|\^/| Maple 18 (X86 64 WINDOWS) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > 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 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > 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 14 # Begin Function number 15 > 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 15 # Begin Function number 16 > 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 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > 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 18 # Begin Function number 19 > 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 19 # Begin Function number 20 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 21 # Begin Function number 22 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 22 # Begin Function number 23 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 23 # Begin Function number 24 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 24 # Begin Function number 25 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 25 # Begin Function number 26 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 27 # Begin Function number 28 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 28 # Begin Function number 29 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 29 # Begin Function number 30 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := sqrt(rcs)*float_abs(glob_h) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 30 # Begin Function number 31 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 31 # Begin Function number 32 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 32 # Begin Function number 33 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 33 # Begin Function number 34 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 35 # Begin Function number 36 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 36 # Begin Function number 37 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 37 # Begin Function number 38 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 38 # Begin Function number 39 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 39 # Begin Function number 40 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 40 # Begin Function number 41 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 41 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(10.0) * exp(c(0.1) * c(x) + c(0.2))); > end; exact_soln_y := proc(x) return c(10.0)*exp(c(0.1)*c(x) + c(0.2)) 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, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > 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_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, 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, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > 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_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, 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, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > 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_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, 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, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > 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_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, 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, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 3 > if (iter >= 0) then # if number 4 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := float_abs(numeric_val - closed_form_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5 > relerr := abserr*glob__100/float_abs(closed_form_val_y); > if (c(relerr) > c(glob_prec)) then # if number 6 > glob_good_digits := -int_trunc(log10(c(relerr))) + 3; > else > glob_good_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 5; > if (glob_good_digits < glob_min_good_digits) then # if number 5 > glob_min_good_digits := glob_good_digits; > fi;# end if 5; > if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5 > glob_min_apfp_est_good_digits := glob_apfp_est_good_digits; > fi;# end if 5; > if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5 > est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*21*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 6 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 5; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > array_est_rel_error[1] := est_rel_err; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," "); > omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," "); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_float(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := float_abs(numeric_val - closed_form_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if c(glob_prec) < c(float_abs(closed_form_val_y)) then relerr := abserr*glob__100/float_abs(closed_form_val_y); if c(glob_prec) < c(relerr) then glob_good_digits := -int_trunc(log10(c(relerr))) + 3 else glob_good_digits := Digits end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits end if; if glob_prec < evalf(float_abs(numeric_val)) then est_rel_err := evalf(array_max_est_error[1]*100.0* sqrt(glob_iter)*21*ATS_MAX_TERMS/float_abs(numeric_val)) ; if glob_prec < evalf(est_rel_err) then glob_est_digits := -int_trunc(log10(est_rel_err)) + 3 else glob_est_digits := Digits end if else relerr := glob__m1; glob_est_digits := -16 end if; array_est_digits[1] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; array_est_rel_error[1] := est_rel_err; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4, " "); omniout_int(INFO, "Estimated correct digits ", 32, glob_est_digits, 4, " "); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > 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_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, 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, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > 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_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, 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, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > 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 mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre exp 1 $eq_no = 1 > array_tmp3[1] := exp(array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[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_tmp4[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 mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre exp ID_LINEAR iii = 2 $eq_no = 1 > array_tmp3[2] := array_tmp3[1] * array_tmp2[2] / c(1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre exp ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := array_tmp3[2] * array_tmp2[2] / c(2); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre exp ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := array_tmp3[3] * array_tmp2[2] / c(3); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre exp ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := array_tmp3[4] * array_tmp2[2] / c(4); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit exp LINEAR $eq_no = 1 > array_tmp3[kkk] := array_tmp3[kkk - 1] * array_tmp2[2] / c(kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp4[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_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, 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] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := exp(array_tmp2[1]); array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp3[1]*array_tmp2[2]/c(1); array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[3] := array_tmp3[2]*array_tmp2[2]/c(2); array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[4] := array_tmp3[3]*array_tmp2[2]/c(3); array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[5] := array_tmp3[4]*array_tmp2[2]/c(4); array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp3[kkk] := array_tmp3[kkk - 1]*array_tmp2[2]/c(kkk - 1); array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > 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 > max_terms:=30; > Digits:=32; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(30) ,(0..30+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 30) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=30) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > 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_const_0D2); > array_const_0D2[1] := c(0.2); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/lin_exppostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(1.0);"); > omniout_str(ALWAYS,"x_end := c(10.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 3;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=100000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(c(10.0) * exp(c(0.1) * c(x) + c(0.2)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(1.0); > x_end := c(10.0) ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_type_given_pole := 3; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=100000; > glob_upper_ratio_limit:=c(1.0000001); > glob_lower_ratio_limit:=c(0.9999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > glob_check_sign := c(my_check_sign(x_start,x_end)); > glob__pi := arccos(glob__m1); > glob_prec = expt(10.0,c(-Digits)); > if (glob_optimize) then # if number 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 ) = exp ( 0.1 * x + 0.2 ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2015-05-02T17:51:13-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"lin_exp") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; ") > ; > 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," 308.maple.seems.ok ") > ; > logitem_str(html_log_file,"lin_exp diffeq.mxt") > ; > logitem_str(html_log_file,"lin_exp maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > fi;# end if 14 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, 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; max_terms := 30; Digits := 32; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y_higher := Array(0 .. 2, 0 .. 31, []); array_y_higher_work := Array(0 .. 2, 0 .. 31, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y_set_initial := Array(0 .. 2, 0 .. 31, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 30 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 30 do term := 1; while term <= 30 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); 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_const_0D2); array_const_0D2[1] := c(0.2); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/lin_exppostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(1.0);"); omniout_str(ALWAYS, "x_end := c(10.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 3;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=100000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(c(10.0) * exp(c(0.1) * c(x) + c(0.2)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(1.0); x_end := c(10.