relative error = 3.9163084266288358098880215752093e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.7706928780432221654063538802089
y[1] (numeric) = -1.770692878043222165406353880279
absolute error = 7.01e-29
relative error = 3.9589022393012006414052673085136e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.7539882282503615789402562020937
y[1] (numeric) = -1.753988228250361578940256202164
absolute error = 7.03e-29
relative error = 4.0080086552305803871508417810723e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.7372835784575009924741585239785
y[1] (numeric) = -1.737283578457500992474158524049
absolute error = 7.05e-29
relative error = 4.0580594253124482049299849934878e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.7205789286646404060080608458633
y[1] (numeric) = -1.720578928664640406008060845934
absolute error = 7.07e-29
relative error = 4.1090820550075561745106649673094e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = -1.7038742788717798195419631677482
y[1] (numeric) = -1.703874278871779819541963167819
absolute error = 7.08e-29
relative error = 4.1552361508080404147601815469404e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=622.4MB, alloc=42.3MB, time=4.20
TOP MAIN SOLVE Loop
x[1] = -1.01
y[1] (closed_form) = -1.687169629078919233075865489633
y[1] (numeric) = -1.687169629078919233075865489704
absolute error = 7.10e-29
relative error = 4.2082312754030078709645402980006e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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
y[1] (closed_form) = -1.6704649792860586466097678115178
y[1] (numeric) = -1.670464979286058646609767811589
absolute error = 7.12e-29
relative error = 4.2622863024898746762929862240820e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (closed_form) = -1.6537603294931980601436701334026
y[1] (numeric) = -1.653760329493198060143670133474
absolute error = 7.14e-29
relative error = 4.3174333503259711140523098456398e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (closed_form) = -1.6370556797003374736775724552874
y[1] (numeric) = -1.637055679700337473677572455359
absolute error = 7.16e-29
relative error = 4.3737058481179062546230482349845e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (closed_form) = -1.6203510299074768872114747771723
y[1] (numeric) = -1.620351029907476887211474777244
absolute error = 7.17e-29
relative error = 4.4249671013628520544742139503456e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (closed_form) = -1.6036463801146163007453770990571
y[1] (numeric) = -1.603646380114616300745377099129
absolute error = 7.19e-29
relative error = 4.4835320860987533536029042238924e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (closed_form) = -1.5869417303217557142792794209419
y[1] (numeric) = -1.586941730321755714279279421014
absolute error = 7.21e-29
relative error = 4.5433300178817262590290406084612e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (closed_form) = -1.5702370805288951278131817428267
y[1] (numeric) = -1.570237080528895127813181742899
absolute error = 7.23e-29
relative error = 4.6044002460856134815919032990846e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (closed_form) = -1.5535324307360345413470840647116
y[1] (numeric) = -1.553532430736034541347084064784
absolute error = 7.24e-29
relative error = 4.6603468693407473505438595297742e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (closed_form) = -1.5368277809431739548809863865964
y[1] (numeric) = -1.536827780943173954880986386669
absolute error = 7.26e-29
relative error = 4.7240166334997084376354237889037e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (closed_form) = -1.5201231311503133684148887084812
y[1] (numeric) = -1.520123131150313368414888708554
absolute error = 7.28e-29
relative error = 4.7890857331346906475202092405415e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (closed_form) = -1.503418481357452781948791030366
y[1] (numeric) = -1.503418481357452781948791030439
absolute error = 7.30e-29
relative error = 4.8556008127615613509579899244380e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (closed_form) = -1.4867138315645921954826933522508
y[1] (numeric) = -1.486713831564592195482693352324
absolute error = 7.32e-29
relative error = 4.9236106132789235308775184888715e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (closed_form) = -1.4700091817717316090165956741357
y[1] (numeric) = -1.470009181771731609016595674209
absolute error = 7.33e-29
relative error = 4.9863634124825685293072633143706e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (closed_form) = -1.4533045319788710225504979960205
y[1] (numeric) = -1.453304531978871022550497996094
absolute error = 7.35e-29
relative error = 5.0574396750775827958726347583305e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (closed_form) = -1.4365998821860104360844003179053
y[1] (numeric) = -1.436599882186010436084400317979
absolute error = 7.37e-29
relative error = 5.1301688740120159988697590265685e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (closed_form) = -1.4198952323931498496183026397901
y[1] (numeric) = -1.419895232393149849618302639864
absolute error = 7.39e-29
relative error = 5.2046093482154946889962273952357e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (closed_form) = -1.403190582600289263152204961675
y[1] (numeric) = -1.403190582600289263152204961749
absolute error = 7.40e-29
relative error = 5.2736955989876057725668970803581e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (closed_form) = -1.3864859328074286766861072835598
y[1] (numeric) = -1.386485932807428676686107283634
absolute error = 7.42e-29
relative error = 5.3516590572077416573192699645810e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (closed_form) = -1.3697812830145680902200096054446
y[1] (numeric) = -1.369781283014568090220009605519
absolute error = 7.44e-29
relative error = 5.4315240631893442709680421874434e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (closed_form) = -1.3530766332217075037539119273294
y[1] (numeric) = -1.353076633221707503753911927404
absolute error = 7.46e-29
relative error = 5.5133610446272827516204877985248e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (closed_form) = -1.3363719834288469172878142492142
y[1] (numeric) = -1.336371983428846917287814249289
absolute error = 7.48e-29
relative error = 5.5972439506011696942892445498831e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (closed_form) = -1.3196673336359863308217165710991
y[1] (numeric) = -1.319667333635986330821716571174
absolute error = 7.49e-29
relative error = 5.6756728071485495173934125334897e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (closed_form) = -1.3029626838431257443556188929839
y[1] (numeric) = -1.302962683843125744355618893059
absolute error = 7.51e-29
relative error = 5.7637874768976805709738415699466e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (closed_form) = -1.2862580340502651578895212148687
y[1] (numeric) = -1.286258034050265157889521214944
absolute error = 7.53e-29
relative error = 5.8541908393675682752966194125451e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (closed_form) = -1.2695533842574045714234235367535
y[1] (numeric) = -1.269553384257404571423423536829
absolute error = 7.55e-29
relative error = 5.9469732376919267086805229878437e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=663.5MB, alloc=42.3MB, time=4.48
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (closed_form) = -1.2528487344645439849573258586384
y[1] (numeric) = -1.252848734464543984957325858714
absolute error = 7.56e-29
relative error = 6.0342480237497102158754636430821e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (closed_form) = -1.2361440846716833984912281805232
y[1] (numeric) = -1.236144084671683398491228180599
absolute error = 7.58e-29
relative error = 6.1319712596555667412505381829906e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (closed_form) = -1.219439434878822812025130502408
y[1] (numeric) = -1.219439434878822812025130502484
absolute error = 7.60e-29
relative error = 6.2323718444903508426632859979650e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (closed_form) = -1.2027347850859622255590328242928
y[1] (numeric) = -1.202734785085962225559032824369
absolute error = 7.62e-29
relative error = 6.3355613344594345024486101411332e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (closed_form) = -1.1860301352931016390929351461776
y[1] (numeric) = -1.186030135293101639092935146254
absolute error = 7.64e-29
relative error = 6.4416575706248303780025349643906e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.7
y[1] (closed_form) = -1.1693254855002410526268374680625
y[1] (numeric) = -1.169325485500241052626837468139
absolute error = 7.65e-29
relative error = 6.5422331890143541881302858375253e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (closed_form) = -1.1526208357073804661607397899473
y[1] (numeric) = -1.152620835707380466160739790024
absolute error = 7.67e-29
relative error = 6.6543999226708473308840588541582e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (closed_form) = -1.1359161859145198796946421118321
y[1] (numeric) = -1.135916185914519879694642111909
absolute error = 7.69e-29
relative error = 6.7698656779054726248952957830450e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (closed_form) = -1.1192115361216592932285444337169
y[1] (numeric) = -1.119211536121659293228544433794
absolute error = 7.71e-29
relative error = 6.8887781721023255396232860530926e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (closed_form) = -1.1025068863287987067624467556017
y[1] (numeric) = -1.102506886328798706762446755679
absolute error = 7.73e-29
relative error = 7.0112940752142346032824275434447e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (closed_form) = -1.0858022365359381202963490774866
y[1] (numeric) = -1.085802236535938120296349077564
absolute error = 7.74e-29
relative error = 7.1283699181658664638089268311136e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (closed_form) = -1.0690975867430775338302513993714
y[1] (numeric) = -1.069097586743077533830251399449
absolute error = 7.76e-29
relative error = 7.2584580642822655126478171301957e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.63
y[1] (closed_form) = -1.0523929369502169473641537212562
y[1] (numeric) = -1.052392936950216947364153721334
absolute error = 7.78e-29
relative error = 7.3926759928150581820847674387726e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (closed_form) = -1.035688287157356360898056043141
y[1] (numeric) = -1.035688287157356360898056043219
absolute error = 7.80e-29
relative error = 7.5312235319456828731164580798842e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (closed_form) = -1.0189836373644957744319583650259
y[1] (numeric) = -1.018983637364495774431958365104
absolute error = 7.81e-29
relative error = 7.6644999130700684338386955263582e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (closed_form) = -1.0022789875716351879658606869107
y[1] (numeric) = -1.002278987571635187965860686989
absolute error = 7.83e-29
relative error = 7.8121961021759641187673413236332e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.59
y[1] (closed_form) = -0.9855743377787746014997630087955
y[1] (numeric) = -0.98557433777877460149976300887382
absolute error = 7.832e-29
relative error = 7.9466354792184104134276014347291e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (closed_form) = -0.96886968798591401503366533068032
y[1] (numeric) = -0.96886968798591401503366533075862
absolute error = 7.830e-29
relative error = 8.0815821746647904676903530934139e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.57
y[1] (closed_form) = -0.95216503819305342856756765256515
y[1] (numeric) = -0.95216503819305342856756765264342
absolute error = 7.827e-29
relative error = 8.2202136037818473022238328345874e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (closed_form) = -0.93546038840019284210146997444997
y[1] (numeric) = -0.93546038840019284210146997452822
absolute error = 7.825e-29
relative error = 8.3648651477185165885816154703655e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (closed_form) = -0.91875573860733225563537229633479
y[1] (numeric) = -0.91875573860733225563537229641302
absolute error = 7.823e-29
relative error = 8.5147767477983374853524083838083e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (closed_form) = -0.90205108881447166916927461821961
y[1] (numeric) = -0.90205108881447166916927461829782
absolute error = 7.821e-29
relative error = 8.6702406293625961931147121458971e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.53
y[1] (closed_form) = -0.88534643902161108270317694010443
y[1] (numeric) = -0.88534643902161108270317694018262
absolute error = 7.819e-29
relative error = 8.8315710724953174936227632197629e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (closed_form) = -0.86864178922875049623707926198926
y[1] (numeric) = -0.86864178922875049623707926206742
absolute error = 7.816e-29
relative error = 8.9979553101396014665908546692482e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.51
y[1] (closed_form) = -0.85193713943588990977098158387408
y[1] (numeric) = -0.85193713943588990977098158395222
absolute error = 7.814e-29
relative error = 9.1720382153711942940497340699979e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (closed_form) = -0.8352324896430293233048839057589
y[1] (numeric) = -0.83523248964302932330488390583702
absolute error = 7.812e-29
relative error = 9.3530844368120508346069686467776e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (closed_form) = -0.81852783985016873683878622764372
y[1] (numeric) = -0.81852783985016873683878622772182
absolute error = 7.810e-29
relative error = 9.5415202999443709074318454511810e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=704.5MB, alloc=42.3MB, time=4.75
TOP MAIN SOLVE Loop
x[1] = -0.48
y[1] (closed_form) = -0.80182319005730815037268854952854
y[1] (numeric) = -0.80182319005730815037268854960662
absolute error = 7.808e-29
relative error = 9.7378076573738709832910921224345e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (closed_form) = -0.78511854026444756390659087141337
y[1] (numeric) = -0.78511854026444756390659087149142
absolute error = 7.805e-29
relative error = 9.9411739752968777935891577453262e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.46
y[1] (closed_form) = -0.76841389047158697744049319329819
y[1] (numeric) = -0.76841389047158697744049319337622
absolute error = 7.803e-29
relative error = 1.0154683689035323674619617582594e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (closed_form) = -0.75170924067872639097439551518301
y[1] (numeric) = -0.75170924067872639097439551526102
absolute error = 7.801e-29
relative error = 1.0377682723384367150362542301518e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (closed_form) = -0.73500459088586580450829783706783
y[1] (numeric) = -0.73500459088586580450829783714582
absolute error = 7.799e-29
relative error = 1.0610818077476548965911963598575e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (closed_form) = -0.71829994109300521804220015895265
y[1] (numeric) = -0.71829994109300521804220015903062
absolute error = 7.797e-29
relative error = 1.0854796936410227610091590537355e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.42
y[1] (closed_form) = -0.70159529130014463157610248083748
y[1] (numeric) = -0.70159529130014463157610248091542
absolute error = 7.794e-29
relative error = 1.1108968513110648484158485363328e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (closed_form) = -0.6848906415072840451100048027223
y[1] (numeric) = -0.68489064150728404511000480280022
absolute error = 7.792e-29
relative error = 1.1376998790422411440694350732408e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.4
y[1] (closed_form) = -0.66818599171442345864390712460712
y[1] (numeric) = -0.66818599171442345864390712468502
absolute error = 7.790e-29
relative error = 1.1658430581599762545057009369943e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.39
y[1] (closed_form) = -0.65148134192156287217780944649194
y[1] (numeric) = -0.65148134192156287217780944656982
absolute error = 7.788e-29
relative error = 1.1954294772324670116310060758121e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (closed_form) = -0.63477669212870228571171176837676
y[1] (numeric) = -0.63477669212870228571171176845462
absolute error = 7.786e-29
relative error = 1.2265730762561414928155378008834e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.37
y[1] (closed_form) = -0.61807204233584169924561409026159
y[1] (numeric) = -0.61807204233584169924561409033942
absolute error = 7.783e-29
relative error = 1.2592383196279492334341144769978e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (closed_form) = -0.60136739254298111277951641214641
y[1] (numeric) = -0.60136739254298111277951641222422
absolute error = 7.781e-29
relative error = 1.2938845864417023586234287534949e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (closed_form) = -0.58466274275012052631341873403123
