|\^/| 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. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > 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