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 3; glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 100000; glob_upper_ratio_limit := c(1.0000001); glob_lower_ratio_limit := c(0.9999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; glob_check_sign := c(my_check_sign(x_start, x_end)); glob__pi := arccos(glob__m1); glob_prec = expt(10.0, c(-Digits)); if glob_optimize then omniout_str(ALWAYS, "START of Optimize"); found_h := false; glob_min_pole_est := glob_larger_float; last_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; glob_min_h := float_abs(glob_min_h)*glob_check_sign; glob_max_h := float_abs(glob_max_h)*glob_check_sign; glob_h := float_abs(glob_min_h)*glob_check_sign; glob_display_interval := c(float_abs(c(glob_display_interval))*glob_check_sign); display_max := c(x_end) - c(x_start)/glob__10; if display_max < glob_display_interval then glob_display_interval := c(display_max) end if; chk_data(); min_value := glob_larger_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := glob_small_float; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); order_diff := 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 ) = exp ( 0.1 * \ x + 0.2 ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2015-05-02T17:51:13-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "lin_exp"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ex\ p ( 0.1 * x + 0.2 ) ; "); 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, " 308.maple.seems.ok "); logitem_str(html_log_file, "lin_exp diffeq.mxt") ; logitem_str(html_log_file, "lin_exp maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/lin_exppostode.ode################# diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; ! #BEGIN FIRST INPUT BLOCK max_terms:=30; Digits:=32; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(1.0); x_end := c(10.0) ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 3; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=100000; glob_upper_ratio_limit:=c(1.0000001); glob_lower_ratio_limit:=c(0.9999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(10.0) * exp(c(0.1) * c(x) + c(0.2))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 13.49858807576003103983744313328 y[1] (numeric) = 13.49858807576003103983744313328 absolute error = 0 relative error = 0 % Desired digits = 8 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=0.11 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 13.512093415380156183862947018688 y[1] (numeric) = 13.512093415380156183862947018686 absolute error = 2e-30 relative error = 1.4801555454934152937323845888408e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.52561226709482271586678337355 y[1] (numeric) = 13.525612267094822715866783373548 absolute error = 2e-30 relative error = 1.4786761297790636950458846792935e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.539144644422883477086497976278 y[1] (numeric) = 13.539144644422883477086497976277 absolute error = 1e-30 relative error = 7.3859909637048254921900108568643e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.552690560896716923281000308256 y[1] (numeric) = 13.552690560896716923281000308254 absolute error = 2e-30 relative error = 1.4757217329011823426487165102656e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.566250030062240657110147010985 y[1] (numeric) = 13.566250030062240657110147010983 absolute error = 2e-30 relative error = 1.4742467487832554648569478235126e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.579823065478924974053473372451 y[1] (numeric) = 13.579823065478924974053473372448 absolute error = 3e-30 relative error = 2.2091598583683003363307065923902e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.593409680719806421881618762549 y[1] (numeric) = 13.593409680719806421881618762546 absolute error = 3e-30 relative error = 2.2069518027217599403373283605180e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.607009889371501373694005490144 y[1] (numeric) = 13.607009889371501373694005490142 absolute error = 2e-30 relative error = 1.4698306360181374525068318007241e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.620623705034219614536344120559 y[1] (numeric) = 13.620623705034219614536344120557 absolute error = 2e-30 relative error = 1.4683615400525267821499815756732e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.634251141321777941611551872143 y[1] (numeric) = 13.634251141321777941611551872143 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.647892211861613778097684303954 y[1] (numeric) = 13.647892211861613778097684303956 absolute error = 2e-30 relative error = 1.4654277517386649631633182835143e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.661546930294798800586494113641 y[1] (numeric) = 13.661546930294798800586494113643 absolute error = 2e-30 relative error = 1.4639630564566252561893185918460e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.675215310276052580156244485206 y[1] (numeric) = 13.675215310276052580156244485208 absolute error = 2e-30 relative error = 1.4624998251377640027660130390527e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.688897365473756237092418060604 y[1] (numeric) = 13.688897365473756237092418060607 absolute error = 3e-30 relative error = 2.1915570844782746431443013482891e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.702593109569966109269976257023 y[1] (numeric) = 13.702593109569966109269976257025 absolute error = 2e-30 relative error = 1.4595777485381135934515691981317e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=45.3MB, alloc=44.3MB, time=0.55 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = 13.716302556260427434210837313244 y[1] (numeric) = 13.716302556260427434210837313245 absolute error = 1e-30 relative error = 7.2905945016762379720181508723997e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.730025719254588044830255123704 y[1] (numeric) = 13.730025719254588044830255123705 absolute error = 1e-30 relative error = 7.2833075512570172025784857772107e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.743762612275612078885794607768 y[1] (numeric) = 13.74376261227561207888579460777 absolute error = 2e-30 relative error = 1.4552055768291909264944385511001e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.757513249060393702142613064349 y[1] (numeric) = 13.75751324906039370214261306435 absolute error = 1e-30 relative error = 7.2687554930633825439977555577971e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.771277643359570845268770678281 y[1] (numeric) = 13.771277643359570845268770678281 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.785055808937538954474307074914 y[1] (numeric) = 13.785055808937538954474307074913 absolute error = 1e-30 relative error = 7.2542325099014118142301757971995e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.798847759572464755907834563142 y[1] (numeric) = 13.798847759572464755907834563141 absolute error = 1e-30 relative error = 7.2469819032990288007176662942107e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.812653509056300033824412464617 y[1] (numeric) = 13.812653509056300033824412464616 absolute error = 1e-30 relative error = 7.2397385436791530014126962669350e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.826473071194795422538480698163 y[1] (numeric) = 13.826473071194795422538480698161 absolute error = 2e-30 relative error = 1.4465004847596848385652289267282e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.840306459807514212175644573469 y[1] (numeric) = 13.840306459807514212175644573469 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.854153688727846168237116547012 y[1] (numeric) = 13.854153688727846168237116547011 absolute error = 1e-30 relative error = 7.2180518743171581164822371437574e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.868014771803021364990634505786 y[1] (numeric) = 13.868014771803021364990634505785 absolute error = 1e-30 relative error = 7.2108374302660701632463080306706e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.881889722894124032701689970918 y[1] (numeric) = 13.881889722894124032701689970917 absolute error = 1e-30 relative error = 7.2036301970530133792197611074026e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.89577855587610641871891345355 y[1] (numeric) = 13.895778555876106418718913453549 absolute error = 1e-30 relative error = 7.1964301674707539507430245725823e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.909681284637802662427478049531 y[1] (numeric) = 13.90968128463780266242747804953 absolute error = 1e-30 relative error = 7.1892373343192616955541847611043e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=86.4MB, alloc=44.3MB, time=0.98 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = 13.92359792308194268408439622747 y[1] (numeric) = 13.923597923081942684084396227469 absolute error = 1e-30 relative error = 7.1820516904057028627582038796822e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.937528485125166087549598646617 y[1] (numeric) = 13.937528485125166087549598646614 absolute error = 3e-30 relative error = 2.1524619685633298819977709126930e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.951472984698036076926697736798 y[1] (numeric) = 13.951472984698036076926697736795 absolute error = 3e-30 relative error = 2.1503105824670968403346553312063e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.965431435745053387127352682333 y[1] (numeric) = 13.965431435745053387127352682329 absolute error = 4e-30 relative error = 2.8642151289088339444305227922259e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.979403852224670228373166375461 y[1] (numeric) = 13.979403852224670228373166375457 absolute error = 4e-30 relative error = 2.8613523454102396951841481294731e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 13.993390248109304244649058842335 y[1] (numeric) = 13.993390248109304244649058842331 absolute error = 4e-30 relative error = 2.8584924232642293022142010386111e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.007390637385352486122075596116 y[1] (numeric) = 14.007390637385352486122075596113 absolute error = 3e-30 relative error = 2.1417265197081602858875763284488e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.021405034053205395539603337146 y[1] (numeric) = 14.021405034053205395539603337143 absolute error = 3e-30 relative error = 2.1395858636948467804907126859780e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.035433452127260808620979399574 y[1] (numeric) = 14.035433452127260808620979399571 absolute error = 3e-30 relative error = 2.1374473472675752687685473989570e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.049475905635937968456495337223 y[1] (numeric) = 14.04947590563593796845649533722 absolute error = 3e-30 relative error = 2.1353109682878291452398605322709e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.063532408621691553927809048855 y[1] (numeric) = 14.063532408621691553927809048853 absolute error = 2e-30 relative error = 1.4221178164128195014179606515576e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.077602975141025722163793864425 y[1] (numeric) = 14.077602975141025722163793864422 absolute error = 3e-30 relative error = 2.1310446141275317429762506427881e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.091687619264508165045867049339 y[1] (numeric) = 14.091687619264508165045867049336 absolute error = 3e-30 relative error = 2.1289146346806259484144001472806e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.10578635507678417977685423322 y[1] (numeric) = 14.105786355076784179776854233218 absolute error = 2e-30 relative error = 1.4178578560990214960248678468028e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=127.5MB, alloc=44.3MB, time=1.50 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = 14.119899196676590753527460333212 y[1] (numeric) = 14.119899196676590753527460333209 absolute error = 3e-30 relative error = 2.1246610604033999204303675492892e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.134026158176770662174431619473 y[1] (numeric) = 14.134026158176770662174431619471 absolute error = 2e-30 relative error = 1.4150249742130033702117483634130e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.148167253704286583144507662196 y[1] (numeric) = 14.148167253704286583144507662193 absolute error = 3e-30 relative error = 2.1204159847732483878376054214912e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.16232249740023522237827600527 y[1] (numeric) = 14.162322497400235222378276005266 absolute error = 4e-30 relative error = 2.8243955048575375932585741564552e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.176491903419861455428056531639 y[1] (numeric) = 14.176491903419861455428056531635 absolute error = 4e-30 relative error = 2.8215725210798175599045180141717e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.190675485932572482703956619399 y[1] (numeric) = 14.190675485932572482703956619394 absolute error = 5e-30 relative error = 3.5234404485935671717741034951543e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.204873259121951998882252335876 y[1] (numeric) = 14.204873259121951998882252335871 absolute error = 5e-30 relative error = 3.5199187692781046072819013787161e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.219085237185774376490265079252 y[1] (numeric) = 14.219085237185774376490265079246 absolute error = 6e-30 relative error = 4.2196807318580455769618287262496e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.233311434336018863681917253788 y[1] (numeric) = 14.233311434336018863681917253783 absolute error = 5e-30 relative error = 3.5128859668862076027530518882576e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.247551864798883796218164755393 y[1] (numeric) = 14.247551864798883796218164755389 absolute error = 4e-30 relative error = 2.8074998694215761478020115667264e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.261806542814800823666518249144 y[1] (numeric) = 14.261806542814800823666518249139 absolute error = 5e-30 relative error = 3.5058672160428619916349747921978e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.276075482638449149833879439474 y[1] (numeric) = 14.27607548263844914983387943947 absolute error = 4e-30 relative error = 2.8018904809410095975924017490777e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.290358698538769787446932767051 y[1] (numeric) = 14.290358698538769787446932767047 absolute error = 4e-30 relative error = 2.7990899909384440337676160368512e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.304656204798979827094347213914 y[1] (numeric) = 14.304656204798979827094347213909 absolute error = 5e-30 relative error = 3.4953653750326283323673552658633e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.318968015716586720445057160277 