y[1] (numeric) = -0.58466274275012052631341873410902
absolute error = 7.779e-29
relative error = 1.3305106399305270909664181315062e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.34
y[1] (closed_form) = -0.56795809295725993984732105591605
y[1] (numeric) = -0.56795809295725993984732105599382
absolute error = 7.777e-29
relative error = 1.3692911671539885722707598258710e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.33
y[1] (closed_form) = -0.55125344316439935338122337780087
y[1] (numeric) = -0.55125344316439935338122337787862
absolute error = 7.775e-29
relative error = 1.4104220293606901433511222289853e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.32
y[1] (closed_form) = -0.5345487933715387669151256996857
y[1] (numeric) = -0.53454879337153876691512569976342
absolute error = 7.772e-29
relative error = 1.4539364967938599887705885241207e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.31
y[1] (closed_form) = -0.51784414357867818044902802157052
y[1] (numeric) = -0.51784414357867818044902802164822
absolute error = 7.770e-29
relative error = 1.5004514575184091262593558789922e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.3
y[1] (closed_form) = -0.50113949378581759398293034345534
y[1] (numeric) = -0.50113949378581759398293034353302
absolute error = 7.768e-29
relative error = 1.5500674156245948729140410575219e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.29
y[1] (closed_form) = -0.48443484399295700751683266534016
y[1] (numeric) = -0.48443484399295700751683266541782
absolute error = 7.766e-29
relative error = 1.6031051639450003262345665931916e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.28
y[1] (closed_form) = -0.46773019420009642105073498722498
y[1] (numeric) = -0.46773019420009642105073498730262
absolute error = 7.764e-29
relative error = 1.6599313228597204547922725242663e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.27
y[1] (closed_form) = -0.45102554440723583458463730910981
y[1] (numeric) = -0.45102554440723583458463730918742
absolute error = 7.761e-29
relative error = 1.7207451099471450979353862924001e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.26
y[1] (closed_form) = -0.43432089461437524811853963099463
y[1] (numeric) = -0.43432089461437524811853963107222
absolute error = 7.759e-29
relative error = 1.7864671251630800352937165142962e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.25
y[1] (closed_form) = -0.41761624482151466165244195287945
y[1] (numeric) = -0.41761624482151466165244195295702
absolute error = 7.757e-29
relative error = 1.8574469015962897676407131539440e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.24
y[1] (closed_form) = -0.40091159502865407518634427476427
y[1] (numeric) = -0.40091159502865407518634427484182
absolute error = 7.755e-29
relative error = 1.9343416593989336443499595135625e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.23
y[1] (closed_form) = -0.38420694523579348872024659664909
y[1] (numeric) = -0.38420694523579348872024659672662
absolute error = 7.753e-29
relative error = 2.0179229178800682929469664261913e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=745.5MB, alloc=42.3MB, time=5.03
TOP MAIN SOLVE Loop
x[1] = -0.22
y[1] (closed_form) = -0.36750229544293290225414891853392
y[1] (numeric) = -0.36750229544293290225414891861142
absolute error = 7.750e-29
relative error = 2.1088303654428325294478194098975e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.21
y[1] (closed_form) = -0.35079764565007231578805124041874
y[1] (numeric) = -0.35079764565007231578805124049622
absolute error = 7.748e-29
relative error = 2.2086807297814037581539631664116e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.2
y[1] (closed_form) = -0.33409299585721172932195356230356
y[1] (numeric) = -0.33409299585721172932195356238102
absolute error = 7.746e-29
relative error = 2.3185161305538321097307212985772e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (closed_form) = -0.31738834606435114285585588418838
y[1] (numeric) = -0.31738834606435114285585588426582
absolute error = 7.744e-29
relative error = 2.4399131524602002877892434446549e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.18
y[1] (closed_form) = -0.3006836962714905563897582060732
y[1] (numeric) = -0.30068369627149055638975820615062
absolute error = 7.742e-29
relative error = 2.5747987323561649300764902736301e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.17
y[1] (closed_form) = -0.28397904647862996992366052795803
y[1] (numeric) = -0.28397904647862996992366052803542
absolute error = 7.739e-29
relative error = 2.7252010653477478618499190670993e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.16
y[1] (closed_form) = -0.26727439668576938345756284984285
y[1] (numeric) = -0.26727439668576938345756284992022
absolute error = 7.737e-29
relative error = 2.8947778372861798078018639760992e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.15
y[1] (closed_form) = -0.25056974689290879699146517172767
y[1] (numeric) = -0.25056974689290879699146517180502
absolute error = 7.735e-29
relative error = 3.0869648454830693465474015396324e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.14
y[1] (closed_form) = -0.23386509710004821052536749361249
y[1] (numeric) = -0.23386509710004821052536749368982
absolute error = 7.733e-29
relative error = 3.3066071405652288193994444693847e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.13
y[1] (closed_form) = -0.21716044730718762405926981549731
y[1] (numeric) = -0.21716044730718762405926981557462
absolute error = 7.731e-29
relative error = 3.5600405579677205188441093883296e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.12
y[1] (closed_form) = -0.20045579751432703759317213738214
y[1] (numeric) = -0.20045579751432703759317213745942
absolute error = 7.728e-29
relative error = 3.8552140151734259712537684386359e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.11
y[1] (closed_form) = -0.18375114772146645112707445926696
y[1] (numeric) = -0.18375114772146645112707445934422
absolute error = 7.726e-29
relative error = 4.2045995879771159025842200673209e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.1
y[1] (closed_form) = -0.16704649792860586466097678115178
y[1] (numeric) = -0.16704649792860586466097678122902
absolute error = 7.724e-29
relative error = 4.6238622753415438201807620217429e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.09
y[1] (closed_form) = -0.1503418481357452781948791030366
y[1] (numeric) = -0.15034184813574527819487910311382
absolute error = 7.722e-29
relative error = 5.1362944487869557194654244104809e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.08
y[1] (closed_form) = -0.13363719834288469172878142492142
y[1] (numeric) = -0.13363719834288469172878142499862
absolute error = 7.720e-29
relative error = 5.7768346655937205935712523964034e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.07
y[1] (closed_form) = -0.11693254855002410526268374680625
y[1] (numeric) = -0.11693254855002410526268374688342
absolute error = 7.717e-29
relative error = 6.5995311790357870940916883409389e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.06
y[1] (closed_form) = -0.10022789875716351879658606869107
y[1] (numeric) = -0.10022789875716351879658606876822
absolute error = 7.715e-29
relative error = 7.6974575898196121553371696439119e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.05
y[1] (closed_form) = -0.08352324896430293233048839057589
y[1] (numeric) = -0.08352324896430293233048839065304
absolute error = 7.7150e-29
relative error = 9.2369491077835345864046035726945e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.04
y[1] (closed_form) = -0.066818599171442345864390712460712
y[1] (numeric) = -0.06681859917144234586439071253786
absolute error = 7.7148e-29
relative error = 1.1545887066871097314840284452791e-25 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.03
y[1] (closed_form) = -0.050113949378581759398293034345534
y[1] (numeric) = -0.05011394937858175939829303442268
absolute error = 7.7146e-29
relative error = 1.5394116998683701862233085919617e-25 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.02
y[1] (closed_form) = -0.033409299585721172932195356230356
y[1] (numeric) = -0.0334092995857211729321953563075
absolute error = 7.7144e-29
relative error = 2.3090576862308910957018688853271e-25 %
Desired digits = 12
Estimated correct digits = 9
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.01
y[1] (closed_form) = -0.016704649792860586466097678115178
y[1] (numeric) = -0.01670464979286058646609767819232
absolute error = 7.7142e-29
relative error = 4.6179956453184538241375497654232e-25 %
Desired digits = 12
Estimated correct digits = 9
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (closed_form) = 0
y[1] (numeric) = -7.7141200000000000000000000000000e-29
absolute error = 7.7141200000000000000000000000000e-29
relative error = -100 %
Desired digits = 12
Estimated correct digits = -16
Correct digits = -16
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (closed_form) = 0.016704649792860586466097678115178
y[1] (numeric) = 0.016704649792860586466097678038038
absolute error = 7.7140e-29
relative error = 4.6178759181751254568713617601922e-25 %
Desired digits = 12
Estimated correct digits = 9
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (closed_form) = 0.033409299585721172932195356230356
y[1] (numeric) = 0.033409299585721172932195356153218
absolute error = 7.7138e-29
relative error = 2.3088780955158985448025868774806e-25 %
Desired digits = 12
Estimated correct digits = 9
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (closed_form) = 0.050113949378581759398293034345534
y[1] (numeric) = 0.050113949378581759398293034268398
absolute error = 7.7136e-29
relative error = 1.5392121546294895741129952499101e-25 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (closed_form) = 0.066818599171442345864390712460712
y[1] (numeric) = 0.066818599171442345864390712383578
absolute error = 7.7134e-29
relative error = 1.1543791841862850887681994361248e-25 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=786.6MB, alloc=42.3MB, time=5.30
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (closed_form) = 0.08352324896430293233048839057589
y[1] (numeric) = 0.083523248964302932330488390498758
absolute error = 7.7132e-29
relative error = 9.2347940192036239756132194785363e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (closed_form) = 0.10022789875716351879658606869107
y[1] (numeric) = 0.10022789875716351879658606861394
absolute error = 7.713e-29
relative error = 7.6954621374308060342340362233950e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (closed_form) = 0.11693254855002410526268374680625
y[1] (numeric) = 0.11693254855002410526268374672914
absolute error = 7.711e-29
relative error = 6.5944000157502856398264881167526e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (closed_form) = 0.13363719834288469172878142492142
y[1] (numeric) = 0.13363719834288469172878142484434
absolute error = 7.708e-29
relative error = 5.7678551298440930486071520040774e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (closed_form) = 0.1503418481357452781948791030366
y[1] (numeric) = 0.15034184813574527819487910295954
absolute error = 7.706e-29
relative error = 5.1256520360466564069153795010575e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = 0.16704649792860586466097678115178
y[1] (numeric) = 0.16704649792860586466097678107474
absolute error = 7.704e-29
relative error = 4.6118895610087070935619614986415e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 0.18375114772146645112707445926696
y[1] (numeric) = 0.18375114772146645112707445918994
absolute error = 7.702e-29
relative error = 4.1915384450685667462728013148467e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 0.20045579751432703759317213738214
y[1] (numeric) = 0.20045579751432703759317213730514
absolute error = 7.700e-29
relative error = 3.8412458484517831235318344950176e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 0.21716044730718762405926981549731
y[1] (numeric) = 0.21716044730718762405926981542034
absolute error = 7.697e-29
relative error = 3.5443839315324724917272163965816e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 0.23386509710004821052536749361249
y[1] (numeric) = 0.23386509710004821052536749353554
absolute error = 7.695e-29
relative error = 3.2903584568278075475596437594614e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 0.25056974689290879699146517172767
y[1] (numeric) = 0.25056974689290879699146517165074
absolute error = 7.693e-29
relative error = 3.0702030454170979292810808072905e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 0.26727439668576938345756284984285
y[1] (numeric) = 0.26727439668576938345756284976594
absolute error = 7.691e-29
relative error = 2.8775670604327270132873382241410e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 0.28397904647862996992366052795803
y[1] (numeric) = 0.28397904647862996992366052788114
absolute error = 7.689e-29
relative error = 2.7075941325053409109399182978326e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 0.3006836962714905563897582060732
y[1] (numeric) = 0.30068369627149055638975820599634
absolute error = 7.686e-29
relative error = 2.5561745100606411331139116821391e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 0.31738834606435114285585588418838
y[1] (numeric) = 0.31738834606435114285585588411154
absolute error = 7.684e-29
relative error = 2.4210088666715107194437689344948e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 0.33409299585721172932195356230356
y[1] (numeric) = 0.33409299585721172932195356222674
absolute error = 7.682e-29
relative error = 2.2993597876212933471406404616150e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 0.35079764565007231578805124041874
y[1] (numeric) = 0.35079764565007231578805124034194
absolute error = 7.680e-29
relative error = 2.1892963351472871531520956528190e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 0.36750229544293290225414891853392
y[1] (numeric) = 0.36750229544293290225414891845714
absolute error = 7.678e-29
relative error = 2.0892386510800087949806912811862e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 0.38420694523579348872024659664909
y[1] (numeric) = 0.38420694523579348872024659657234
absolute error = 7.675e-29
relative error = 1.9976213587939538434629133652803e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = 0.40091159502865407518634427476427
y[1] (numeric) = 0.40091159502865407518634427468754
absolute error = 7.673e-29
relative error = 1.9138882724136709030428419532643e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 0.41761624482151466165244195287945
y[1] (numeric) = 0.41761624482151466165244195280274
absolute error = 7.671e-29
relative error = 1.8368538329438105978563762542097e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 0.43432089461437524811853963099463
y[1] (numeric) = 0.43432089461437524811853963091794
absolute error = 7.669e-29
relative error = 1.7657451195870164699919463781593e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 0.45102554440723583458463730910981
y[1] (numeric) = 0.45102554440723583458463730903314
absolute error = 7.667e-29
relative error = 1.6999037183307256108582150114459e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 0.46773019420009642105073498722498
y[1] (numeric) = 0.46773019420009642105073498714834
absolute error = 7.664e-29
relative error = 1.6385514758367977286872715901567e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 0.48443484399295700751683266534016
y[1] (numeric) = 0.48443484399295700751683266526354
absolute error = 7.662e-29
relative error = 1.5816368485895689543663725517685e-26 %
Desired digits = 12
Estimated correct digits = 10
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 0.50113949378581759398293034345534
y[1] (numeric) = 0.50113949378581759398293034337874
absolute error = 7.660e-29
relative error = 1.5285165298254887650002001159395e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 0.51784414357867818044902802157052
y[1] (numeric) = 0.51784414357867818044902802149394
absolute error = 7.658e-29
relative error = 1.4788233284010266523673291275833e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=827.6MB, alloc=42.3MB, time=5.58
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 0.5345487933715387669151256996857
y[1] (numeric) = 0.53454879337153876691512569960914
absolute error = 7.656e-29
relative error = 1.4322359520655934217740125759994e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 0.55125344316439935338122337780087
y[1] (numeric) = 0.55125344316439935338122337772434
absolute error = 7.653e-29
relative error = 1.3882906483212040729345515650706e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 0.56795809295725993984732105591605
y[1] (numeric) = 0.56795809295725993984732105583954
absolute error = 7.651e-29
relative error = 1.3471064317725558141241588565950e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 0.58466274275012052631341873403123
y[1] (numeric) = 0.58466274275012052631341873395474
absolute error = 7.649e-29
relative error = 1.3082755990266874558172171600322e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 0.60136739254298111277951641214641
y[1] (numeric) = 0.60136739254298111277951641206994
absolute error = 7.647e-29
relative error = 1.2716020347667006729717722243896e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 0.61807204233584169924561409026159
y[1] (numeric) = 0.61807204233584169924561409018514
absolute error = 7.645e-29
relative error = 1.2369108253315780405504053933763e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 0.63477669212870228571171176837676
y[1] (numeric) = 0.63477669212870228571171176830034
absolute error = 7.642e-29
relative error = 1.2038879333097140108009683886914e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = 0.65148134192156287217780944649194
y[1] (numeric) = 0.65148134192156287217780944641554
absolute error = 7.640e-29
relative error = 1.1727120192675973252261025191583e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 0.66818599171442345864390712460712
y[1] (numeric) = 0.66818599171442345864390712453074
absolute error = 7.638e-29
relative error = 1.1430949009275864739299799431018e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 0.6848906415072840451100048027223
y[1] (numeric) = 0.68489064150728404511000480264594
absolute error = 7.636e-29
relative error = 1.1149225200675761519653755414870e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 0.70159529130014463157610248083748
y[1] (numeric) = 0.70159529130014463157610248076114
absolute error = 7.634e-29
relative error = 1.0880916811532806072371808732826e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = 0.71829994109300521804220015895265
y[1] (numeric) = 0.71829994109300521804220015887634
absolute error = 7.631e-29
relative error = 1.0623695706264774514891487417027e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = 0.73500459088586580450829783706783
y[1] (numeric) = 0.73500459088586580450829783699154
absolute error = 7.629e-29
relative error = 1.0379527005137657656230589856844e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 0.75170924067872639097439551518301
y[1] (numeric) = 0.75170924067872639097439551510674
absolute error = 7.627e-29
relative error = 1.0146210246282857102399065521558e-26 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = 0.76841389047158697744049319329819
y[1] (numeric) = 0.76841389047158697744049319322194
absolute error = 7.625e-29
relative error = 9.9230376943347870074297813747634e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 0.78511854026444756390659087141337
y[1] (numeric) = 0.78511854026444756390659087133714
absolute error = 7.623e-29
relative error = 9.7093618467249326611825944257043e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = 0.80182319005730815037268854952854
y[1] (numeric) = 0.80182319005730815037268854945234
absolute error = 7.620e-29
relative error = 9.5033420016891517536729152116997e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 0.81852783985016873683878622764372
y[1] (numeric) = 0.81852783985016873683878622756754
absolute error = 7.618e-29
relative error = 9.3069528354643044267369780598076e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 0.8352324896430293233048839057589
y[1] (numeric) = 0.83523248964302932330488390568274
absolute error = 7.616e-29
relative error = 9.1184192358884509928784783939911e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 0.85193713943588990977098158387408
y[1] (numeric) = 0.85193713943588990977098158379794
absolute error = 7.614e-29
relative error = 8.9372791108057682819163904797753e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = 0.86864178922875049623707926198926
y[1] (numeric) = 0.86864178922875049623707926191314
absolute error = 7.612e-29
relative error = 8.7631059136108810598374597930294e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 0.88534643902161108270317694010443
y[1] (numeric) = 0.88534643902161108270317694002834
absolute error = 7.609e-29
relative error = 8.5943757885428917775899226677549e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 0.90205108881447166916927461821961
y[1] (numeric) = 0.90205108881447166916927461814354
absolute error = 7.607e-29
relative error = 8.4330035120267573508532943733333e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 0.91875573860733225563537229633479
y[1] (numeric) = 0.91875573860733225563537229625874
absolute error = 7.605e-29
relative error = 8.2774993182930278123616343805269e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 0.93546038840019284210146997444997
y[1] (numeric) = 0.93546038840019284210146997437394
absolute error = 7.603e-29
relative error = 8.1275488457640743288161051017494e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 0.95216503819305342856756765256515
y[1] (numeric) = 0.95216503819305342856756765248914
absolute error = 7.601e-29
relative error = 7.9828597933238560552195417625781e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=868.7MB, alloc=42.3MB, time=5.84
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = 0.96886968798591401503366533068032
y[1] (numeric) = 0.96886968798591401503366533060434
absolute error = 7.598e-29
relative error = 7.8421278880080559353143426313868e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 0.9855743377787746014997630087955
y[1] (numeric) = 0.98557433777877460149976300871954
absolute error = 7.596e-29
relative error = 7.7071811925616758810515909727021e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 1.0022789875716351879658606869107
y[1] (numeric) = 1.0022789875716351879658606868347
absolute error = 7.60e-29
relative error = 7.5827190774632601919069979641906e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = 1.0189836373644957744319583650259
y[1] (numeric) = 1.0189836373644957744319583649497
absolute error = 7.62e-29
relative error = 7.4780396078865456422344250846158e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = 1.035688287157356360898056043141
y[1] (numeric) = 1.0356882871573563608980560430647
absolute error = 7.63e-29
relative error = 7.3670814806084051694716121986559e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 1.0523929369502169473641537212562
y[1] (numeric) = 1.0523929369502169473641537211797
absolute error = 7.65e-29
relative error = 7.2691479877937268757003175972507e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = 1.0690975867430775338302513993714
y[1] (numeric) = 1.0690975867430775338302513992947
absolute error = 7.67e-29
relative error = 7.1742749166295072786093759521393e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = 1.0858022365359381202963490774866
y[1] (numeric) = 1.0858022365359381202963490774097
absolute error = 7.69e-29
relative error = 7.0823210168857252075827709730314e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 1.1025068863287987067624467556017
y[1] (numeric) = 1.1025068863287987067624467555247
absolute error = 7.70e-29
relative error = 6.9840833608214238609669718091234e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = 1.1192115361216592932285444337169
y[1] (numeric) = 1.1192115361216592932285444336397
absolute error = 7.72e-29
relative error = 6.8977130335447410072492565927205e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 1.1359161859145198796946421118321
y[1] (numeric) = 1.1359161859145198796946421117547
absolute error = 7.74e-29
relative error = 6.8138830100114900021702977062117e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = 1.1526208357073804661607397899473
y[1] (numeric) = 1.1526208357073804661607397898697
absolute error = 7.76e-29
relative error = 6.7324828422328259827458013961235e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 1.1693254855002410526268374680625
y[1] (numeric) = 1.1693254855002410526268374679847
absolute error = 7.78e-29
relative error = 6.6534083935335523638762906948950e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = 1.1860301352931016390929351461776
y[1] (numeric) = 1.1860301352931016390929351460997
absolute error = 7.79e-29
relative error = 6.5681299051266267859476109126443e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 1.2027347850859622255590328242928
y[1] (numeric) = 1.2027347850859622255590328242147
absolute error = 7.81e-29
relative error = 6.4935346485732524231133392653872e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = 1.219439434878822812025130502408
y[1] (numeric) = 1.2194394348788228120251305023297
absolute error = 7.83e-29
relative error = 6.4209830976788746181649380742192e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = 1.2361440846716833984912281805232
y[1] (numeric) = 1.2361440846716833984912281804447
absolute error = 7.85e-29
relative error = 6.3503923995113718890259531314612e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 1.2528487344645439849573258586384
y[1] (numeric) = 1.2528487344645439849573258585597
absolute error = 7.87e-29
relative error = 6.2816841199616692326640077871767e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = 1.2695533842574045714234235367535
y[1] (numeric) = 1.2695533842574045714234235366747
absolute error = 7.88e-29
relative error = 6.2069071672864082734307975025441e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = 1.2862580340502651578895212148687
y[1] (numeric) = 1.2862580340502651578895212147897
absolute error = 7.90e-29
relative error = 6.1418469629487104083457228896556e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 1.3029626838431257443556188929839
y[1] (numeric) = 1.3029626838431257443556188929047
absolute error = 7.92e-29
relative error = 6.0784549689786458218525732668411e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 1.3196673336359863308217165710991
y[1] (numeric) = 1.3196673336359863308217165710197
absolute error = 7.94e-29
relative error = 6.0166678356154183134984907230853e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = 1.3363719834288469172878142492142
y[1] (numeric) = 1.3363719834288469172878142491347
absolute error = 7.95e-29
relative error = 5.9489424341282485387165099159854e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 1.3530766332217075037539119273294
y[1] (numeric) = 1.3530766332217075037539119272497
absolute error = 7.97e-29
relative error = 5.8902798291795500711012450072711e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 1.3697812830145680902200096054446
y[1] (numeric) = 1.3697812830145680902200096053647
absolute error = 7.99e-29
relative error = 5.8330480194735027856229377792571e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = 1.3864859328074286766861072835598
y[1] (numeric) = 1.3864859328074286766861072834797
absolute error = 8.01e-29
relative error = 5.7771952895194084467826620507134e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 1.403190582600289263152204961675
y[1] (numeric) = 1.4031905826002892631522049615947
absolute error = 8.03e-29
relative error = 5.7226723864689830207719166966588e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=909.8MB, alloc=42.3MB, time=6.11
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 1.4198952323931498496183026397901
y[1] (numeric) = 1.4198952323931498496183026397097
absolute error = 8.04e-29
relative error = 5.6623896021180754126562473961698e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 1.4365998821860104360844003179053
y[1] (numeric) = 1.4365998821860104360844003178247
absolute error = 8.06e-29
relative error = 5.6104696234106986364844311742391e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 1.4533045319788710225504979960205
y[1] (numeric) = 1.4533045319788710225504979959397
absolute error = 8.08e-29
relative error = 5.5597432074322270735579440608585e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = 1.4700091817717316090165956741357
y[1] (numeric) = 1.4700091817717316090165956740547
absolute error = 8.10e-29
relative error = 5.5101696645441753188797862000548e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = 1.4867138315645921954826933522508
y[1] (numeric) = 1.4867138315645921954826933521697
absolute error = 8.11e-29
relative error = 5.4549838898486434201388900197743e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 1.503418481357452781948791030366
y[1] (numeric) = 1.5034184813574527819487910302847
absolute error = 8.13e-29
relative error = 5.4076759736645881894915696007782e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 1.5201231311503133684148887084812
y[1] (numeric) = 1.5201231311503133684148887083997
absolute error = 8.15e-29
relative error = 5.3614077919021605463310034767052e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = 1.5368277809431739548809863865964
y[1] (numeric) = 1.5368277809431739548809863865147
absolute error = 8.17e-29
relative error = 5.3161454401780465475869713988076e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = 1.5535324307360345413470840647116
y[1] (numeric) = 1.5535324307360345413470840646297
absolute error = 8.19e-29
relative error = 5.2718564723619780111815206559186e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 1.5702370805288951278131817428267
y[1] (numeric) = 1.5702370805288951278131817427447
absolute error = 8.20e-29
relative error = 5.2221413579394233124555473101651e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = 1.5869417303217557142792794209419
y[1] (numeric) = 1.5869417303217557142792794208597
absolute error = 8.22e-29
relative error = 5.1797743061009417266600157838489e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = 1.6036463801146163007453770990571
y[1] (numeric) = 1.6036463801146163007453770989747
absolute error = 8.24e-29
relative error = 5.1382899011757618405685578309977e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (closed_form) = 1.6203510299074768872114747771723
y[1] (numeric) = 1.6203510299074768872114747770897
absolute error = 8.26e-29
relative error = 5.0976608448057403026439340627413e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = 1.6370556797003374736775724552874
y[1] (numeric) = 1.6370556797003374736775724552047
absolute error = 8.27e-29
relative error = 5.0517524251305984253816492881734e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 1.6537603294931980601436701334026
y[1] (numeric) = 1.6537603294931980601436701333197
absolute error = 8.29e-29
relative error = 5.0128182736978011954472897227386e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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
y[1] (closed_form) = 1.6704649792860586466097678115178
y[1] (numeric) = 1.6704649792860586466097678114347
absolute error = 8.31e-29
relative error = 4.9746628052936599101116173486125e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 1.687169629078919233075865489633
y[1] (numeric) = 1.6871696290789192330758654895497
absolute error = 8.33e-29
relative error = 4.9372628907193036007231860115978e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.7038742788717798195419631677482
y[1] (numeric) = 1.7038742788717798195419631676647
absolute error = 8.35e-29
relative error = 4.9005963078032680032835474458972e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.7205789286646404060080608458633
y[1] (numeric) = 1.7205789286646404060080608457797
absolute error = 8.36e-29
relative error = 4.8588297001220890550083676275398e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.7372835784575009924741585239785
y[1] (numeric) = 1.7372835784575009924741585238947
absolute error = 8.38e-29
relative error = 4.8236224090947965896898261341032e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.7539882282503615789402562020937
y[1] (numeric) = 1.7539882282503615789402562020097
absolute error = 8.40e-29
relative error = 4.7890857331346906475202092405415e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.7706928780432221654063538802089
y[1] (numeric) = 1.7706928780432221654063538801247
absolute error = 8.42e-29
relative error = 4.7552006925700584023726605902546e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.787397527836082751872451558324
y[1] (numeric) = 1.7873975278360827518724515582397
absolute error = 8.43e-29
relative error = 4.7163542909258694110508602684306e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8041021776289433383385492364392
y[1] (numeric) = 1.8041021776289433383385492363547
absolute error = 8.45e-29
relative error = 4.6837701903921453670770564910390e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8208068274218039248046469145544
y[1] (numeric) = 1.8208068274218039248046469144697
absolute error = 8.47e-29
relative error = 4.6517839632627098376715793884618e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8375114772146645112707445926696
y[1] (numeric) = 1.8375114772146645112707445925847
absolute error = 8.49e-29
relative error = 4.6203793038992640451643836877497e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=950.8MB, alloc=42.3MB, time=6.39
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = 1.8542161270075250977368422707848
y[1] (numeric) = 1.8542161270075250977368422706997
absolute error = 8.51e-29
relative error = 4.5895404942540785372068671888522e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8709207768003856842029399488999