y[1] (numeric) = 14.318968015716586720445057160272 absolute error = 5e-30 relative error = 3.4918717567578679356111515871497e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=168.8MB, alloc=44.3MB, time=1.94 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = 14.333294145603402577756905512456 y[1] (numeric) = 14.33329414560340257775690551245 absolute error = 6e-30 relative error = 4.1860579564261863432547755830290e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.34763460878555847968994661176 y[1] (numeric) = 14.347634608785558479689946611754 absolute error = 6e-30 relative error = 4.1818739908012364281371759707579e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.361989419603518803438720738841 y[1] (numeric) = 14.361989419603518803438720738836 absolute error = 5e-30 relative error = 3.4814118392088548364723785407340e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.376358592412095563197826346978 y[1] (numeric) = 14.376358592412095563197826346973 absolute error = 5e-30 relative error = 3.4779321674954753093482182380658e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.390742141580462764975130491041 y[1] (numeric) = 14.390742141580462764975130491036 absolute error = 5e-30 relative error = 3.4744559737145531053896528294185e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.405140081492170775766972266571 y[1] (numeric) = 14.405140081492170775766972266567 absolute error = 4e-30 relative error = 2.7767866035119153231933228986258e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.419552426545160707109728435358 y[1] (numeric) = 14.419552426545160707109728435353 absolute error = 5e-30 relative error = 3.4675140060487788411019825203022e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.433979191151778813022124790276 y[1] (numeric) = 14.43397919115177881302212479027 absolute error = 6e-30 relative error = 4.1568578702663502438015462812764e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.448420389738790902352691202912 y[1] (numeric) = 14.448420389738790902352691202906 absolute error = 6e-30 relative error = 4.1527030901323825494650263632135e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.462876036747396765546772702613 y[1] (numeric) = 14.462876036747396765546772702608 absolute error = 5e-30 relative error = 3.4571270522515425384278629682976e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.477346146633244615847523355192 y[1] (numeric) = 14.477346146633244615847523355186 absolute error = 6e-30 relative error = 4.1444059838241279573296397854368e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.491830733866445544945324143472 y[1] (numeric) = 14.491830733866445544945324143465 absolute error = 7e-30 relative error = 4.8303075909115230698257376307579e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.506329812931587993090080500295 y[1] (numeric) = 14.506329812931587993090080500288 absolute error = 7e-30 relative error = 4.8254796976695569599359588191586e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.520843398327752233680869607509 y[1] (numeric) = 14.520843398327752233680869607504 absolute error = 5e-30 relative error = 3.4433261642197790306604879884110e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.535371504568524872347422051772 y[1] (numeric) = 14.535371504568524872347422051768 absolute error = 4e-30 relative error = 2.7519076473159176885732953297500e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=209.9MB, alloc=44.3MB, time=2.38 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = 14.549914146182013360537936919875 y[1] (numeric) = 14.549914146182013360537936919872 absolute error = 3e-30 relative error = 2.0618678363729165956356070174396e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.564471337710860523627743922601 y[1] (numeric) = 14.564471337710860523627743922597 absolute error = 4e-30 relative error = 2.7464093321692041601110177693095e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.579043093712259103563340656996 y[1] (numeric) = 14.579043093712259103563340656993 absolute error = 3e-30 relative error = 2.0577482216880604220230219812591e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.593629428757966316056347652308 y[1] (numeric) = 14.593629428757966316056347652305 absolute error = 3e-30 relative error = 2.0556915019976108910473926309775e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.608230357434318422341938394742 y[1] (numeric) = 14.60823035743431842234193839474 absolute error = 2e-30 relative error = 1.3690912253325564435423540332914e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.6228458943422453155163160907 y[1] (numeric) = 14.622845894342245315516316090697 absolute error = 3e-30 relative error = 2.0515842276370675748232058988574e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.637476054097285121467823507183 y[1] (numeric) = 14.637476054097285121467823507179 absolute error = 4e-30 relative error = 2.7327115584795987823446100068353e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.652120851329598814416286821681 y[1] (numeric) = 14.652120851329598814416286821676 absolute error = 5e-30 relative error = 3.4124752660269504214514899899315e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.666780300683984847075209022125 y[1] (numeric) = 14.666780300683984847075209022121 absolute error = 4e-30 relative error = 2.7272515971439622118967628801130e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.681454416819893795451443020301 y[1] (numeric) = 14.681454416819893795451443020296 absolute error = 5e-30 relative error = 3.4056571358977356269606875344717e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.696143214411443018296989279622 y[1] (numeric) = 14.696143214411443018296989279617 absolute error = 5e-30 relative error = 3.4022531810229381915568333996718e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.710846708147431331227577410286 y[1] (numeric) = 14.71084670814743133122757741028 absolute error = 6e-30 relative error = 4.0786231540819263602388481240048e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.725564912731353695522705851613 y[1] (numeric) = 14.725564912731353695522705851605 absolute error = 8e-30 relative error = 5.4327287594130944770800347689936e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.740297842881415921621828442831 y[1] (numeric) = 14.740297842881415921621828442822 absolute error = 9e-30 relative error = 6.1057110893769366911412650145510e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.755045513330549387331391379721 y[1] (numeric) = 14.755045513330549387331391379711 absolute error = 1.0e-29 relative error = 6.7773427001397114241984338246570e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=251.2MB, alloc=44.3MB, time=2.81 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 14.769807938826425770757438765387 y[1] (numeric) = 14.769807938826425770757438765377 absolute error = 1.0e-29 relative error = 6.7705687449816469987507238709242e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.78458513413147179797851968898 y[1] (numeric) = 14.784585134131471797978519688969 absolute error = 1.1e-29 relative error = 7.4401817164321809459339917683274e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.799377114022884005473644506515 y[1] (numeric) = 14.799377114022884005473644506504 absolute error = 1.1e-29 relative error = 7.4327452535668866405868363995123e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.814183893292643517320052752968 y[1] (numeric) = 14.814183893292643517320052752956 absolute error = 1.2e-29 relative error = 8.1003449710335985064561076796898e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.829005486747530837175569884649 y[1] (numeric) = 14.829005486747530837175569884637 absolute error = 1.2e-29 relative error = 8.0922486748853303764588055624288e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.843841909209140655060344835447 y[1] (numeric) = 14.843841909209140655060344835435 absolute error = 1.2e-29 relative error = 8.0841604709864114858705988171136e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.858693175513896668952775169906 y[1] (numeric) = 14.858693175513896668952775169892 absolute error = 1.4e-29 relative error = 9.4220937431234101387148466136856e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.87355930051306642121444143031 y[1] (numeric) = 14.873559300513066421214441430296 absolute error = 1.4e-29 relative error = 9.4126763588572018418288994228503e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.888440299072776149858887103929 y[1] (numeric) = 14.888440299072776149858887103916 absolute error = 1.3e-29 relative error = 8.7316063596061270210198324025100e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.903336186074025654679095480461 y[1] (numeric) = 14.903336186074025654679095480449 absolute error = 1.2e-29 relative error = 8.0518884162413508135154073851435e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.918246976412703178248529528372 y[1] (numeric) = 14.918246976412703178248529528359 absolute error = 1.3e-29 relative error = 8.7141605984633109096776280269219e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.933172684999600301810615792419 y[1] (numeric) = 14.933172684999600301810615792405 absolute error = 1.4e-29 relative error = 9.3751008545310843441061332916393e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.948113326760426856071568203083 y[1] (numeric) = 14.94811332676042685607156820307 absolute error = 1.3e-29 relative error = 8.6967496939745075339261976601078e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.96306891663582584691146259198 y[1] (numeric) = 14.963068916635825846911462591966 absolute error = 1.4e-29 relative error = 9.3563693905298443329210605530140e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 14.97803946958138839602848762556 y[1] (numeric) = 14.978039469581388396028487625547 absolute error = 1.3e-29 relative error = 8.6793735764960757240096246197160e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=292.5MB, alloc=44.3MB, time=3.25 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = 14.993025000567668696531312802597 y[1] (numeric) = 14.993025000567668696531312802584 absolute error = 1.3e-29 relative error = 8.6706985411601672018237582085684e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.008025524580198983494529109084 y[1] (numeric) = 15.008025524580198983494529109071 absolute error = 1.3e-29 relative error = 8.6620321765235223980409422426010e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.023041056619504519492132887216 y[1] (numeric) = 15.023041056619504519492132887205 absolute error = 1.1e-29 relative error = 7.3220860933167334993855579947943e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.038071611701118595124038453205 y[1] (numeric) = 15.038071611701118595124038453193 absolute error = 1.2e-29 relative error = 7.9797465458688226559419695389190e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.053117204855597544550619991671 y[1] (numeric) = 15.053117204855597544550619991661 absolute error = 1.0e-29 relative error = 6.6431423232221678608376304010892e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.068177851128535776050298262424 y[1] (numeric) = 15.068177851128535776050298262413 absolute error = 1.1e-29 relative error = 7.3001527514995130250138889159623e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.083253565580580817615202678457 y[1] (numeric) = 15.083253565580580817615202678446 absolute error = 1.1e-29 relative error = 7.2928562476080012487023125664838e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.098344363287448377599954352081 y[1] (numeric) = 15.098344363287448377599954352069 absolute error = 1.2e-29 relative error = 7.9478913126254670746540474768775e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.113450259339937420438630759226 y[1] (numeric) = 15.113450259339937420438630759214 absolute error = 1.2e-29 relative error = 7.9399473939341804641253218610666e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.128571268843945257444987740145 y[1] (numeric) = 15.128571268843945257444987740133 absolute error = 1.2e-29 relative error = 7.9320114151909494500819436287714e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.143707406920482652711029637988 y[1] (numeric) = 15.143707406920482652711029637975 absolute error = 1.3e-29 relative error = 8.5844236491647775136247576526683e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.158858688705688944119033475074 y[1] (numeric) = 15.158858688705688944119033475061 absolute error = 1.3e-29 relative error = 8.5758435162970576564328660187250e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.17402512935084717948214818016 y[1] (numeric) = 15.174025129350847179482148180146 absolute error = 1.4e-29 relative error = 9.2262928792176894230217961317373e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.189206744022399267828705008548 