y[1] (numeric) = 1.8709207768003856842029399488147
absolute error = 8.52e-29
relative error = 4.5539074158825406603651989653365e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8876254265932462706690376270151
y[1] (numeric) = 1.8876254265932462706690376269297
absolute error = 8.54e-29
relative error = 4.5242026726737011205555958975913e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9043300763861068571351353051303
y[1] (numeric) = 1.9043300763861068571351353050447
absolute error = 8.56e-29
relative error = 4.4950190653106306954794946380521e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9210347261789674436012329832455
y[1] (numeric) = 1.9210347261789674436012329831597
absolute error = 8.58e-29
relative error = 4.4663429989451788864916734004180e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9377393759718280300673306613606
y[1] (numeric) = 1.9377393759718280300673306612747
absolute error = 8.59e-29
relative error = 4.4330006947873914506679523034755e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9544440257646886165334283394758
y[1] (numeric) = 1.9544440257646886165334283393897
absolute error = 8.61e-29
relative error = 4.4053448891335135123022437565239e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.971148675557549202999526017591
y[1] (numeric) = 1.9711486755575492029995260175047
absolute error = 8.63e-29
relative error = 4.3781578259483453695020556934188e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9878533253504097894656236957062
y[1] (numeric) = 1.9878533253504097894656236956197
absolute error = 8.65e-29
relative error = 4.3514276881948607249001901187693e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.0045579751432703759317213738214
y[1] (numeric) = 2.0045579751432703759317213737347
absolute error = 8.67e-29
relative error = 4.3251430527372674910416889703640e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.0212626249361309623978190519365
y[1] (numeric) = 2.0212626249361309623978190518497
absolute error = 8.68e-29
relative error = 4.2943454714472226054210140710642e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.0379672747289915488639167300517
y[1] (numeric) = 2.0379672747289915488639167299647
absolute error = 8.70e-29
relative error = 4.2689596186753902288346127451549e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.0546719245218521353300144081669
y[1] (numeric) = 2.0546719245218521353300144080797
absolute error = 8.72e-29
relative error = 4.2439865439974087852008358310490e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.0713765743147127217961120862821
y[1] (numeric) = 2.0713765743147127217961120861947
absolute error = 8.74e-29
relative error = 4.2194162608464915583998617703964e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.0880812241075733082622097643972
y[1] (numeric) = 2.0880812241075733082622097643097
absolute error = 8.75e-29
relative error = 4.1904500164928543165801830854740e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.1047858739004338947283074425124
y[1] (numeric) = 2.1047858739004338947283074424247
absolute error = 8.77e-29
relative error = 4.1666946309118290653524042697966e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.1214905236932944811944051206276
y[1] (numeric) = 2.1214905236932944811944051205397
absolute error = 8.79e-29
relative error = 4.1433133458911349204431731520040e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.1381951734861550676605027987428
y[1] (numeric) = 2.1381951734861550676605027986547
absolute error = 8.81e-29
relative error = 4.1202973934488891215481487704268e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.154899823279015654126600476858
y[1] (numeric) = 2.1548998232790156541266004767697
absolute error = 8.83e-29
relative error = 4.0976382774786161257367681777114e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.1716044730718762405926981549731
y[1] (numeric) = 2.1716044730718762405926981548847
absolute error = 8.84e-29
relative error = 4.0707228731644870503921778544604e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.1883091228647368270587958330883
y[1] (numeric) = 2.1883091228647368270587958329997
absolute error = 8.86e-29
relative error = 4.0487881293486029710905585754960e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.2050137726575974135248935112035
y[1] (numeric) = 2.2050137726575974135248935111147
absolute error = 8.88e-29
relative error = 4.0271857301359898626874486795463e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.2217184224504579999909911893187
y[1] (numeric) = 2.2217184224504579999909911892297
absolute error = 8.90e-29
relative error = 4.0059081790318371017791223910544e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.2384230722433185864570888674339
y[1] (numeric) = 2.2384230722433185864570888673447
absolute error = 8.92e-29
relative error = 3.9849482033172985611828606740326e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.255127722036179172923186545549
y[1] (numeric) = 2.2551277220361791729231865454597
absolute error = 8.93e-29
relative error = 3.9598644071197025446625433812997e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.2718323718290397593892842236642
y[1] (numeric) = 2.2718323718290397593892842235747
absolute error = 8.95e-29
relative error = 3.9395512234885552661126721234234e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.2885370216219003458553819017794
y[1] (numeric) = 2.2885370216219003458553819016897
absolute error = 8.97e-29
relative error = 3.9195345826841400646219230736914e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=991.9MB, alloc=42.3MB, time=6.66
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 2.3052416714147609323214795798946
y[1] (numeric) = 2.3052416714147609323214795798047
absolute error = 8.99e-29
relative error = 3.8998080381232671124281414014917e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.3219463212076215187875772580097
y[1] (numeric) = 2.3219463212076215187875772579197
absolute error = 9.00e-29
relative error = 3.8760585969615302003311046011578e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.3386509710004821052536749361249
y[1] (numeric) = 2.3386509710004821052536749360347
absolute error = 9.02e-29
relative error = 3.8569244029352597893421685133647e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.3553556207933426917197726142401
y[1] (numeric) = 2.3553556207933426917197726141497
absolute error = 9.04e-29
relative error = 3.8380616159164542068778981856822e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.3720602705862032781858702923553
y[1] (numeric) = 2.3720602705862032781858702922647
absolute error = 9.06e-29
relative error = 3.8194645019542515199412936372629e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.3887649203790638646519679704705
y[1] (numeric) = 2.3887649203790638646519679703797
absolute error = 9.08e-29
relative error = 3.8011274874880236957590471944158e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.4054695701719244511180656485856
y[1] (numeric) = 2.4054695701719244511180656484947
absolute error = 9.09e-29
relative error = 3.7788879613015918390589151038649e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.4221742199647850375841633267008
y[1] (numeric) = 2.4221742199647850375841633266097
absolute error = 9.11e-29
relative error = 3.7610837093842268792163022570115e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.438878869757645624050261004816
y[1] (numeric) = 2.4388788697576456240502610047247
absolute error = 9.13e-29
relative error = 3.7435233513287436311523553395671e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.4555835195505062105163586829312
y[1] (numeric) = 2.4555835195505062105163586828397
absolute error = 9.15e-29
relative error = 3.7262019097093894068715913733805e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.4722881693433667969824563610463
y[1] (numeric) = 2.4722881693433667969824563609547
absolute error = 9.16e-29
relative error = 3.7050697057021762104125943110947e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.4889928191362273834485540391615
y[1] (numeric) = 2.4889928191362273834485540390697
absolute error = 9.18e-29
relative error = 3.6882388448134614214962685258533e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.5056974689290879699146517172767
y[1] (numeric) = 2.5056974689290879699146517171847
absolute error = 9.20e-29
relative error = 3.6716323954032628297654937510819e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.5224021187219485563807493953919
y[1] (numeric) = 2.5224021187219485563807493952997
absolute error = 9.22e-29
relative error = 3.6552458989653847491834709600822e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.5391067685148091428468470735071
y[1] (numeric) = 2.5391067685148091428468470734147
absolute error = 9.24e-29
relative error = 3.6390750143227419065038432058062e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.5558114183076697293129447516222
y[1] (numeric) = 2.5558114183076697293129447515297
absolute error = 9.25e-29
relative error = 3.6192028620503176870557136825989e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.5725160681005303157790424297374
y[1] (numeric) = 2.5725160681005303157790424296447
absolute error = 9.27e-29
relative error = 3.6034760345907940180610665308296e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.5892207178933909022451401078526
y[1] (numeric) = 2.5892207178933909022451401077597
absolute error = 9.29e-29
relative error = 3.5879521339371996867308664390831e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.6059253676862514887112377859678
y[1] (numeric) = 2.6059253676862514887112377858747
absolute error = 9.31e-29
relative error = 3.5726272576509591288792586562052e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.6226300174791120751773354640829
y[1] (numeric) = 2.6226300174791120751773354639897
absolute error = 9.32e-29
relative error = 3.5536846363706462448159514428223e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.6393346672719726616434331421981
y[1] (numeric) = 2.6393346672719726616434331421047
absolute error = 9.34e-29
relative error = 3.5387706287561717284682558786913e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.6560393170648332481095308203133
y[1] (numeric) = 2.6560393170648332481095308202197
absolute error = 9.36e-29
relative error = 3.5240442187217534953450596298325e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.6727439668576938345756284984285
y[1] (numeric) = 2.6727439668576938345756284983347
absolute error = 9.38e-29
relative error = 3.5095018888127654901359033340843e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.6894486166505544210417261765437
y[1] (numeric) = 2.6894486166505544210417261764497
absolute error = 9.40e-29
relative error = 3.4951402089647587023827614022585e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.7061532664434150075078238546588
y[1] (numeric) = 2.7061532664434150075078238545647
absolute error = 9.41e-29
relative error = 3.4772605516047406630528679748068e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.722857916236275593973921532774
y[1] (numeric) = 2.7228579162362755939739215326797
absolute error = 9.43e-29
relative error = 3.4632728883021574237818691056984e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.7395625660291361804400192108892
y[1] (numeric) = 2.7395625660291361804400192107947
absolute error = 9.45e-29
relative error = 3.4494558062593617849897848569449e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1033.0MB, alloc=42.3MB, time=6.94
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = 2.7562672158219967669061168890044
y[1] (numeric) = 2.7562672158219967669061168889097
absolute error = 9.47e-29
relative error = 3.4358062039989030630315440536309e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.7729718656148573533722145671195
y[1] (numeric) = 2.7729718656148573533722145670247
absolute error = 9.48e-29
relative error = 3.4187148155208484441635228614710e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.7896765154077179398383122452347
y[1] (numeric) = 2.7896765154077179398383122451397
absolute error = 9.50e-29
relative error = 3.4054127593397875113354781276306e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.8063811652005785263044099233499
y[1] (numeric) = 2.8063811652005785263044099232547
absolute error = 9.52e-29
relative error = 3.3922690609704058753268148787169e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.8230858149934391127705076014651
y[1] (numeric) = 2.8230858149934391127705076013697
absolute error = 9.54e-29
relative error = 3.3792809093272891107502068161809e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.8397904647862996992366052795803
y[1] (numeric) = 2.8397904647862996992366052794847
absolute error = 9.56e-29
relative error = 3.3664455594682090139921470837924e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.8564951145791602857027029576954
y[1] (numeric) = 2.8564951145791602857027029575997
absolute error = 9.57e-29
relative error = 3.3502595369955401678924270783613e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.8731997643720208721688006358106
y[1] (numeric) = 2.8731997643720208721688006357147
absolute error = 9.59e-29
relative error = 3.3377421642995409382063086204065e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.8899044141648814586348983139258
y[1] (numeric) = 2.8899044141648814586348983138297
absolute error = 9.61e-29
relative error = 3.3253695011144781157997984683240e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.906609063957742045100995992041
y[1] (numeric) = 2.9066090639577420451009959919447
absolute error = 9.63e-29
relative error = 3.3131390524487838315818688927022e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.9233137137506026315670936701562
y[1] (numeric) = 2.9233137137506026315670936700597
absolute error = 9.65e-29
relative error = 3.3010483803392689106121442265161e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.9400183635434632180331913482713
y[1] (numeric) = 2.9400183635434632180331913481747
absolute error = 9.66e-29
relative error = 3.2856937629318971345912799192920e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.9567230133363238044992890263865
y[1] (numeric) = 2.9567230133363238044992890262897
absolute error = 9.68e-29
relative error = 3.2738947667191953014121204412742e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.9734276631291843909653867045017
y[1] (numeric) = 2.9734276631291843909653867044047
absolute error = 9.70e-29
relative error = 3.2622283434976474214147492719981e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 2.9901323129220449774314843826169
y[1] (numeric) = 2.9901323129220449774314843825197
absolute error = 9.72e-29
relative error = 3.2506922713735470037637174453955e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 3.006836962714905563897582060732
y[1] (numeric) = 3.0068369627149055638975820606347
absolute error = 9.73e-29
relative error = 3.2359586238472597222480302715604e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.0235416125077661503636797388472
y[1] (numeric) = 3.0235416125077661503636797387497
absolute error = 9.75e-29
relative error = 3.2246951587060244346216878518840e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.0402462623006267368297774169624
y[1] (numeric) = 3.0402462623006267368297774168647
absolute error = 9.77e-29
relative error = 3.2135554679070005237824480961601e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.0569509120934873232958750950776
y[1] (numeric) = 3.0569509120934873232958750949797
absolute error = 9.79e-29
relative error = 3.2025375223626107540452765344878e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.0736555618863479097619727731928
y[1] (numeric) = 3.0736555618863479097619727730947
absolute error = 9.81e-29
relative error = 3.1916393370958773948487264028337e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.0903602116792084962280704513079
y[1] (numeric) = 3.0903602116792084962280704512097
absolute error = 9.82e-29
relative error = 3.1776231013096393350438145096026e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.1070648614720690826941681294231
y[1] (numeric) = 3.1070648614720690826941681293247
absolute error = 9.84e-29
relative error = 3.1669760493310051056182028848743e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.1237695112649296691602658075383
y[1] (numeric) = 3.1237695112649296691602658074397
absolute error = 9.86e-29
relative error = 3.1564428695660461085928651812660e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.1404741610577902556263634856535
y[1] (numeric) = 3.1404741610577902556263634855547
absolute error = 9.88e-29
relative error = 3.1460217449049696540890736234408e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.1571788108506508420924611637686
y[1] (numeric) = 3.1571788108506508420924611636697
absolute error = 9.89e-29
relative error = 3.1325435119511964619030998273119e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.1738834606435114285585588418838
y[1] (numeric) = 3.1738834606435114285585588417847
absolute error = 9.91e-29
relative error = 3.1223578694318937050608732614320e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1074.0MB, alloc=42.3MB, time=7.20
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 3.190588110436372015024656519999
y[1] (numeric) = 3.1905881104363720150246565198997
absolute error = 9.93e-29
relative error = 3.1122788828552014482902930470273e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.2072927602292326014907541981142
y[1] (numeric) = 3.2072927602292326014907541980147
absolute error = 9.95e-29
relative error = 3.1023048857220164025277397098560e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.2239974100220931879568518762294
y[1] (numeric) = 3.2239974100220931879568518761297
absolute error = 9.97e-29
relative error = 3.0924342460720767976539174953496e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.2407020598149537744229495543445
y[1] (numeric) = 3.2407020598149537744229495542447
absolute error = 9.98e-29
relative error = 3.0795796144770755581347737255545e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.2574067096078143608890472324597
y[1] (numeric) = 3.2574067096078143608890472323597
absolute error = 1.000e-28
relative error = 3.0699267520094170817437238721420e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.2741113594006749473551449105749
y[1] (numeric) = 3.2741113594006749473551449104747
absolute error = 1.002e-28
relative error = 3.0603723881383673653158479968256e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.2908160091935355338212425886901
y[1] (numeric) = 3.2908160091935355338212425885897
absolute error = 1.004e-28
relative error = 3.0509150228852978490547525872485e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.3075206589863961202873402668052
y[1] (numeric) = 3.3075206589863961202873402667047
absolute error = 1.005e-28
relative error = 3.0385297738638662252258903325406e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.3242253087792567067534379449204
y[1] (numeric) = 3.3242253087792567067534379448197
absolute error = 1.007e-28
relative error = 3.0292772193885888706362127545386e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.3409299585721172932195356230356
y[1] (numeric) = 3.3409299585721172932195356229347
absolute error = 1.009e-28
relative error = 3.0201171904580642895924319523165e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.3576346083649778796856333011508
y[1] (numeric) = 3.3576346083649778796856333010497
absolute error = 1.011e-28
relative error = 3.0110483060940125899520718545942e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.374339258157838466151730979266
y[1] (numeric) = 3.3743392581578384661517309791647
absolute error = 1.013e-28
relative error = 3.0020692126642584318923093816018e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.3910439079506990526178286573811
y[1] (numeric) = 3.3910439079506990526178286572797
absolute error = 1.014e-28
relative error = 2.9902296387922267959270271982199e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.4077485577435596390839263354963
y[1] (numeric) = 3.4077485577435596390839263353947
absolute error = 1.016e-28
relative error = 2.9814406279809103540934635958273e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.4244532075364202255500240136115
y[1] (numeric) = 3.4244532075364202255500240135097
absolute error = 1.018e-28
relative error = 2.9727373636165335848631542724825e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.4411578573292808120161216917267
y[1] (numeric) = 3.4411578573292808120161216916247
absolute error = 1.020e-28
relative error = 2.9641185969644323182467314474225e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.4578625071221413984822193698418
y[1] (numeric) = 3.4578625071221413984822193697397
absolute error = 1.021e-28
relative error = 2.9526911434363038352162642720972e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.474567156915001984948317047957
y[1] (numeric) = 3.4745671569150019849483170478547
absolute error = 1.023e-28
relative error = 2.9442516255990315699598401761262e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.4912718067078625714144147260722
y[1] (numeric) = 3.4912718067078625714144147259697
absolute error = 1.025e-28
relative error = 2.9358928686980011445623292293990e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.5079764565007231578805124041874
y[1] (numeric) = 3.5079764565007231578805124040847
absolute error = 1.027e-28
relative error = 2.9276137190055519613114612440691e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.5246811062935837443466100823026
y[1] (numeric) = 3.5246811062935837443466100821997
absolute error = 1.029e-28
relative error = 2.9194130446656378414089427183159e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.5413857560864443308127077604177
y[1] (numeric) = 3.5413857560864443308127077603147
absolute error = 1.030e-28
relative error = 2.9084659817976010418312591496214e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.5580904058793049172788054385329
y[1] (numeric) = 3.5580904058793049172788054384297
absolute error = 1.032e-28
relative error = 2.9004322045745309555404084132857e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.5747950556721655037449031166481
y[1] (numeric) = 3.5747950556721655037449031165447
absolute error = 1.034e-28
relative error = 2.8924735093815830195887245062617e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.5914997054650260902110007947633
y[1] (numeric) = 3.5914997054650260902110007946597
absolute error = 1.036e-28
relative error = 2.8845888485625229714133353332564e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.6082043552578866766770984728784
y[1] (numeric) = 3.6082043552578866766770984727747
absolute error = 1.037e-28
relative error = 2.8740057322110383110407737166908e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.6249090050507472631431961509936
y[1] (numeric) = 3.6249090050507472631431961508897
absolute error = 1.039e-28
relative error = 2.8662788460408661191091574890108e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1115.0MB, alloc=42.3MB, time=7.48
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 3.6416136548436078496092938291088
y[1] (numeric) = 3.6416136548436078496092938290047
absolute error = 1.041e-28
relative error = 2.8586228487346404610484735203003e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.658318304636468436075391507224
y[1] (numeric) = 3.6583183046364684360753915071197
absolute error = 1.043e-28
relative error = 2.8510367692120333021481610946831e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.6750229544293290225414891853392
y[1] (numeric) = 3.6750229544293290225414891852347
absolute error = 1.045e-28
relative error = 2.8435196540487225719651242365715e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.6917276042221896090075868634543
y[1] (numeric) = 3.6917276042221896090075868633497
absolute error = 1.046e-28
relative error = 2.8333618081781031772093545619946e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 3.7084322540150501954736845415695
y[1] (numeric) = 3.7084322540150501954736845414647
absolute error = 1.048e-28
relative error = 2.8259920317146147514646279752745e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.7251369038079107819397822196847
y[1] (numeric) = 3.7251369038079107819397822195797
absolute error = 1.050e-28
relative error = 2.8186883519010230829014684431438e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.7418415536007713684058798977999
y[1] (numeric) = 3.7418415536007713684058798976947
absolute error = 1.052e-28
relative error = 2.8114498835143384828076228354072e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.758546203393631954871977575915
y[1] (numeric) = 3.7585462033936319548719775758097
absolute error = 1.053e-28
relative error = 2.8016151538837940287993224057168e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.7752508531864925413380752540302
y[1] (numeric) = 3.7752508531864925413380752539247
absolute error = 1.055e-28
relative error = 2.7945162878634395094766707681258e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.7919555029793531278041729321454
y[1] (numeric) = 3.7919555029793531278041729320397
absolute error = 1.057e-28
relative error = 2.7874799669181541929674345634650e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.8086601527722137142702706102606
y[1] (numeric) = 3.8086601527722137142702706101547
absolute error = 1.059e-28
relative error = 2.7805053680864240108135425360381e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.8253648025650743007363682883758
y[1] (numeric) = 3.8253648025650743007363682882697
absolute error = 1.061e-28
relative error = 2.7735916827816085027395971638726e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.8420694523579348872024659664909
y[1] (numeric) = 3.8420694523579348872024659663847
absolute error = 1.062e-28
relative error = 2.7641353524940442759056859855735e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.8587741021507954736685636446061
y[1] (numeric) = 3.8587741021507954736685636444997
absolute error = 1.064e-28
relative error = 2.7573523918048218879661810778876e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.8754787519436560601346613227213
y[1] (numeric) = 3.8754787519436560601346613226147
absolute error = 1.066e-28
relative error = 2.7506279049146445206123615573369e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.8921834017365166466007590008365
y[1] (numeric) = 3.8921834017365166466007590007297
absolute error = 1.068e-28
relative error = 2.7439611389419794053388323331000e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.9088880515293772330668566789517
y[1] (numeric) = 3.9088880515293772330668566788447
absolute error = 1.070e-28
relative error = 2.7373513538750635645548204526599e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.9255927013222378195329543570668
y[1] (numeric) = 3.9255927013222378195329543569597
absolute error = 1.071e-28
relative error = 2.7282504362698157890926298386277e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.942297351115098405999052035182
y[1] (numeric) = 3.9422973511150984059990520350747
absolute error = 1.073e-28
relative error = 2.7217632371046202673671528152018e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.9590020009079589924651497132972
y[1] (numeric) = 3.9590020009079589924651497131897
absolute error = 1.075e-28
relative error = 2.7153307822361774504663633615940e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.9757066507008195789312473914124
y[1] (numeric) = 3.9757066507008195789312473913047
absolute error = 1.077e-28
relative error = 2.7089523816103265900101183571761e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 3.9924113004936801653973450695275
y[1] (numeric) = 3.9924113004936801653973450694197
absolute error = 1.078e-28
relative error = 2.7001226047694542458299087663723e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.0091159502865407518634427476427
y[1] (numeric) = 4.0091159502865407518634427475347
absolute error = 1.080e-28
relative error = 2.6938607248882634892301176978046e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.0258206000794013383295404257579
y[1] (numeric) = 4.0258206000794013383295404256497
absolute error = 1.082e-28
relative error = 2.6876508108152153945108228206774e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.0425252498722619247956381038731
y[1] (numeric) = 4.0425252498722619247956381037647
absolute error = 1.084e-28
relative error = 2.6814922183460767881776378185677e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.0592298996651225112617357819883
y[1] (numeric) = 4.0592298996651225112617357818797
absolute error = 1.086e-28
relative error = 2.6753843138807994049418452856111e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.0759345494579830977278334601034
y[1] (numeric) = 4.0759345494579830977278334599947
memory used=1156.1MB, alloc=42.3MB, time=7.75
absolute error = 1.087e-28
relative error = 2.6668730491380167693926575022893e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.0926391992508436841939311382186
y[1] (numeric) = 4.0926391992508436841939311381097
absolute error = 1.089e-28
relative error = 2.6608746751957541403824019708927e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.1093438490437042706600288163338
y[1] (numeric) = 4.1093438490437042706600288162247
absolute error = 1.091e-28
relative error = 2.6549250685213147847787338828409e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.126048498836564857126126494449
y[1] (numeric) = 4.1260484988365648571261264943397
absolute error = 1.093e-28
relative error = 2.6490236367997048976414922570404e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.1427531486294254435922241725641
y[1] (numeric) = 4.1427531486294254435922241724547
absolute error = 1.094e-28
relative error = 2.6407559435732618792273734421132e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.1594577984222860300583218506793
y[1] (numeric) = 4.1594577984222860300583218505697
absolute error = 1.096e-28
relative error = 2.6349588170259141313665408271253e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.1761624482151466165244195287945
y[1] (numeric) = 4.1761624482151466165244195286847
absolute error = 1.098e-28
relative error = 2.6292080674909451654885948730573e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.1928670980080072029905172069097
y[1] (numeric) = 4.1928670980080072029905172067997
absolute error = 1.100e-28
relative error = 2.6235031406614341196574851417309e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.2095717478008677894566148850249
y[1] (numeric) = 4.2095717478008677894566148849147
absolute error = 1.102e-28
relative error = 2.6178434910289826853012254876373e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.22627639759372837592271256314
y[1] (numeric) = 4.2262763975937283759227125630297
absolute error = 1.103e-28
relative error = 2.6098624326321955455606673875086e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.2429810473865889623888102412552
y[1] (numeric) = 4.2429810473865889623888102411447
absolute error = 1.105e-28
relative error = 2.6043010507449966365697988242118e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.2596856971794495488549079193704
y[1] (numeric) = 4.2596856971794495488549079192597
absolute error = 1.107e-28
relative error = 2.5987832875392659543161135437645e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.2763903469723101353210055974856
y[1] (numeric) = 4.2763903469723101353210055973747
absolute error = 1.109e-28
relative error = 2.5933086318585800430175351795706e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.2930949967651707217871032756007
y[1] (numeric) = 4.2930949967651707217871032754897
absolute error = 1.110e-28
relative error = 2.5855472586476199507526421483469e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.3097996465580313082532009537159
y[1] (numeric) = 4.3097996465580313082532009536047
absolute error = 1.112e-28
relative error = 2.5801663445958217054469344357957e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.3265042963508918947192986318311
y[1] (numeric) = 4.3265042963508918947192986317197
absolute error = 1.114e-28
relative error = 2.5748269820038829060509233078973e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.3432089461437524811853963099463
y[1] (numeric) = 4.3432089461437524811853963098347
absolute error = 1.116e-28
relative error = 2.5695286914318820974194968809829e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.3599135959366130676514939880615
y[1] (numeric) = 4.3599135959366130676514939879497
absolute error = 1.118e-28
relative error = 2.5642710007876360842565105033168e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.3766182457294736541175916661766
y[1] (numeric) = 4.3766182457294736541175916660647
absolute error = 1.119e-28
relative error = 2.5567685760389879935949972042777e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 4.3933228955223342405836893442918
y[1] (numeric) = 4.3933228955223342405836893441797
absolute error = 1.121e-28
relative error = 2.5515993853821236767443700373798e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.410027545315194827049787022407
y[1] (numeric) = 4.4100275453151948270497870222947
absolute error = 1.123e-28
relative error = 2.5464693552605386350213991368978e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.4267321951080554135158847005222
y[1] (numeric) = 4.4267321951080554135158847004097
absolute error = 1.125e-28
relative error = 2.5413780423474183860661487715138e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.4434368449009159999819823786373
y[1] (numeric) = 4.4434368449009159999819823785247
absolute error = 1.126e-28
relative error = 2.5340744997695778520243212428806e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.4601414946937765864480800567525
y[1] (numeric) = 4.4601414946937765864480800566397
absolute error = 1.128e-28
relative error = 2.5290677467115782071174138686006e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.4768461444866371729141777348677
y[1] (numeric) = 4.4768461444866371729141777347547
absolute error = 1.130e-28