y[1] (numeric) = 15.189206744022399267828705008534 absolute error = 1.4e-29 relative error = 9.2170711979475802145708768181928e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.204403547901961145845390440623 y[1] (numeric) = 15.204403547901961145845390440608 absolute error = 1.5e-29 relative error = 9.8655629290172539746345757320175e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=333.7MB, alloc=44.3MB, time=3.69 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 15.219615556186337959494448003237 y[1] (numeric) = 15.219615556186337959494448003224 absolute error = 1.3e-29 relative error = 8.5416086575957381608347570904196e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.23484278408753926082009063243 y[1] (numeric) = 15.234842784087539260820090632417 absolute error = 1.3e-29 relative error = 8.5330713183192256068029023838331e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.25008524683279421995932038514 y[1] (numeric) = 15.250085246832794219959320385128 absolute error = 1.2e-29 relative error = 7.8688084727213007335048160540842e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.265342959664566852372367512021 y[1] (numeric) = 15.265342959664566852372367512009 absolute error = 1.2e-29 relative error = 7.8609435973416755160920146559536e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.28061593784057126130797612304 y[1] (numeric) = 15.280615937840571261307976123028 absolute error = 1.2e-29 relative error = 7.8530865829063027190096771109583e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.295904196633786895518778912449 y[1] (numeric) = 15.295904196633786895518778912436 absolute error = 1.3e-29 relative error = 8.4990072066880145231449300276514e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.311207751332473822242018659738 y[1] (numeric) = 15.311207751332473822242018659724 absolute error = 1.4e-29 relative error = 9.1436287896894582987707370453977e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.3265266172401880154608894886 y[1] (numeric) = 15.326526617240188015460889488587 absolute error = 1.3e-29 relative error = 8.4820261789627060003681221662168e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.341860809675796659461786146494 y[1] (numeric) = 15.34186080967579665946178614648 absolute error = 1.4e-29 relative error = 9.1253598071822470232084992785228e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.35721034397349346770276486335 y[1] (numeric) = 15.357210343973493467702764863337 absolute error = 1.3e-29 relative error = 8.4650790793534226981618485914621e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.372575235482814017008534659144 y[1] (numeric) = 15.372575235482814017008534659131 absolute error = 1.3e-29 relative error = 8.4566182314031150800472014803428e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.387955499568651097107313296613 y[1] (numeric) = 15.387955499568651097107313296601 absolute error = 1.2e-29 relative error = 7.7983069292969940768526848762765e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.403351151611270075524897417249 y[1] (numeric) = 15.403351151611270075524897417237 absolute error = 1.2e-29 relative error = 7.7905125202217687742036973369685e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.418762207006324277851311755918 y[1] (numeric) = 15.418762207006324277851311755906 absolute error = 1.2e-29 relative error = 7.7827259016597129027218094616985e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.43418868116487038339541770204 y[1] (numeric) = 15.434188681164870383395417702027 absolute error = 1.3e-29 relative error = 8.4228593213095578557551019650725e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=374.9MB, alloc=44.3MB, time=4.14 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = 15.449630589513383836242876863213 y[1] (numeric) = 15.449630589513383836242876863201 absolute error = 1.2e-29 relative error = 7.7671760049364153366950203662411e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.465087947493774271732880690543 y[1] (numeric) = 15.465087947493774271732880690529 absolute error = 1.4e-29 relative error = 9.0526481630961548935324134809157e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.480560770563400958369072643675 y[1] (numeric) = 15.480560770563400958369072643662 absolute error = 1.3e-29 relative error = 8.3976286083381182317489628257979e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.496049074195088255180104807756 y[1] (numeric) = 15.496049074195088255180104807742 absolute error = 1.4e-29 relative error = 9.0345609600021239108005997906849e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.511552873877141084545286324161 y[1] (numeric) = 15.511552873877141084545286324146 absolute error = 1.5e-29 relative error = 9.6702116944470192779099345394909e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.527072185113360420500796461917 y[1] (numeric) = 15.527072185113360420500796461901 absolute error = 1.6e-29 relative error = 1.0304582737330261736514944480143e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.542607023423058792541950637344 y[1] (numeric) = 15.542607023423058792541950637328 absolute error = 1.6e-29 relative error = 1.0294283305167298955444429996367e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.558157404341075804937023185458 y[1] (numeric) = 15.558157404341075804937023185443 absolute error = 1.5e-29 relative error = 9.6412445318329679987283407473572e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.573723343417793671568146198251 y[1] (numeric) = 15.573723343417793671568146198236 absolute error = 1.5e-29 relative error = 9.6316081063169284967666277507498e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.589304856219152766314819272056 y[1] (numeric) = 15.58930485621915276631481927204 absolute error = 1.6e-29 relative error = 1.0263446733237117808820294114401e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.604901958326667188995580548785 y[1] (numeric) = 15.604901958326667188995580548769 absolute error = 1.6e-29 relative error = 1.0253188416517100412130273449549e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.620514665337440346883404994018 y[1] (numeric) = 15.620514665337440346883404994001 absolute error = 1.7e-29 relative error = 1.0883124125048001087745763403997e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.636142992864180551810411428642 y[1] (numeric) = 15.636142992864180551810411428626 absolute error = 1.6e-29 relative error = 1.0232702532396814082489271135300e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.651786956535216632877475420034 y[1] (numeric) = 15.651786956535216632877475420018 absolute error = 1.6e-29 relative error = 1.0222474944510659322094892915805e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.667446571994513564784360743721 y[1] (numeric) = 15.667446571994513564784360743704 absolute error = 1.7e-29 relative error = 1.0850523677794069754381542304787e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=416.1MB, alloc=44.3MB, time=4.56 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 15.683121854901688111795997746932 y[1] (numeric) = 15.683121854901688111795997746915 absolute error = 1.7e-29 relative error = 1.0839678577570145983443638451308e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.698812820932024487360552581636 y[1] (numeric) = 15.69881282093202448736055258162 absolute error = 1.6e-29 relative error = 1.0191853474847720554569373276023e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.714519485776490029394946926437 y[1] (numeric) = 15.714519485776490029394946926422 absolute error = 1.5e-29 relative error = 9.5453125458763055509787069903801e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.730241865141750891253503484149 y[1] (numeric) = 15.730241865141750891253503484132 absolute error = 1.7e-29 relative error = 1.0807208271649042987905228446809e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.745979974750187748395408225012 y[1] (numeric) = 15.745979974750187748395408224996 absolute error = 1.6e-29 relative error = 1.0161323731934850448122573477813e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.761733830339911520766696044306 y[1] (numeric) = 15.761733830339911520766696044291 absolute error = 1.5e-29 relative error = 9.5167195192234227315022909474912e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.777503447664779110912482217678 y[1] (numeric) = 15.777503447664779110912482217663 absolute error = 1.5e-29 relative error = 9.5072075564782354512987713795208e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.793288842494409157835177767706 y[1] (numeric) = 15.793288842494409157835177767693 absolute error = 1.3e-29 relative error = 8.2313444208158773277663538460324e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.809090030614197806614442601243 y[1] (numeric) = 15.809090030614197806614442601229 absolute error = 1.4e-29 relative error = 8.8556646669030874122661382087842e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.824907027825334493804646038798 y[1] (numeric) = 15.824907027825334493804646038784 absolute error = 1.4e-29 relative error = 8.8468134285929425774899434834529e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.840739849944817748625620134736 y[1] (numeric) = 15.840739849944817748625620134722 absolute error = 1.4e-29 relative error = 8.8379710370969635701332834754647e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.856588512805471009962506980365 y[1] (numeric) = 15.856588512805471009962506980349 absolute error = 1.6e-29 relative error = 1.0090442838368866465544192305954e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.872453032255958459190516991073 y[1] (numeric) = 15.872453032255958459190516991056 absolute error = 1.7e-29 relative error = 1.0710379779012508952839135944968e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.888333424160800868840431003602 y[1] (numeric) = 15.888333424160800868840431003586 absolute error = 1.6e-29 relative error = 1.0070282120130605957858374119417e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.904229704400391467120694850268 y[1] (numeric) = 15.904229704400391467120694850251 absolute error = 1.7e-29 relative error = 1.0688980425940672985971180500007e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=457.3MB, alloc=44.3MB, time=5.00 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = 15.920141888871011818311970933552 y[1] (numeric) = 15.920141888871011818311970933533 absolute error = 1.9e-29 relative error = 1.1934566998603175457941032056442e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.936069993484847719050027196939 y[1] (numeric) = 15.93606999348484771905002719692 absolute error = 1.9e-29 relative error = 1.1922638396899474258490414315687e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.952014034170005110512859776214 y[1] (numeric) = 15.952014034170005110512859776196 absolute error = 1.8e-29 relative error = 1.1283841627422786484812866964111e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.96797402687052600652796151966 y[1] (numeric) = 15.967974026870526006527961519643 absolute error = 1.7e-29 relative error = 1.0646309902178451248728095856965e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.983949987546404437615664485769 y[1] (numeric) = 15.983949987546404437615664485751 absolute error = 1.8e-29 relative error = 1.1261296496813593140582398396945e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 15.999941932173602410984500463115 y[1] (numeric) = 15.999941932173602410984500463096 absolute error = 1.9e-29 relative error = 1.1875043097371315127829895776653e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.0159498767440658864945395091 y[1] (numeric) = 16.015949876744065886494539509082 absolute error = 1.8e-29 relative error = 1.1238796411405402114722252025994e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.031973837265740768604682472234 y[1] (numeric) = 16.031973837265740768604682472216 absolute error = 1.8e-29 relative error = 1.1227563232519537869617132455836e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.04801382976258891431989944657 y[1] (numeric) = 16.048013829762588914319899446552 absolute error = 1.8e-29 relative error = 1.1216341281197841774350446807168e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.06406987027460415715442210687 y[1] (numeric) = 16.064069870274604157154422106853 absolute error = 1.7e-29 relative error = 1.0582623293650674818059933027662e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.080141974857828347126913889043 y[1] (numeric) = 16.080141974857828347126913889025 absolute error = 1.8e-29 relative error = 1.1193931016370361349048019149360e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.09623015958436740680365801233 y[1] (numeric) = 16.096230159584367406803658012313 absolute error = 1.7e-29 relative error = 1.0561479198206848639342513928668e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.112334440542407403405819387801 y[1] (numeric) = 16.112334440542407403405819387785 absolute error = 1.6e-29 relative error = 9.9302804686949970209210493228994e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.128454833836230636996852521731 y[1] (numeric) = 16.128454833836230636996852521715 absolute error = 1.6e-29 relative error = 9.9203551517119033055637877025245e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=498.5MB, alloc=44.3MB, time=5.45 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = 16.144591355586231744766143602628 y[1] (numeric) = 16.144591355586231744766143602611 absolute error = 1.7e-29 relative error = 1.0529842239777587248300032775071e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.16074402192893382142499105688 y[1] (numeric) = 16.160744021928933821424991056863 absolute error = 1.7e-29 relative error = 1.0519317660704394498908353777480e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.176912849017004555731044970359 y[1] (numeric) = 16.176912849017004555731044970342 absolute error = 1.7e-29 relative error = 1.0508803600949739063745452715141e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.193097853019272383157341901757 y[1] (numeric) = 16.193097853019272383157341901741 absolute error = 1.6e-29 relative error = 9.8807529882348802936322061159017e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.209299050120742654722087758036 y[1] (numeric) = 16.209299050120742654722087758019 absolute error = 1.7e-29 relative error = 1.0487806997350306418149959173832e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.225516456522613821995357563122 y[1] (numeric) = 16.225516456522613821995357563106 absolute error = 1.6e-29 relative error = 9.8610112305966342198284199116054e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.241750088442293638298897127901 y[1] (numeric) = 16.241750088442293638298897127886 absolute error = 1.5e-29 relative error = 9.2354579514642766926245039375117e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.257999962113415376115227822654 y[1] (numeric) = 16.257999962113415376115227822641 absolute error = 1.3e-29 relative error = 7.9960634950758725712970774072301e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.274266093785854060722271862396 y[1] (numeric) = 16.274266093785854060722271862382 absolute error = 1.4e-29 relative error = 8.6025384612248308663393895642107e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.290548499725742720069731741093 y[1] (numeric) = 16.29054849972574272006973174108 absolute error = 1.3e-29 relative error = 7.9800873495566215618888058220136e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.3068471962154886509134736925 y[1] (numeric) = 16.306847196215488650913473692487 absolute error = 1.3e-29 relative error = 7.9721112509210575975281798513725e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.323162199553789701224181313345 y[1] (numeric) = 16.323162199553789701224181313331 absolute error = 1.4e-29 relative error = 8.5767695185818249658401195522667e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.339493526055650568886561758877 y[1] (numeric) = 16.339493526055650568886561758862 absolute error = 1.5e-29 relative error = 9.1802111100202480063841752764487e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.355841192052399116705403211345 y[1] (numeric) = 16.35584119205239911670540321133 absolute error = 1.5e-29 relative error = 9.1710354874861300158056596909931e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.372205213891702703734798628821 y[1] (numeric) = 16.372205213891702703734798628805 absolute error = 1.6e-29 relative error = 9.7726603050541480152959205558005e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=539.7MB, alloc=44.3MB, time=5.89 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = 16.38858560793758453294686710495 y[1] (numeric) = 16.388585607937584532946867104932 absolute error = 1.8e-29 relative error = 1.0983254095632236388299685219645e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.404982390570440015256320509714 y[1] (numeric) = 16.404982390570440015256320509696 absolute error = 1.8e-29 relative error = 1.0972276331333567162832993173098e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.421395578187053149917239437142 y[1] (numeric) = 16.421395578187053149917239437124 absolute error = 1.8e-29 relative error = 1.0961309539312143627324886969384e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.437825187200612921308438858105 y[1] (numeric) = 16.437825187200612921308438858088 absolute error = 1.7e-29 relative error = 1.0342000724789996577205106322986e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.454271234040729712123820264918 y[1] (numeric) = 16.4542712340407297121238202649 absolute error = 1.8e-29 relative error = 1.0939408828244823196259024934131e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.470733735153451732984123499494 y[1] (numeric) = 16.470733735153451732984123499478 absolute error = 1.6e-29 relative error = 9.7141998998206341407302414145651e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.487212707001281468486507878142 y[1] (numeric) = 16.487212707001281468486507878126 absolute error = 1.6e-29 relative error = 9.7044905554021347776607925598587e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.503708166063192139708408663979 y[1] (numeric) = 16.503708166063192139708408663963 absolute error = 1.6e-29 relative error = 9.6947909154749995242993617958676e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.520220128834644183182131392183 y[1] (numeric) = 16.520220128834644183182131392167 absolute error = 1.6e-29 relative error = 9.6851009703395876452073415564447e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.536748611827601746356663024044 y[1] (numeric) = 16.536748611827601746356663024029 absolute error = 1.5e-29 relative error = 9.0707069159118311226350605144362e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.553293631570549199563195393012 y[1] (numeric) = 16.553293631570549199563195392997 absolute error = 1.5e-29 relative error = 9.0616407428379706319875500159088e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.569855204608507664500872909628 y[1] (numeric) = 16.569855204608507664500872909613 absolute error = 1.5e-29 relative error = 9.0525836314056081160644125605530e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.586433347503051559259293012479 y[1] (numeric) = 16.586433347503051559259293012465 absolute error = 1.4e-29 relative error = 8.4406332010537892952275663006194e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.603028076832325159894304389042 y[1] (numeric) = 16.603028076832325159894304389028 absolute error = 1.4e-29 relative error = 8.4321967867629154553745101251513e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.619639409191059178573664543598 y[1] (numeric) = 16.619639409191059178573664543585 absolute error = 1.3e-29 relative error = 7.8220710329074216999883316933412e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=580.8MB, alloc=44.3MB, time=6.33 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = 16.636267361190587358309134859266 y[1] (numeric) = 16.636267361190587358309134859255 absolute error = 1.1e-29 relative error = 6.6120601221287276069728650109408e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.652911949458863084291607887622 y[1] (numeric) = 16.652911949458863084291607887611 absolute error = 1.1e-29 relative error = 6.6054513669349253707886774821948e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.669573190640476011845878202418 y[1] (numeric) = 16.669573190640476011845878202408 absolute error = 1.0e-29 relative error = 5.9989538338118550216625337535641e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.686251101396668711021684773561 y[1] (numeric) = 16.68625110139666871102168477355 absolute error = 1.1e-29 relative error = 6.5922536663009227740291834948520e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.702945698405353327837669453779 y[1] (numeric) = 16.702945698405353327837669453769 absolute error = 1.0e-29 relative error = 5.9869679160572915269480522269077e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.719656998361128262194912823323 y[1] (numeric) = 16.719656998361128262194912823314 absolute error = 9e-30 relative error = 5.3828855465648523166536625737240e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.736385017975294862476725307627 y[1] (numeric) = 16.736385017975294862476725307618 absolute error = 9e-30 relative error = 5.3775053515641373977168943280384e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.753129773975874136851388169108 y[1] (numeric) = 16.753129773975874136851388169097 absolute error = 1.1e-29 relative error = 6.5659373194179382057958527686062e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.769891283107623481294555677248 y[1] (numeric) = 16.769891283107623481294555677236 absolute error = 1.2e-29 relative error = 7.1556814516070515810954031853008e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.78666956213205342434804648074 y[1] (numeric) = 16.786669562132053424348046480728 absolute error = 1.2e-29 relative error = 7.1485293468038548515453316235851e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.803464627827444388631768941903 y[1] (numeric) = 16.803464627827444388631768941891 absolute error = 1.2e-29 relative error = 7.1413843905306006366488689547564e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.820276496988863469125541946667 y[1] (numeric) = 16.820276496988863469125541946655 absolute error = 1.2e-29 relative error = 7.1342465756423320677387576640665e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.837105186428181228237589473365 y[1] (numeric) = 16.837105186428181228237589473355 absolute error = 1.0e-29 relative error = 5.9392632458343613847737513820220e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.85395071297408850767650399022 y[1] (numeric) = 16.85395071297408850767650399021 absolute error = 1.0e-29 relative error = 5.9333269512305201527469069682770e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.870813093472113257143490554882 y[1] (numeric) = 16.870813093472113257143490554872 absolute error = 1.0e-29 relative error = 5.9273965899541245951692993088328e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=622.0MB, alloc=44.3MB, time=6.75 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = 16.88769234478463737986172030968 y[1] (numeric) = 16.887692344784637379861720309668 absolute error = 1.2e-29 relative error = 7.1057665872897755297382975838712e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.904588483790913594959638903331 y[1] (numeric) = 16.904588483790913594959638903321 absolute error = 1.0e-29 relative error = 5.9155536436681508185702595480061e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.921501527387082316725092223825 y[1] (numeric) = 16.921501527387082316725092223815 absolute error = 1.0e-29 relative error = 5.9096410468156253266628274526955e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.93843149248618855074714869802 y[1] (numeric) = 16.93843149248618855074714869801 absolute error = 1.0e-29 relative error = 5.9037343596046391204843723255237e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.955378396018198806962514301173 y[1] (numeric) = 16.955378396018198806962514301163 absolute error = 1.0e-29 relative error = 5.8978335761285044968247373317206e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.972342254930018029623453324238 y[1] (numeric) = 16.972342254930018029623453324228 absolute error = 1.0e-29 relative error = 5.8919386904864374878173260760334e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 16.989323086185506544204144868253 y[1] (numeric) = 16.989323086185506544204144868243 absolute error = 1.0e-29 relative error = 5.8860496967835519601546430041178e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.006320906765497021262421973596 y[1] (numeric) = 17.006320906765497021262421973588 absolute error = 8e-30 relative error = 4.7041332713046829761613350836110e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.023335733667811457273857247253 y[1] (numeric) = 17.023335733667811457273857247244 absolute error = 9e-30 relative error = 5.2868604254807111625010586466850e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.040367583907278172455175823604 y[1] (numeric) = 17.040367583907278172455175823594 absolute error = 1.0e-29 relative error = 5.8684180084494666991650966018107e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.057416474515748825593993483557 y[1] (numeric) = 17.057416474515748825593993483546 absolute error = 1.1e-29 relative error = 6.4488077760394158834106601827682e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.074482422542115445901894763181 y[1] (numeric) = 17.074482422542115445901894763171 absolute error = 1.0e-29 relative error = 5.8566929014479380343831946855591e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.091565445052327481907882906341 