relative error = 2.5240983574823696043366774448750e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.4935507942794977593802754129829
y[1] (numeric) = 4.4935507942794977593802754128697
absolute error = 1.132e-28
relative error = 2.5191659153849766789000357157495e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.5102554440723583458463730910981
y[1] (numeric) = 4.5102554440723583458463730909847
absolute error = 1.134e-28
relative error = 2.5142700098957125899481098512843e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1197.2MB, alloc=42.3MB, time=8.03
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 4.5269600938652189323124707692132
y[1] (numeric) = 4.5269600938652189323124707690997
absolute error = 1.135e-28
relative error = 2.5072012486659934893613641549883e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.5436647436580795187785684473284
y[1] (numeric) = 4.5436647436580795187785684472147
absolute error = 1.137e-28
relative error = 2.5023853302270878980838593320293e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.5603693934509401052446661254436
y[1] (numeric) = 4.5603693934509401052446661253297
absolute error = 1.139e-28
relative error = 2.4976046932419471829329296359784e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.5770740432438006917107638035588
y[1] (numeric) = 4.5770740432438006917107638034447
absolute error = 1.141e-28
relative error = 2.4928589514172819474546344632563e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.593778693036661278176861481674
y[1] (numeric) = 4.5937786930366612781768614815597
absolute error = 1.143e-28
relative error = 2.4881477240786142773252723463359e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.6104833428295218646429591597891
y[1] (numeric) = 4.6104833428295218646429591596747
absolute error = 1.144e-28
relative error = 2.4813016660806549369398185557878e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.6271879926223824511090568379043
y[1] (numeric) = 4.6271879926223824511090568377897
absolute error = 1.146e-28
relative error = 2.4766661778756116796291334790887e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.6438926424152430375751545160195
y[1] (numeric) = 4.6438926424152430375751545159047
absolute error = 1.148e-28
relative error = 2.4720640385065759277667267122939e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.6605972922081036240412521941347
y[1] (numeric) = 4.6605972922081036240412521940197
absolute error = 1.150e-28
relative error = 2.4674948893839131920467027897055e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.6773019420009642105073498722498
y[1] (numeric) = 4.6773019420009642105073498721347
absolute error = 1.151e-28
relative error = 2.4608203923384057746856075160104e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.694006591793824796973447550365
y[1] (numeric) = 4.6940065917938247969734475502497
absolute error = 1.153e-28
relative error = 2.4563237768257554789104987786230e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.7107112415866853834395452284802
y[1] (numeric) = 4.7107112415866853834395452283647
absolute error = 1.155e-28
relative error = 2.4518590522032658235309581883092e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.7274158913795459699056429065954
y[1] (numeric) = 4.7274158913795459699056429064797
absolute error = 1.157e-28
relative error = 2.4474258804049633741965026905064e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.7441205411724065563717405847106
y[1] (numeric) = 4.7441205411724065563717405845947
absolute error = 1.159e-28
relative error = 2.4430239281263672801390504004347e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.7608251909652671428378382628257
y[1] (numeric) = 4.7608251909652671428378382627097
absolute error = 1.160e-28
relative error = 2.4365523905422110311944924206264e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.7775298407581277293039359409409
y[1] (numeric) = 4.7775298407581277293039359408247
absolute error = 1.162e-28
relative error = 2.4322192403420063515815048677925e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.7942344905509883157700336190561
y[1] (numeric) = 4.7942344905509883157700336189397
absolute error = 1.164e-28
relative error = 2.4279162863104442132898621759540e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.8109391403438489022361312971713
y[1] (numeric) = 4.8109391403438489022361312970547
absolute error = 1.166e-28
relative error = 2.4236432139041012565141336694754e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.8276437901367094887022289752864
y[1] (numeric) = 4.8276437901367094887022289751697
absolute error = 1.167e-28
relative error = 2.4173283090692837308201056157924e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.8443484399295700751683266534016
y[1] (numeric) = 4.8443484399295700751683266532847
absolute error = 1.169e-28
relative error = 2.4131212163941609340306571561177e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.8610530897224306616344243315168
y[1] (numeric) = 4.8610530897224306616344243313997
absolute error = 1.171e-28
relative error = 2.4089430384453276409992117786401e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.877757739515291248100522009632
y[1] (numeric) = 4.8777577395152912481005220095147
absolute error = 1.173e-28
relative error = 2.4047934781536781376460639722411e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.8944623893081518345666196877472
y[1] (numeric) = 4.8944623893081518345666196876297
absolute error = 1.175e-28
relative error = 2.4006722425056576411417431133261e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.9111670391010124210327173658623
y[1] (numeric) = 4.9111670391010124210327173657447
absolute error = 1.176e-28
relative error = 2.3945428665673453237601046202708e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.9278716888938730074988150439775
y[1] (numeric) = 4.9278716888938730074988150438597
absolute error = 1.178e-28
relative error = 2.3904843193358752469401722395585e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.9445763386867335939649127220927
y[1] (numeric) = 4.9445763386867335939649127219747
absolute error = 1.180e-28
relative error = 2.3864531947208340219906448073644e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.9612809884795941804310104002079
y[1] (numeric) = 4.9612809884795941804310104000897
absolute error = 1.182e-28
relative error = 2.3824492157260961049532354050169e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1238.3MB, alloc=42.3MB, time=8.30
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 4.977985638272454766897108078323
y[1] (numeric) = 4.9779856382724547668971080782047
absolute error = 1.183e-28
relative error = 2.3764632643868871795370836961245e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 4.9946902880653153533632057564382
y[1] (numeric) = 4.9946902880653153533632057563197
absolute error = 1.185e-28
relative error = 2.3725194789985821142606387751011e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.0113949378581759398293034345534
y[1] (numeric) = 5.0113949378581759398293034344347
absolute error = 1.187e-28
relative error = 2.3686019855128657494193701535512e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.0280995876510365262954011126686
y[1] (numeric) = 5.0280995876510365262954011125497
absolute error = 1.189e-28
relative error = 2.3647105218841973338461498284900e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.0448042374438971127614987907838
y[1] (numeric) = 5.0448042374438971127614987906647
absolute error = 1.191e-28
relative error = 2.3608448295378379806277190420054e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.0615088872367576992275964688989
y[1] (numeric) = 5.0615088872367576992275964687797
absolute error = 1.192e-28
relative error = 2.3550289578781152029059774813224e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.0782135370296182856936941470141
y[1] (numeric) = 5.0782135370296182856936941468947
absolute error = 1.194e-28
relative error = 2.3512205449682650629683922011540e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.0949181868224788721597918251293
y[1] (numeric) = 5.0949181868224788721597918250097
absolute error = 1.196e-28
relative error = 2.3474371052578237764074468244622e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.1116228366153394586258895032445
y[1] (numeric) = 5.1116228366153394586258895031247
absolute error = 1.198e-28
relative error = 2.3436783939115030211312135090559e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.1283274864082000450919871813596
y[1] (numeric) = 5.1283274864082000450919871812397
absolute error = 1.199e-28
relative error = 2.3379942158096474293064865144175e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.1450321362010606315580848594748
y[1] (numeric) = 5.1450321362010606315580848593547
absolute error = 1.201e-28
relative error = 2.3342905704118358229187383514166e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.16173678599392121802418253759
y[1] (numeric) = 5.1617367859939212180241825374697
absolute error = 1.203e-28
relative error = 2.3306108968288967835626260988558e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.1784414357867818044902802157052
y[1] (numeric) = 5.1784414357867818044902802155847
absolute error = 1.205e-28
relative error = 2.3269549630755250928475210221180e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.1951460855796423909563778938204
y[1] (numeric) = 5.1951460855796423909563778936997
absolute error = 1.207e-28
relative error = 2.3233225401501493615582365568061e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.2118507353725029774224755719355
y[1] (numeric) = 5.2118507353725029774224755718147
absolute error = 1.208e-28
relative error = 2.3177946977671098967165115234672e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.2285553851653635638885732500507
y[1] (numeric) = 5.2285553851653635638885732499297
absolute error = 1.210e-28
relative error = 2.3142147512352139311100052639997e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.2452600349582241503546709281659
y[1] (numeric) = 5.2452600349582241503546709280447
absolute error = 1.212e-28
relative error = 2.3106576069105274939468525475861e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.2619646847510847368207686062811
y[1] (numeric) = 5.2619646847510847368207686061597
absolute error = 1.214e-28
relative error = 2.3071230476291723992418785785783e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.2786693345439453232868662843962
y[1] (numeric) = 5.2786693345439453232868662842747
absolute error = 1.215e-28
relative error = 2.3017164421513643737092777797698e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.2953739843368059097529639625114
y[1] (numeric) = 5.2953739843368059097529639623897
absolute error = 1.217e-28
relative error = 2.2982323884956303304542959959539e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.3120786341296664962190616406266
y[1] (numeric) = 5.3120786341296664962190616405047
absolute error = 1.219e-28
relative error = 2.2947702471270392686034335944262e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.3287832839225270826851593187418
y[1] (numeric) = 5.3287832839225270826851593186197
absolute error = 1.221e-28
relative error = 2.2913298119739252667014794211212e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.345487933715387669151256996857
y[1] (numeric) = 5.3454879337153876691512569967347
absolute error = 1.223e-28
relative error = 2.2879108795405182273114124613993e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.3621925835082482556173546749721
y[1] (numeric) = 5.3621925835082482556173546748497
absolute error = 1.224e-28
relative error = 2.2826483400922357291918754324077e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.3788972333011088420834523530873
y[1] (numeric) = 5.3788972333011088420834523529647
absolute error = 1.226e-28
relative error = 2.2792776043568054091070561059410e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.3956018830939694285495500312025
y[1] (numeric) = 5.3956018830939694285495500310797
absolute error = 1.228e-28
relative error = 2.2759277400500774439453625957372e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1279.4MB, alloc=42.3MB, time=8.58
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = 5.4123065328868300150156477093177
y[1] (numeric) = 5.4123065328868300150156477091947
absolute error = 1.230e-28
relative error = 2.2725985539180823674575066997940e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.4290111826796906014817453874328
y[1] (numeric) = 5.4290111826796906014817453873097
absolute error = 1.231e-28
relative error = 2.2674478990341554565759144519641e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.445715832472551187947843065548
y[1] (numeric) = 5.4457158324725511879478430654247
absolute error = 1.233e-28
relative error = 2.2641651491392153253038412552100e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.4624204822654117744139407436632
y[1] (numeric) = 5.4624204822654117744139407435397
absolute error = 1.235e-28
relative error = 2.2609024772252840021741048975798e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.4791251320582723608800384217784
y[1] (numeric) = 5.4791251320582723608800384216547
absolute error = 1.237e-28
relative error = 2.2576596996522912846732083957888e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.4958297818511329473461360998936
y[1] (numeric) = 5.4958297818511329473461360997697
absolute error = 1.239e-28
relative error = 2.2544366350128729909869070095102e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.5125344316439935338122337780087
y[1] (numeric) = 5.5125344316439935338122337778847
absolute error = 1.240e-28
relative error = 2.2494190564723546980776740372241e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.5292390814368541202783314561239
y[1] (numeric) = 5.5292390814368541202783314559997
absolute error = 1.242e-28
relative error = 2.2462403627467091330136328839700e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.5459437312297147067444291342391
y[1] (numeric) = 5.5459437312297147067444291341147
absolute error = 1.244e-28
relative error = 2.2430808177784469749680498099524e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.5626483810225752932105268123543
y[1] (numeric) = 5.5626483810225752932105268122297
absolute error = 1.246e-28
relative error = 2.2399402490562404454993170847278e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.5793530308154358796766244904695
y[1] (numeric) = 5.5793530308154358796766244903447
absolute error = 1.248e-28
relative error = 2.2368184861347656916561456333068e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.5960576806082964661427221685846
y[1] (numeric) = 5.5960576806082964661427221684597
absolute error = 1.249e-28
relative error = 2.2319283883153838129674407990434e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.6127623304011570526088198466998
y[1] (numeric) = 5.6127623304011570526088198465747
absolute error = 1.251e-28
relative error = 2.2288490521396941964463473809217e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.629466980194017639074917524815
y[1] (numeric) = 5.6294669801940176390749175246897
absolute error = 1.253e-28
relative error = 2.2257879909561451711212248436196e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.6461716299868782255410152029302
y[1] (numeric) = 5.6461716299868782255410152028047
absolute error = 1.255e-28
relative error = 2.2227450425606644832240616112720e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.6628762797797388120071128810453
y[1] (numeric) = 5.6628762797797388120071128809197
absolute error = 1.256e-28
relative error = 2.2179541595933523057836957249706e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.6795809295725993984732105591605
y[1] (numeric) = 5.6795809295725993984732105590347
absolute error = 1.258e-28
relative error = 2.2149521515747944244780967737505e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.6962855793654599849393082372757
y[1] (numeric) = 5.6962855793654599849393082371497
absolute error = 1.260e-28
relative error = 2.2119677506413893753209177577281e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.7129902291583205714054059153909
y[1] (numeric) = 5.7129902291583205714054059152647
absolute error = 1.262e-28
relative error = 2.2090008023450217825915585020334e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.7296948789511811578715035935061
y[1] (numeric) = 5.7296948789511811578715035933797
absolute error = 1.264e-28
relative error = 2.2060511540387204732017290379171e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.7463995287440417443376012716212
y[1] (numeric) = 5.7463995287440417443376012714947
absolute error = 1.265e-28
relative error = 2.2013784347439620890672473434902e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.7631041785369023308036989497364
y[1] (numeric) = 5.7631041785369023308036989496097
absolute error = 1.267e-28
relative error = 2.1984679796672655979739511260022e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 5.7798088283297629172697966278516
y[1] (numeric) = 5.7798088283297629172697966277247