y[1] (numeric) = 17.091565445052327481907882906332 absolute error = 9e-30 relative error = 5.2657552223253623851347824663026e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.108665559129408867409250556203 y[1] (numeric) = 17.108665559129408867409250556194 absolute error = 9e-30 relative error = 5.2604920991032416776368957286840e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.1257827818734751044969371379 y[1] (numeric) = 17.125782781873475104496937137892 absolute error = 8e-30 relative error = 4.6713193212210297313216809271839e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=663.2MB, alloc=44.3MB, time=7.19 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = 17.142917130401750363672455959148 y[1] (numeric) = 17.14291713040175036367245595914 absolute error = 8e-30 relative error = 4.6666503367811106912855968347089e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.16006862184858460107349114715 y[1] (numeric) = 17.160068621848584601073491147142 absolute error = 8e-30 relative error = 4.6619860189919173199012320382220e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.177237273365470692825281648827 y[1] (numeric) = 17.177237273365470692825281648818 absolute error = 9e-30 relative error = 5.2394921585877728691923097346565e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.194423102121061586534926647178 y[1] (numeric) = 17.194423102121061586534926647169 absolute error = 9e-30 relative error = 5.2342552853022339656297057448399e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.211626125301187469945763889502 y[1] (numeric) = 17.211626125301187469945763889493 absolute error = 9e-30 relative error = 5.2290236462724165522560488358340e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.228846360108872956768989583302 y[1] (numeric) = 17.228846360108872956768989583294 absolute error = 8e-30 relative error = 4.6433753211259388118079928446222e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.246083823764354289709705692916 y[1] (numeric) = 17.246083823764354289709705692907 absolute error = 9e-30 relative error = 5.2185760500586173574439644534590e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.263338533505096560704597664348 y[1] (numeric) = 17.263338533505096560704597664339 absolute error = 9e-30 relative error = 5.2133600824270384915732953303046e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.28061050658581094838846281743 y[1] (numeric) = 17.28061050658581094838846281742 absolute error = 1.0e-29 relative error = 5.7868325868399738882545943589215e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.297899760278471972806826873261 y[1] (numeric) = 17.297899760278471972806826873253 absolute error = 8e-30 relative error = 4.6248389173641570450844035774725e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.315206311872334767391903330999 y[1] (numeric) = 17.315206311872334767391903330992 absolute error = 7e-30 relative error = 4.0426893413336830286058700560941e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.332530178673952368219167671373 y[1] (numeric) = 17.332530178673952368219167671367 absolute error = 6e-30 relative error = 3.4616988622829201719162197892895e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.349871378007193020561835644969 y[1] (numeric) = 17.349871378007193020561835644962 absolute error = 7e-30 relative error = 4.0346120426421399233394504404787e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.367229927213257502760552201173 y[1] (numeric) = 17.367229927213257502760552201168 absolute error = 5e-30 relative error = 2.8789853194523227423319013574558e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.384605843650696467425614928937 y[1] (numeric) = 17.384605843650696467425614928933 absolute error = 4e-30 relative error = 2.3008862185166553543277208287233e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=704.5MB, alloc=44.3MB, time=7.64 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = 17.401999144695427799989073213005 y[1] (numeric) = 17.401999144695427799989073213002 absolute error = 3e-30 relative error = 1.7239398617683970789774069784026e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.419409847740753994624061659172 y[1] (numeric) = 17.419409847740753994624061659169 absolute error = 3e-30 relative error = 1.7222167835893080722660384010168e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.436837970197379547548743709341 y[1] (numeric) = 17.436837970197379547548743709338 absolute error = 3e-30 relative error = 1.7204954276271461729328251342708e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.454283529493428367732258751777 y[1] (numeric) = 17.454283529493428367732258751773 absolute error = 4e-30 relative error = 2.2917010562140737004927105109981e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.471746543074461205020083433949 y[1] (numeric) = 17.471746543074461205020083433945 absolute error = 4e-30 relative error = 2.2894105006265330262430716782017e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.489227028403493095696235304792 y[1] (numeric) = 17.489227028403493095696235304787 absolute error = 5e-30 relative error = 2.8589027930621047034265051332778e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.506725002961010825499764350019 y[1] (numeric) = 17.506725002961010825499764350014 absolute error = 5e-30 relative error = 2.8560453192440744280612373341563e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.524240484244990410112995438455 y[1] (numeric) = 17.524240484244990410112995438451 absolute error = 4e-30 relative error = 2.2825525611772811204439477828025e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.54177348977091459313900216908 y[1] (numeric) = 17.541773489770914593139002169078 absolute error = 2e-30 relative error = 1.1401355747560270442198990031077e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.559324037071790361585810097709 y[1] (numeric) = 17.559324037071790361585810097706 absolute error = 3e-30 relative error = 1.7084940135886249433188975704299e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.576892143698166478874844828986 y[1] (numeric) = 17.576892143698166478874844828981 absolute error = 5e-30 relative error = 2.8446439558956088057312802621614e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.594477827218151035391157983586 y[1] (numeric) = 17.594477827218151035391157983582 absolute error = 4e-30 relative error = 2.2734405870301618575019440489556e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.612081105217429016592981592322 y[1] (numeric) = 17.612081105217429016592981592318 absolute error = 4e-30 relative error = 2.2711682827846131539692890164688e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.62970199529927988869817902818 y[1] (numeric) = 17.629701995299279888698179028176 absolute error = 4e-30 relative error = 2.2688982497075364990796621385987e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.64734051508459520196517816418 y[1] (numeric) = 17.647340515084595201965178164176 absolute error = 4e-30 relative error = 2.2666304855288986265869791303496e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=745.7MB, alloc=44.3MB, time=8.06 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = 17.664996682211896211585990039486 y[1] (numeric) = 17.664996682211896211585990039484 absolute error = 2e-30 relative error = 1.1321824939904675844365064899354e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.682670514337351516208933928238 y[1] (numeric) = 17.682670514337351516208933928237 absolute error = 1e-30 relative error = 5.6552543869953709729570933746479e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.700362029134794714108707335301 y[1] (numeric) = 17.700362029134794714108707335301 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.718071244295742077021457090478 y[1] (numeric) = 17.718071244295742077021457090479 absolute error = 1e-30 relative error = 5.6439551811935837011186698759264e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.735798177529410241662525377732 y[1] (numeric) = 17.735798177529410241662525377733 absolute error = 1e-30 relative error = 5.6383140470495566351178987448548e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.753542846562733918944562218627 y[1] (numeric) = 17.753542846562733918944562218626 absolute error = 1e-30 relative error = 5.6326785512200464781933455118117e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.771305269140383620913713629587 y[1] (numeric) = 17.771305269140383620913713629586 absolute error = 1e-30 relative error = 5.6270486880695569312101851389092e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.789085463024783405421612390635 y[1] (numeric) = 17.789085463024783405421612390635 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.806883445996128638550916099082 y[1] (numeric) = 17.806883445996128638550916099081 absolute error = 1e-30 relative error = 5.6158058372918122381146533989464e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.824699235852403774812154935176 y[1] (numeric) = 17.824699235852403774812154935176 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.842532850409400155129669338057 y[1] (numeric) = 17.842532850409400155129669338055 absolute error = 2e-30 relative error = 1.1209170899489808908765657508156e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.860384307500733822634435579423 y[1] (numeric) = 17.860384307500733822634435579422 absolute error = 1e-30 relative error = 5.5989836656540203251198326987286e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.878253624977863356281595029227 y[1] (numeric) = 17.878253624977863356281595029228 absolute error = 1e-30 relative error = 5.5933874805472684318648523309214e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.896140820710107722310520732418 y[1] (numeric) = 17.896140820710107722310520732419 absolute error = 1e-30 relative error = 5.5877968888284632015172199547258e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=786.9MB, alloc=44.3MB, time=8.50 x[1] = 3.83 y[1] (closed_form) = 17.914045912584664143565272758274 y[1] (numeric) = 17.914045912584664143565272758275 absolute error = 1e-30 relative error = 5.5822118849070124493890464593187e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.931968918506625986693311644282 y[1] (numeric) = 17.931968918506625986693311644284 absolute error = 2e-30 relative error = 1.1153264926395823577225141496795e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.949909856399000667240357134765 y[1] (numeric) = 17.949909856399000667240357134766 absolute error = 1e-30 relative error = 5.5710586181217390451353074553697e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.967868744202727572659297310596 y[1] (numeric) = 17.967868744202727572659297310597 absolute error = 1e-30 relative error = 5.5654903441046486782974079390080e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 17.985845599876696003251071120425 y[1] (numeric) = 17.985845599876696003251071120426 absolute error = 1e-30 relative error = 5.5599276355783662069856551364538e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.003840441397763131055465255772 y[1] (numeric) = 18.003840441397763131055465255773 absolute error = 1e-30 relative error = 5.5543704869801826413585184271134e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.021853286760771976709784262299 y[1] (numeric) = 18.021853286760771976709784262299 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.039884153978569404293370747409 y[1] (numeric) = 18.03988415397856940429337074741 absolute error = 1e-30 relative error = 5.5432728473450703534536116388089e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.057933061082024134175970530218 y[1] (numeric) = 18.057933061082024134175970530219 absolute error = 1e-30 relative error = 5.5377323452105010712602199021371e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.076000026120044773887955583742 y[1] (numeric) = 18.076000026120044773887955583743 absolute error = 1e-30 relative error = 5.5321973808087384772787162242299e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.094085067159597867030435641032 y[1] (numeric) = 18.094085067159597867030435641033 absolute error = 1e-30 relative error = 5.5266679486048177084994577684668e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.112188202285725960243307376886 y[1] (numeric) = 18.112188202285725960243307376887 absolute error = 1e-30 relative error = 5.5211440430693061002156434026575e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.130309449601565688249308134672 y[1] (numeric) = 18.130309449601565688249308134673 absolute error = 1e-30 relative error = 5.5156256586782976565901882061710e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.148448827228365876992159243832 y[1] (numeric) = 18.148448827228365876992159243833 absolute error = 1e-30 relative error = 5.5101127899134075267492673073364e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.166606353305505664886902067728 