absolute error = 1.269e-28
relative error = 2.1955743480303187975806161583263e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.7965134781226235037358943059668
y[1] (numeric) = 5.7965134781226235037358943058397
absolute error = 1.271e-28
relative error = 2.1926973943855157827803263489655e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.8132181279154840902019919840819
y[1] (numeric) = 5.8132181279154840902019919839547
absolute error = 1.272e-28
relative error = 2.1881167573805052096428542219716e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.8299227777083446766680896621971
y[1] (numeric) = 5.8299227777083446766680896620697
absolute error = 1.274e-28
relative error = 2.1852776590306575519128748468660e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.8466274275012052631341873403123
y[1] (numeric) = 5.8466274275012052631341873401847
absolute error = 1.276e-28
relative error = 2.1824547840999518807984953539039e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1320.4MB, alloc=42.3MB, time=8.84
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 5.8633320772940658496002850184275
y[1] (numeric) = 5.8633320772940658496002850182997
absolute error = 1.278e-28
relative error = 2.1796479939266861280380439492208e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.8800367270869264360663826965427
y[1] (numeric) = 5.8800367270869264360663826964147
absolute error = 1.280e-28
relative error = 2.1768571514248593852364587457007e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.8967413768797870225324803746578
y[1] (numeric) = 5.8967413768797870225324803745297
absolute error = 1.281e-28
relative error = 2.1723862691733494049126728176819e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.913446026672647608998578052773
y[1] (numeric) = 5.9134460266726476089985780526447
absolute error = 1.283e-28
relative error = 2.1696317074900452333221851891295e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.9301506764655081954646757308882
y[1] (numeric) = 5.9301506764655081954646757307597
absolute error = 1.285e-28
relative error = 2.1668926644641117894589679134140e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.9468553262583687819307734090034
y[1] (numeric) = 5.9468553262583687819307734088747
absolute error = 1.287e-28
relative error = 2.1641690093203465110107125325059e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.9635599760512293683968710871185
y[1] (numeric) = 5.9635599760512293683968710869897
absolute error = 1.288e-28
relative error = 2.1597837620019193116267610300482e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.9802646258440899548629687652337
y[1] (numeric) = 5.9802646258440899548629687651047
absolute error = 1.290e-28
relative error = 2.1570951800781253265716026258026e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.9969692756369505413290664433489
y[1] (numeric) = 5.9969692756369505413290664432197
absolute error = 1.292e-28
relative error = 2.1544215763266087453329074995751e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.0136739254298111277951641214641
y[1] (numeric) = 6.0136739254298111277951641213347
absolute error = 1.294e-28
relative error = 2.1517628259292672562122051240489e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.0303785752226717142612617995793
y[1] (numeric) = 6.0303785752226717142612617994497
absolute error = 1.296e-28
relative error = 2.1491188054510246119065758918774e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.0470832250155323007273594776944
y[1] (numeric) = 6.0470832250155323007273594775647
absolute error = 1.297e-28
relative error = 2.1448357029957506111304252019967e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.0637878748083928871934571558096
y[1] (numeric) = 6.0637878748083928871934571556797
absolute error = 1.299e-28
relative error = 2.1422253331067366222895150838373e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.0804925246012534736595548339248
y[1] (numeric) = 6.0804925246012534736595548337947
absolute error = 1.301e-28
relative error = 2.1396293059094205125081704058876e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.09719717439411406012565251204
y[1] (numeric) = 6.0971971743941140601256525119097
absolute error = 1.303e-28
relative error = 2.1370475035186650389448056987759e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.1139018241869746465917501901551
y[1] (numeric) = 6.1139018241869746465917501900247
absolute error = 1.304e-28
relative error = 2.1328441926255589495786724213341e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.1306064739798352330578478682703
y[1] (numeric) = 6.1306064739798352330578478681397
absolute error = 1.306e-28
relative error = 2.1302949480496954992034718215761e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.1473111237726958195239455463855
y[1] (numeric) = 6.1473111237726958195239455462547
absolute error = 1.308e-28
relative error = 2.1277595580639182632324842685558e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.1640157735655564059900432245007
y[1] (numeric) = 6.1640157735655564059900432243697
absolute error = 1.310e-28
relative error = 2.1252379100292834513046999001048e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.1807204233584169924561409026159
y[1] (numeric) = 6.1807204233584169924561409024847
absolute error = 1.312e-28
relative error = 2.1227298925245655843062549066184e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.197425073151277578922238580731
y[1] (numeric) = 6.1974250731512775789222385805997
absolute error = 1.313e-28
relative error = 2.1186218219696256132729227536493e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.2141297229441381653883362588462
y[1] (numeric) = 6.2141297229441381653883362587147
absolute error = 1.315e-28
relative error = 2.1161450736129429440487483707366e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.2308343727369987518544339369614
y[1] (numeric) = 6.2308343727369987518544339368297
absolute error = 1.317e-28
relative error = 2.1136816054083068306917277378664e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.2475390225298593383205316150766
y[1] (numeric) = 6.2475390225298593383205316149447
absolute error = 1.319e-28
relative error = 2.1112313108304334772991831511612e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.2642436723227199247866292931918
y[1] (numeric) = 6.2642436723227199247866292930597
absolute error = 1.321e-28
relative error = 2.1087940844903087817913988022518e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.2809483221155805112527269713069
y[1] (numeric) = 6.2809483221155805112527269711747
absolute error = 1.322e-28
relative error = 2.1047777058524139082519004707433e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.2976529719084410977188246494221
y[1] (numeric) = 6.2976529719084410977188246492897
absolute error = 1.324e-28
relative error = 2.1023705274105870083941502103704e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1361.5MB, alloc=42.3MB, time=9.13
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 6.3143576217013016841849223275373
y[1] (numeric) = 6.3143576217013016841849223274047
absolute error = 1.326e-28
relative error = 2.0999760853626322085356473058724e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.3310622714941622706510200056525
y[1] (numeric) = 6.3310622714941622706510200055197
absolute error = 1.328e-28
relative error = 2.0975942788927668799165032557517e-27 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.3477669212870228571171176837676
y[1] (numeric) = 6.3477669212870228571171176836347
absolute error = 1.329e-28
relative error = 2.0936496510973696942613020002236e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.3644715710798834435832153618828
y[1] (numeric) = 6.3644715710798834435832153617497
absolute error = 1.331e-28
relative error = 2.0912969523629505419453407149478e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.381176220872744030049313039998
y[1] (numeric) = 6.3811762208727440300493130398647
absolute error = 1.333e-28
relative error = 2.0889565714229524323116619494901e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.3978808706656046165154107181132
y[1] (numeric) = 6.3978808706656046165154107179797
absolute error = 1.335e-28
relative error = 2.0866284117933459577152347702751e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.4145855204584652029815083962284
y[1] (numeric) = 6.4145855204584652029815083960947
absolute error = 1.337e-28
relative error = 2.0843123779951436835073306492852e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.4312901702513257894476060743435
y[1] (numeric) = 6.4312901702513257894476060742097
absolute error = 1.338e-28
relative error = 2.0804534775760441838902727155340e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.4479948200441863759137037524587
y[1] (numeric) = 6.4479948200441863759137037523247
absolute error = 1.340e-28
relative error = 2.0781654411918670555949094502350e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 6.4646994698370469623798014305739
y[1] (numeric) = 6.4646994698370469623798014304397
absolute error = 1.342e-28
relative error = 2.0758892292851275351977134369531e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.4814041196299075488458991086891
y[1] (numeric) = 6.4814041196299075488458991085547
absolute error = 1.344e-28
relative error = 2.0736247504294536824314308051829e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.4981087694227681353119967868042
y[1] (numeric) = 6.4981087694227681353119967866697
absolute error = 1.345e-28
relative error = 2.0698330048413107072347948035117e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.5148134192156287217780944649194
y[1] (numeric) = 6.5148134192156287217780944647847
absolute error = 1.347e-28
relative error = 2.0675956674783424045543980278877e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.5315180690084893082441921430346
y[1] (numeric) = 6.5315180690084893082441921428997
absolute error = 1.349e-28
relative error = 2.0653697742962588502253076296325e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.5482227188013498947102898211498
y[1] (numeric) = 6.5482227188013498947102898210147
absolute error = 1.351e-28
relative error = 2.0631552377120430691325901415726e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.564927368594210481176387499265
y[1] (numeric) = 6.5649273685942104811763874991297
absolute error = 1.353e-28
relative error = 2.0609519710341082843813114193552e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.5816320183870710676424851773801
y[1] (numeric) = 6.5816320183870710676424851772447
absolute error = 1.354e-28
relative error = 2.0572405084595086093725771927961e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.5983366681799316541085828554953
y[1] (numeric) = 6.5983366681799316541085828553597
absolute error = 1.356e-28
relative error = 2.0550633715603292778599378892957e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.6150413179727922405746805336105
y[1] (numeric) = 6.6150413179727922405746805334747
absolute error = 1.358e-28
relative error = 2.0528972303020548924660492893483e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.6317459677656528270407782117257
y[1] (numeric) = 6.6317459677656528270407782115897
absolute error = 1.360e-28
relative error = 2.0507420015942000253864875841110e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.6484506175585134135068758898408
y[1] (numeric) = 6.6484506175585134135068758897047
absolute error = 1.361e-28
relative error = 2.0470934933405508703753155704702e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.665155267351373999972973567956
y[1] (numeric) = 6.6651552673513739999729735678197
absolute error = 1.363e-28
relative error = 2.0449636134907842583239489958829e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.6818599171442345864390712460712
y[1] (numeric) = 6.6818599171442345864390712459347
absolute error = 1.365e-28
relative error = 2.0428443830402664793328392541685e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.6985645669370951729051689241864
y[1] (numeric) = 6.6985645669370951729051689240497
absolute error = 1.367e-28
relative error = 2.0407357223176814573441789375998e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.7152692167299557593712666023016
y[1] (numeric) = 6.7152692167299557593712666021647
absolute error = 1.369e-28
relative error = 2.0386375524444625299922781250937e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.7319738665228163458373642804167
y[1] (numeric) = 6.7319738665228163458373642802797
absolute error = 1.370e-28
relative error = 2.0350643468965651945107588894361e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1402.6MB, alloc=42.3MB, time=9.39
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 6.7486785163156769323034619585319
y[1] (numeric) = 6.7486785163156769323034619583947
absolute error = 1.372e-28
relative error = 2.0329906020608897179448412988933e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.7653831661085375187695596366471
y[1] (numeric) = 6.7653831661085375187695596365097
absolute error = 1.374e-28
relative error = 2.0309270979404521449669035483037e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.7820878159013981052356573147623
y[1] (numeric) = 6.7820878159013981052356573146247
absolute error = 1.376e-28
relative error = 2.0288737588649428358952610575693e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.7987924656942586917017549928774
y[1] (numeric) = 6.7987924656942586917017549927397
absolute error = 1.377e-28
relative error = 2.0253596604811022793720295221824e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.8154971154871192781678526709926
y[1] (numeric) = 6.8154971154871192781678526708547
absolute error = 1.379e-28
relative error = 2.0233300324732654420742550682313e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.8322017652799798646339503491078
y[1] (numeric) = 6.8322017652799798646339503489697
absolute error = 1.381e-28
relative error = 2.0213103292967627702400394135660e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.848906415072840451100048027223
y[1] (numeric) = 6.8489064150728404511000480270847
absolute error = 1.383e-28
relative error = 2.0193004783308771846098931035576e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.8656110648657010375661457053382
y[1] (numeric) = 6.8656110648657010375661457051997
absolute error = 1.385e-28
relative error = 2.0173004076616625750655382597780e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.8823157146585616240322433834533
y[1] (numeric) = 6.8823157146585616240322433833147
absolute error = 1.386e-28
relative error = 2.0138570467611290162205734245724e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.8990203644514222104983410615685
y[1] (numeric) = 6.8990203644514222104983410614297
absolute error = 1.388e-28
relative error = 2.0118798418858809378807658673946e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.9157250142442827969644387396837
y[1] (numeric) = 6.9157250142442827969644387395447
absolute error = 1.390e-28
relative error = 2.0099121887250060386633728394785e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.9324296640371433834305364177989
y[1] (numeric) = 6.9324296640371433834305364176597
absolute error = 1.392e-28
relative error = 2.0079540182299666811289551996487e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.949134313830003969896634095914
y[1] (numeric) = 6.9491343138300039698966340957747
absolute error = 1.393e-28
relative error = 2.0045662338511490600948471971377e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.9658389636228645563627317740292
y[1] (numeric) = 6.9658389636228645563627317738897
absolute error = 1.395e-28
relative error = 2.0026302750967906035044040439315e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.9825436134157251428288294521444
y[1] (numeric) = 6.9825436134157251428288294520047
absolute error = 1.397e-28
relative error = 2.0007035793029793165627189919368e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 6.9992482632085857292949271302596
y[1] (numeric) = 6.9992482632085857292949271301197
absolute error = 1.399e-28
relative error = 1.9987860801478019737114477110733e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.0159529130014463157610248083748
y[1] (numeric) = 7.0159529130014463157610248082347
absolute error = 1.401e-28
relative error = 1.9968777119409826182070872458329e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.0326575627943069022271224864899
y[1] (numeric) = 7.0326575627943069022271224863497
absolute error = 1.402e-28
relative error = 1.9935564720471604179998020650948e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.0493622125871674886932201646051
y[1] (numeric) = 7.0493622125871674886932201644647
absolute error = 1.404e-28
relative error = 1.9916695406756829588620775396091e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.0660668623800280751593178427203
y[1] (numeric) = 7.0660668623800280751593178425797
absolute error = 1.406e-28
relative error = 1.9897915309655363624153115225181e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.0827715121728886616254155208355