y[1] (numeric) = 18.166606353305505664886902067729 absolute error = 1e-30 relative error = 5.5046054312617664863970051441973e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=828.1MB, alloc=44.3MB, time=8.94 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = 18.184782045990512642200548033659 y[1] (numeric) = 18.18478204599051264220054803366 absolute error = 1e-30 relative error = 5.4991035772160154249457917628524e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.202975923459081008581182027221 y[1] (numeric) = 18.202975923459081008581182027222 absolute error = 1e-30 relative error = 5.4936072222742998381567132832387e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.221188003905089748753676681629 y[1] (numeric) = 18.221188003905089748753676681628 absolute error = 1e-30 relative error = 5.4881163609402643262845891723256e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.239418305540620826400193259218 y[1] (numeric) = 18.239418305540620826400193259218 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.257666846595977396243663007155 y[1] (numeric) = 18.257666846595977396243663007156 absolute error = 1e-30 relative error = 5.4771510971372744781376106064484e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.275933645319702034352461072352 y[1] (numeric) = 18.275933645319702034352461072353 absolute error = 1e-30 relative error = 5.4716766837030554251008939629513e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.294218719978594986684503281767 y[1] (numeric) = 18.294218719978594986684503281769 absolute error = 2e-30 relative error = 1.0932415483891952096383553554275e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.312522088857732435889014333731 y[1] (numeric) = 18.312522088857732435889014333733 absolute error = 2e-30 relative error = 1.0921488532794188269171441050207e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.330843770260484786384234203567 y[1] (numeric) = 18.330843770260484786384234203569 absolute error = 2e-30 relative error = 1.0910572503185867360222334701957e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.349183782508534967729347842752 y[1] (numeric) = 18.349183782508534967729347842755 absolute error = 3e-30 relative error = 1.6349501076226438277319241817058e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.36754214394189675630894154506 y[1] (numeric) = 18.367542143941896756308941545062 absolute error = 2e-30 relative error = 1.0888773164784342799474462034572e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.385918872918933115348307665684 y[1] (numeric) = 18.385918872918933115348307665687 absolute error = 3e-30 relative error = 1.6316834751287698394309311430196e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.404313987816374553277937710156 y[1] (numeric) = 18.40431398781637455327793771016 absolute error = 4e-30 relative error = 2.1734034762979991484506563512664e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.422727507029337500465562159103 y[1] (numeric) = 18.422727507029337500465562159106 absolute error = 3e-30 relative error = 1.6284233693709719444662112708087e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.441159448971342704334113762392 y[1] (numeric) = 18.441159448971342704334113762394 absolute error = 2e-30 relative error = 1.0845305066279664003455638158023e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=869.4MB, alloc=44.3MB, time=9.37 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = 18.459609832074333642884009422182 y[1] (numeric) = 18.459609832074333642884009422183 absolute error = 1e-30 relative error = 5.4172325910294092161264268931183e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.478078674788694956638164188678 y[1] (numeric) = 18.478078674788694956638164188679 absolute error = 1e-30 relative error = 5.4118180661520288959985511529975e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.496565995583270899028169315154 y[1] (numeric) = 18.496565995583270899028169315153 absolute error = 1e-30 relative error = 5.4064089530931657127534502420656e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.515071812945383805240084759946 y[1] (numeric) = 18.515071812945383805240084759943 absolute error = 3e-30 relative error = 1.6203015739331118470305512953927e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.533596145380852579538314982761 y[1] (numeric) = 18.533596145380852579538314982757 absolute error = 4e-30 relative error = 2.1582427763199772513101019722089e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.552139011414011201086055360707 y[1] (numeric) = 18.552139011414011201086055360701 absolute error = 6e-30 relative error = 3.2341284184581423201911129665460e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.570700429587727248280815046038 y[1] (numeric) = 18.570700429587727248280815046031 absolute error = 7e-30 relative error = 3.7693785576591745209815675404016e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.589280418463420441623540602681 y[1] (numeric) = 18.589280418463420441623540602672 absolute error = 9e-30 relative error = 4.8414999383520704260349567513025e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.607878996621081205139883292207 y[1] (numeric) = 18.607878996621081205139883292201 absolute error = 6e-30 relative error = 3.2244405722379817093847410684440e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.626496182659289246372171432076 y[1] (numeric) = 18.626496182659289246372171432069 absolute error = 7e-30 relative error = 3.7580873672402169776930631263352e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.645131995195232154960667819651 y[1] (numeric) = 18.645131995195232154960667819645 absolute error = 6e-30 relative error = 3.2179981356775448930959558706222e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.663786452864724019832710804818 y[1] (numeric) = 18.663786452864724019832710804812 absolute error = 6e-30 relative error = 3.2147817460047362208058532177145e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.682459574322224065018356201881 y[1] (numeric) = 18.682459574322224065018356201877 absolute error = 4e-30 relative error = 2.1410457140759609678264900320882e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.701151378240855304111155857939 y[1] (numeric) = 18.701151378240855304111155857934 absolute error = 5e-30 relative error = 2.6736321731599878561152076144784e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.719861883312423213392727340073 y[1] (numeric) = 18.719861883312423213392727340067 absolute error = 6e-30 relative error = 3.2051518528289045581484186710536e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=910.7MB, alloc=44.3MB, time=9.81 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = 18.738591108247434423639787867474 y[1] (numeric) = 18.738591108247434423639787867468 absolute error = 6e-30 relative error = 3.2019483030179436138597852949483e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.757339071775115430632344297095 y[1] (numeric) = 18.757339071775115430632344297087 absolute error = 8e-30 relative error = 4.2649972735407366887318820999068e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.776105792643431324381749672586 y[1] (numeric) = 18.77610579264343132438174967258 absolute error = 6e-30 relative error = 3.1955508060413831371290361110119e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.794891289619104537097355566127 y[1] (numeric) = 18.794891289619104537097355566121 absolute error = 6e-30 relative error = 3.1923568524782860950016777548996e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.81369558148763360991050818136 y[1] (numeric) = 18.813695581487633609910508181354 absolute error = 6e-30 relative error = 3.1891660912723075609069885823884e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.832518687053311978374654943006 y[1] (numeric) = 18.832518687053311978374654943 absolute error = 6e-30 relative error = 3.1859785192326860629696584706853e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.851360625139246776760347074814 y[1] (numeric) = 18.851360625139246776760347074808 absolute error = 6e-30 relative error = 3.1827941331718492959371773263019e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.870221414587377661163942462428 y[1] (numeric) = 18.870221414587377661163942462422 absolute error = 6e-30 relative error = 3.1796129299054109336072642015093e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.889101074258495651448831911433 y[1] (numeric) = 18.889101074258495651448831911426 absolute error = 7e-30 relative error = 3.7058407239608620185148216809421e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.907999623032261992038030743384 y[1] (numeric) = 18.907999623032261992038030743377 absolute error = 7e-30 relative error = 3.7021367355397773954204777156413e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.926917079807227031576996523978 y[1] (numeric) = 18.926917079807227031576996523971 absolute error = 7e-30 relative error = 3.6984364492557368235084411989391e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.94585346350084912148555258776 y[1] (numeric) = 18.945853463500849121485552587752 absolute error = 8e-30 relative error = 4.2225598416096613832925024040130e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.964808793049513533417815912859 y[1] (numeric) = 18.964808793049513533417815912853 absolute error = 6e-30 relative error = 3.1637545442582913434621676513979e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 18.983783087408551395649046807268 y[1] (numeric) = 18.983783087408551395649046807261 absolute error = 7e-30 relative error = 3.6873577662415019796282969756993e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.00277636555225864840835679508 y[1] (numeric) = 19.002776365552258648408356795072 absolute error = 8e-30 relative error = 4.2099111446168429484306370729993e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=952.0MB, alloc=44.3MB, time=10.25 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = 19.021788646473915018176230036983 y[1] (numeric) = 19.021788646473915018176230036975 absolute error = 8e-30 relative error = 4.2057033377263219343551525867721e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.040819949185803010965832584107 y[1] (numeric) = 19.0408199491858030109658325841 absolute error = 7e-30 relative error = 3.6763122694720529816550002221714e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.059870292719226924607102748117 y[1] (numeric) = 19.059870292719226924607102748113 absolute error = 4e-30 relative error = 2.0986501684263714869532713727856e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.078939696124531880052634873233 y[1] (numeric) = 19.078939696124531880052634873228 absolute error = 5e-30 relative error = 2.6206907090416771585652255012944e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.098028178471122871724387817631 y[1] (numeric) = 19.098028178471122871724387817625 absolute error = 6e-30 relative error = 3.1416855938895808692188642257676e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.117135758847483836920268492545 y[1] (numeric) = 19.117135758847483836920268492539 absolute error = 6e-30 relative error = 3.1385454786150048448818781051684e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.136262456361196744299659867213 y[1] (numeric) = 19.136262456361196744299659867208 absolute error = 5e-30 relative error = 2.6128404182384741508458385824100e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.155408290138960701466981926821 y[1] (numeric) = 19.155408290138960701466981926815 absolute error = 6e-30 relative error = 3.1322746605660962873676488232530e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.174573279326611081672393168558 y[1] (numeric) = 19.174573279326611081672393168552 absolute error = 6e-30 relative error = 3.1291439515209451827136599863884e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.193757443089138669648759338116 y[1] (numeric) = 19.19375744308913866964875933811 absolute error = 6e-30 relative error = 3.1260163716200063610095060086363e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.212960800610708826604035245173 y[1] (numeric) = 19.212960800610708826604035245167 absolute error = 6e-30 relative error = 3.1228919177356996606846980865519e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.232183371094680674388224651844 y[1] (numeric) = 19.232183371094680674388224651837 absolute error = 7e-30 relative error = 3.6397323512008327599049318891855e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.25142517376362629885410240267 y[1] (numeric) = 19.251425173763626298854102402662 absolute error = 8e-30 relative error = 4.1555365006963852505331653556705e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.270686227859349972430902158449 y[1] (numeric) = 19.270686227859349972430902158442 absolute error = 7e-30 relative error = 