y[1] (numeric) = 7.0827715121728886616254155206947
absolute error = 1.408e-28
relative error = 1.9879223797917583819895208168286e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.0994761619657492480915131989506
y[1] (numeric) = 7.0994761619657492480915131988097
absolute error = 1.409e-28
relative error = 1.9846534699961115065752867117421e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.1161808117586098345576108770658
y[1] (numeric) = 7.1161808117586098345576108769247
absolute error = 1.411e-28
relative error = 1.9828051553559414623389129220669e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.132885461551470421023708555181
y[1] (numeric) = 7.1328854615514704210237085550397
absolute error = 1.413e-28
relative error = 1.9809654979272007859912340915940e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.1495901113443310074898062332962
y[1] (numeric) = 7.1495901113443310074898062331547
absolute error = 1.415e-28
relative error = 1.9791344370285009539255537603289e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 7.1662947611371915939559039114114
y[1] (numeric) = 7.1662947611371915939559039112697
absolute error = 1.417e-28
relative error = 1.9773119125442472749231166940115e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.1829994109300521804220015895265
y[1] (numeric) = 7.1829994109300521804220015893847
absolute error = 1.418e-28
relative error = 1.9741056888328463192394350881070e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1443.7MB, alloc=42.3MB, time=9.67
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 7.1997040607229127668880992676417
y[1] (numeric) = 7.1997040607229127668880992674997
absolute error = 1.420e-28
relative error = 1.9723032891679990485727079818936e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.2164087105157733533541969457569
y[1] (numeric) = 7.2164087105157733533541969456147
absolute error = 1.422e-28
relative error = 1.9705092339460445893442527604312e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.2331133603086339398202946238721
y[1] (numeric) = 7.2331133603086339398202946237297
absolute error = 1.424e-28
relative error = 1.9687234653532908435533423667815e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.2498180101014945262863923019873
y[1] (numeric) = 7.2498180101014945262863923018447
absolute error = 1.426e-28
relative error = 1.9669459261088908016600859380796e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.2665226598943551127524899801024
y[1] (numeric) = 7.2665226598943551127524899799597
absolute error = 1.427e-28
relative error = 1.9638003853974722856354421224864e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.2832273096872156992185876582176
y[1] (numeric) = 7.2832273096872156992185876580747
absolute error = 1.429e-28
relative error = 1.9620422914706057727369205862196e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.2999319594800762856846853363328
y[1] (numeric) = 7.2999319594800762856846853361897
absolute error = 1.431e-28
relative error = 1.9602922437402008914763785535512e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.316636609272936872150783014448
y[1] (numeric) = 7.3166366092729368721507830143047
absolute error = 1.433e-28
relative error = 1.9585501870953229731439668497991e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.3333412590657974586168806925631
y[1] (numeric) = 7.3333412590657974586168806924197
absolute error = 1.434e-28
relative error = 1.9554524320373423657585364609728e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.3500459088586580450829783706783
y[1] (numeric) = 7.3500459088586580450829783705347
absolute error = 1.436e-28
relative error = 1.9537292934038112982497217242664e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.3667505586515186315490760487935
y[1] (numeric) = 7.3667505586515186315490760486497
absolute error = 1.438e-28
relative error = 1.9520139694579606437454821110824e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.3834552084443792180151737269087
y[1] (numeric) = 7.3834552084443792180151737267647
absolute error = 1.440e-28
relative error = 1.9503064071589237931077775187726e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.4001598582372398044812714050239
y[1] (numeric) = 7.4001598582372398044812714048797
absolute error = 1.442e-28
relative error = 1.9486065539447584406670828794754e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.416864508030100390947369083139
y[1] (numeric) = 7.4168645080301003909473690829947
absolute error = 1.443e-28
relative error = 1.9455660790859680755550850039700e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.4335691578229609774134667612542
y[1] (numeric) = 7.4335691578229609774134667611097
absolute error = 1.445e-28
relative error = 1.9438845180841651645131186383659e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.4502738076158215638795644393694
y[1] (numeric) = 7.4502738076158215638795644392247
absolute error = 1.447e-28
relative error = 1.9422104977146573337897261129663e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.4669784574086821503456621174846
y[1] (numeric) = 7.4669784574086821503456621173397
absolute error = 1.449e-28
relative error = 1.9405439673691741466042458583738e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.4836831072015427368117597955997
y[1] (numeric) = 7.4836831072015427368117597954547
absolute error = 1.450e-28
relative error = 1.9375486364523720532657096536789e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.5003877569944033232778574737149
y[1] (numeric) = 7.5003877569944033232778574735697
absolute error = 1.452e-28
relative error = 1.9358999121691455512804409290831e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.5170924067872639097439551518301
y[1] (numeric) = 7.5170924067872639097439551516847
absolute error = 1.454e-28
relative error = 1.9342585155494000559706622877076e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.5337970565801244962100528299453
y[1] (numeric) = 7.5337970565801244962100528297997
absolute error = 1.456e-28
relative error = 1.9326243978503629664050511791099e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.5505017063729850826761505080605
y[1] (numeric) = 7.5505017063729850826761505079147
absolute error = 1.458e-28
relative error = 1.9309975107606136515720312701077e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.5672063561658456691422481861756
y[1] (numeric) = 7.5672063561658456691422481860297
absolute error = 1.459e-28
relative error = 1.9280563147471064168686493603615e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.5839110059587062556083458642908
y[1] (numeric) = 7.5839110059587062556083458641447
absolute error = 1.461e-28
relative error = 1.9264466564178918050735202919689e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.600615655751566842074443542406
y[1] (numeric) = 7.6006156557515668420744435422597
absolute error = 1.463e-28
relative error = 1.9248440735099045102533148678330e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.6173203055444274285405412205212
y[1] (numeric) = 7.6173203055444274285405412203747
absolute error = 1.465e-28
relative error = 1.9232485194743206684805664850311e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.6340249553372880150066388986363
y[1] (numeric) = 7.6340249553372880150066388984897
absolute error = 1.466e-28
relative error = 1.9203500231880351447660357622084e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1484.8MB, alloc=42.3MB, time=9.94
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 7.6507296051301486014727365767515
y[1] (numeric) = 7.6507296051301486014727365766047
absolute error = 1.468e-28
relative error = 1.9187712489742701611789484620947e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.6674342549230091879388342548667
y[1] (numeric) = 7.6674342549230091879388342547197
absolute error = 1.470e-28
relative error = 1.9171993539509790990889726534848e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.6841389047158697744049319329819
y[1] (numeric) = 7.6841389047158697744049319328347
absolute error = 1.472e-28
relative error = 1.9156342932538762590080836962166e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.7008435545087303608710296110971
y[1] (numeric) = 7.7008435545087303608710296109497
absolute error = 1.474e-28
relative error = 1.9140760224079539084720142138173e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.7175482043015909473371272892122
y[1] (numeric) = 7.7175482043015909473371272890647
absolute error = 1.475e-28
relative error = 1.9112287490188497578712956249456e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.7342528540944515338032249673274
y[1] (numeric) = 7.7342528540944515338032249671797
absolute error = 1.477e-28
relative error = 1.9096867245788169779663469352807e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.7509575038873121202693226454426
y[1] (numeric) = 7.7509575038873121202693226452947
absolute error = 1.479e-28
relative error = 1.9081513467958533048713333692783e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.7676621536801727067354203235578
y[1] (numeric) = 7.7676621536801727067354203234097
absolute error = 1.481e-28
relative error = 1.9066225727883002282197392164629e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.7843668034730332932015180016729
y[1] (numeric) = 7.7843668034730332932015180015247
absolute error = 1.482e-28
relative error = 1.9038157340412048121311561412239e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.8010714532658938796676156797881
y[1] (numeric) = 7.8010714532658938796676156796397
absolute error = 1.484e-28
relative error = 1.9023027912130302250856505655684e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.8177761030587544661337133579033
y[1] (numeric) = 7.8177761030587544661337133577547
absolute error = 1.486e-28
relative error = 1.9007963139524974097796556975013e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.8344807528516150525998110360185
y[1] (numeric) = 7.8344807528516150525998110358697
absolute error = 1.488e-28
relative error = 1.8992962609020308324920232808971e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 7.8511854026444756390659087141337
y[1] (numeric) = 7.8511854026444756390659087139847
absolute error = 1.490e-28
relative error = 1.8978025910560343257460403639380e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.8678900524373362255320063922488
y[1] (numeric) = 7.8678900524373362255320063920997
absolute error = 1.491e-28
relative error = 1.8950442749744755189630127329213e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.884594702230196811998104070364
y[1] (numeric) = 7.8845947022301968119981040702147
absolute error = 1.493e-28
relative error = 1.8935659426827577162997013760934e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.9012993520230573984642017484792
y[1] (numeric) = 7.9012993520230573984642017483297
absolute error = 1.495e-28
relative error = 1.8920938612675376633305266423387e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.9180040018159179849302994265944
y[1] (numeric) = 7.9180040018159179849302994264447
absolute error = 1.497e-28
relative error = 1.8906279911663058806270446289796e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.9347086516087785713963971047096
y[1] (numeric) = 7.9347086516087785713963971045597
absolute error = 1.499e-28
relative error = 1.8891682931497108633244193819926e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.9514133014016391578624947828247
y[1] (numeric) = 7.9514133014016391578624947826747
absolute error = 1.500e-28
relative error = 1.8864570902578875975000824214318e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.9681179511944997443285924609399
y[1] (numeric) = 7.9681179511944997443285924607897
absolute error = 1.502e-28
relative error = 1.8850122565954678596895582492907e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 7.9848226009873603307946901390551
y[1] (numeric) = 7.9848226009873603307946901389047
absolute error = 1.504e-28
relative error = 1.8835734682621795852171534251502e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.0015272507802209172607878171703
y[1] (numeric) = 8.0015272507802209172607878170197
absolute error = 1.506e-28
relative error = 1.8821406873958361469638400616533e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.0182319005730815037268854952854
y[1] (numeric) = 8.0182319005730815037268854951347
absolute error = 1.507e-28
relative error = 1.8794667187067653140137904493480e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.0349365503659420901929831734006
y[1] (numeric) = 8.0349365503659420901929831732497
absolute error = 1.509e-28
relative error = 1.8780484332900852877099781039442e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.0516412001588026766590808515158
y[1] (numeric) = 8.0516412001588026766590808513647
absolute error = 1.511e-28
relative error = 1.8766360328751342241709118678574e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.068345849951663263125178529631
y[1] (numeric) = 8.0683458499516632631251785294797
absolute error = 1.513e-28
relative error = 1.8752294809091063534415312062472e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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=1525.8MB, alloc=42.3MB, time=10.22
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 8.0850504997445238495912762077462
y[1] (numeric) = 8.0850504997445238495912762075947
absolute error = 1.515e-28
relative error = 1.8738287411412852094507017043958e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.1017551495373844360573738858613
y[1] (numeric) = 8.1017551495373844360573738857097
absolute error = 1.516e-28
relative error = 1.8711994771732451086702673218198e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.1184597993302450225234715639765
y[1] (numeric) = 8.1184597993302450225234715638247
absolute error = 1.518e-28
relative error = 1.8698127939553653299731681139769e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.1351644491231056089895692420917
y[1] (numeric) = 8.1351644491231056089895692419397
absolute error = 1.520e-28
relative error = 1.8684318055350949138169194162277e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.1518690989159661954556669202069
y[1] (numeric) = 8.1518690989159661954556669200547
absolute error = 1.522e-28
relative error = 1.8670564769034321633006553442890e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.168573748708826781921764598322
y[1] (numeric) = 8.1685737487088267819217645981697
absolute error = 1.523e-28
relative error = 1.8644625694182346258111653050472e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.1852783985016873683878622764372
y[1] (numeric) = 8.1852783985016873683878622762847
absolute error = 1.525e-28
relative error = 1.8631009548546947034357956866903e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.2019830482945479548539599545524
y[1] (numeric) = 8.2019830482945479548539599543997
absolute error = 1.527e-28
relative error = 1.8617448865826559620069652521148e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.2186876980874085413200576326676
y[1] (numeric) = 8.2186876980874085413200576325147
absolute error = 1.529e-28
relative error = 1.8603943307832677845676829087368e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.2353923478802691277861553107828
y[1] (numeric) = 8.2353923478802691277861553106297
absolute error = 1.531e-28
relative error = 1.8590492539120718512559432929181e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.2520969976731297142522529888979
y[1] (numeric) = 8.2520969976731297142522529887447
absolute error = 1.532e-28
relative error = 1.8564978095046422246965993311006e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.2688016474659903007183506670131
y[1] (numeric) = 8.2688016474659903007183506668597
absolute error = 1.534e-28
relative error = 1.8551660390476301649737376199472e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.2855062972588508871844483451283
y[1] (numeric) = 8.2855062972588508871844483449747
absolute error = 1.536e-28
relative error = 1.8538396386327834764594358350483e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.3022109470517114736505460232435
y[1] (numeric) = 8.3022109470517114736505460230897
absolute error = 1.538e-28
relative error = 1.8525185758453607182812076991833e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.3189155968445720601166437013586
y[1] (numeric) = 8.3189155968445720601166437012047
absolute error = 1.539e-28
relative error = 1.8500007387786869745315266117454e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 8.3356202466374326465827413794738
y[1] (numeric) = 8.3356202466374326465827413793197
absolute error = 1.541e-28
relative error = 1.8486926640181759238047701502191e-27 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 32
h = 0.001
NO POLE (given) for Equation 1
NO 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 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ;
Iterations = 10000
Total Elapsed Time = 10 Seconds
Elapsed Time(since restart) = 10 Seconds
Time to Timeout = 2 Minutes 49 Seconds
Percent Done = 100 %
> quit
memory used=1551.1MB, alloc=42.3MB, time=10.38