3.6324601611125825457451444070240e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.289966552642907395930192309217 y[1] (numeric) = 19.289966552642907395930192309208 absolute error = 9e-30 relative error = 4.6656379498838037619883542570549e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=993.2MB, alloc=44.3MB, time=10.69 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = 19.309266167394624959603181873842 y[1] (numeric) = 19.309266167394624959603181873832 absolute error = 1.0e-29 relative error = 5.1788607155283143753944677480043e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.32858509141411902346871744515 y[1] (numeric) = 19.328585091414119023468717445142 absolute error = 8e-30 relative error = 4.1389475547041728922410998399754e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.347923344020315216931251510197 y[1] (numeric) = 19.347923344020315216931251510188 absolute error = 9e-30 relative error = 4.6516620104252931382281451655259e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.367280944551467757708081765234 y[1] (numeric) = 19.367280944551467757708081765224 absolute error = 1.0e-29 relative error = 5.1633474149675442627688681080510e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.38665791236517879008518035425 y[1] (numeric) = 19.386657912365178790085180354239 absolute error = 1.1e-29 relative error = 5.6740053132025355358623926012094e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.406054266838417742520951288509 y[1] (numeric) = 19.406054266838417742520951288499 absolute error = 1.0e-29 relative error = 5.1530310399514167445512977121829e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.425470027367540704617273652457 y[1] (numeric) = 19.425470027367540704617273652446 absolute error = 1.1e-29 relative error = 5.6626686430251976099032889581253e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.444905213368309823477207568665 y[1] (numeric) = 19.444905213368309823477207568655 absolute error = 1.0e-29 relative error = 5.1427352770663197409700685497029e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.464359844275912719468759281124 y[1] (numeric) = 19.464359844275912719468759281114 absolute error = 1.0e-29 relative error = 5.1375951122999836459988077980906e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.483833939544981921414121122268 y[1] (numeric) = 19.483833939544981921414121122257 absolute error = 1.1e-29 relative error = 5.6457060936421067823466380558837e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.503327518649614321223821554603 y[1] (numeric) = 19.503327518649614321223821554592 absolute error = 1.1e-29 relative error = 5.6400632094607956717248559066110e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.522840601083390647995239922694 y[1] (numeric) = 19.522840601083390647995239922685 absolute error = 9e-30 relative error = 4.6099848807353160222397096835689e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.542373206359394961594960015662 y[1] (numeric) = 19.542373206359394961594960015653 absolute error = 9e-30 relative error = 4.6053772000788823047128202309538e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.561925354010234165744456024157 y[1] (numeric) = 19.561925354010234165744456024146 absolute error = 1.1e-29 relative error = 5.6231683747555952136286721377331e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.581497063588057540628623979132 y[1] (numeric) = 19.581497063588057540628623979118 absolute error = 1.4e-29 relative error = 7.1496065671266301149853638693997e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1034.4MB, alloc=44.3MB, time=11.12 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = 19.601088354664576295046691282562 y[1] (numeric) = 19.601088354664576295046691282547 absolute error = 1.5e-29 relative error = 7.6526362866123040653941090571141e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.620699246831083138125056482665 y[1] (numeric) = 19.620699246831083138125056482649 absolute error = 1.6e-29 relative error = 8.1546533070599621146268059396603e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.640329759698471870611631008079 y[1] (numeric) = 19.640329759698471870611631008064 absolute error = 1.5e-29 relative error = 7.6373463091132373505564846786192e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.659979912897256995771274156975 y[1] (numeric) = 19.659979912897256995771274156959 absolute error = 1.6e-29 relative error = 8.1383602988850194959303078751734e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.679649726077593349901932238183 y[1] (numeric) = 19.679649726077593349901932238168 absolute error = 1.5e-29 relative error = 7.6220868810095902184381640611330e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.699339218909295752491112382096 y[1] (numeric) = 19.699339218909295752491112382082 absolute error = 1.4e-29 relative error = 7.1068373636418581200958191112044e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.719048411081858676032341179464 y[1] (numeric) = 19.719048411081858676032341179449 absolute error = 1.5e-29 relative error = 7.6068579412636299085437677477842e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.738777322304475935521277966183 y[1] (numeric) = 19.738777322304475935521277966167 absolute error = 1.6e-29 relative error = 8.1058718778494337521143537556383e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.758525972306060397651172251827 y[1] (numeric) = 19.758525972306060397651172251809 absolute error = 1.8e-29 relative error = 9.1099913147514925581316250159779e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.778294380835263709727374489023 y[1] (numeric) = 19.778294380835263709727374489006 absolute error = 1.7e-29 relative error = 8.5952811059747546146733971404118e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.798082567660496048320629099831 y[1] (numeric) = 19.798082567660496048320629099814 absolute error = 1.7e-29 relative error = 8.5866901210771440615375812277356e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.817890552569945887678898414053 y[1] (numeric) = 19.817890552569945887678898414035 absolute error = 1.8e-29 relative error = 9.0827022948039213279668137398439e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.83771835537159978791748593296 y[1] (numeric) = 19.837718355371599787917485932941 absolute error = 1.9e-29 relative error = 9.5777143619216849887763033900840e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.857565995893262203007247110196 y[1] (numeric) = 19.857565995893262203007247110177 absolute error = 1.9e-29 relative error = 9.5681414348210575292738348451986e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.877433493982575308580695639724 y[1] (numeric) = 19.877433493982575308580695639706 absolute error = 1.8e-29 relative error = 9.0554950192383115919763557369081e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1075.6MB, alloc=44.3MB, time=11.55 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = 19.897320869507038849575833058582 y[1] (numeric) = 19.897320869507038849575833058564 absolute error = 1.8e-29 relative error = 9.0464440504577109665097084865984e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.917228142354030007737549309913 y[1] (numeric) = 19.917228142354030007737549309894 absolute error = 1.9e-29 relative error = 9.5394800241286877062898446169597e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.937155332430823288996461769344 y[1] (numeric) = 19.937155332430823288996461769323 absolute error = 2.1e-29 relative error = 1.0533097450387166212258708566365e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.957102459664610430745080115201 y[1] (numeric) = 19.957102459664610430745080115181 absolute error = 2.0e-29 relative error = 1.0021494874028977894473913850335e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.977069544002520329031204320385 y[1] (numeric) = 19.977069544002520329031204320365 absolute error = 2.0e-29 relative error = 1.0011478388232554264184768202937e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 19.997056605411638985688482960969 y[1] (numeric) = 19.997056605411638985688482960949 absolute error = 2.0e-29 relative error = 1.0001471913915353156343382449182e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 20.017063663879029475424078973737 y[1] (numeric) = 20.017063663879029475424078973717 absolute error = 2.0e-29 relative error = 9.9914754410708994198757611851634e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 20.037090739411751932883409951988 y[1] (numeric) = 20.037090739411751932883409951966 absolute error = 2.2e-29 relative error = 1.0979637855672991315017610117881e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 20.057137852036883559711950046024 y[1] (numeric) = 20.057137852036883559711950046003 absolute error = 2.1e-29 relative error = 1.0470088082815547369605230162031e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 20.07720502180153865163410053178 y[1] (numeric) = 20.07720502180153865163410053176 absolute error = 2.0e-29 relative error = 9.9615459314592330628323569927863e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 20.097292268772888645569156128137 y[1] (numeric) = 20.097292268772888645569156128115 absolute error = 2.2e-29 relative error = 1.0946748301104986574113373293420e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 20.117399613038182186804414180557 y[1] (numeric) = 20.117399613038182186804414180536 absolute error = 2.1e-29 relative error = 1.0438724886883392380737171919391e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5 y[1] (closed_form) = 20.137527074704765216245493885831 y[1] (numeric) = 20.13752707470476521624549388581 absolute error = 2.1e-29 relative error = 1.0428291379619599808800801961348e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.01 y[1] (closed_form) = 20.157674673900101077763952809906 y[1] (numeric) = 20.157674673900101077763952809885 absolute error = 2.1e-29 relative error = 1.0417868300648055880774843247330e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=1116.9MB, alloc=44.3MB, time=12.00 x[1] = 5.02 y[1] (closed_form) = 20.177842430771790645662308048117 y[1] (numeric) = 20.177842430771790645662308048097 absolute error = 2.0e-29 relative error = 9.9118625138530292919289757171934e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.03 y[1] (closed_form) = 20.1980303654875924722765894945 y[1] (numeric) = 20.198030365487592472276589494481 absolute error = 1.9e-29 relative error = 9.4068578253379255644360498310371e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.04 y[1] (closed_form) = 20.218238498235442955736572824417 y[1] (numeric) = 20.218238498235442955736572824398 absolute error = 1.9e-29 relative error = 9.3974556693740825443100454883470e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.05 y[1] (closed_form) = 20.238466849223476527903859952429 y[1] (numeric) = 20.23846684922347652790385995241 absolute error = 1.9e-29 relative error = 9.3880629108666920195984706732399e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.06 y[1] (closed_form) = 20.258715438680045862507994905152 y[1] (numeric) = 20.258715438680045862507994905134 absolute error = 1.8e-29 relative error = 8.8850648277691528738555884953063e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.07 y[1] (closed_form) = 20.278984286853742103500823246915 y[1] (numeric) = 20.278984286853742103500823246896 absolute error = 1.9e-29 relative error = 9.3693055486596193604124479131639e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.08 y[1] (closed_form) = 20.299273414013415113649323414258 y[1] (numeric) = 20.299273414013415113649323414237 absolute error = 2.1e-29 relative error = 1.0345197865802844345830905256261e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.09 y[1] (closed_form) = 20.319582840448193743387158553785 y[1] (numeric) = 20.319582840448193743387158553764 absolute error = 2.1e-29 relative error = 1.0334857838812205722322232390317e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.1 y[1] (closed_form) = 20.339912586467506119945217716624 y[1] (numeric) = 20.339912586467506119945217716603 absolute error = 2.1e-29 relative error = 1.0324528146680267149201224136036e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.11 y[1] (closed_form) = 20.360262672401099956781435541719 y[1] (numeric) = 20.360262672401099956781435541697 absolute error = 2.2e-29 relative error = 1.0805361578081018282946439160951e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.12 y[1] (closed_form) = 20.380633118599062883330199859456 y[1] (numeric) = 20.380633118599062883330199859434 absolute error = 2.2e-29 relative error = 1.0794561617383282842195210009256e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.13 y[1] (closed_form) = 20.401023945431842795091676966752 y[1] (numeric) = 20.401023945431842795091676966731 absolute error = 2.1e-29 relative error = 1.0293600976191334134669244892063e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.14 y[1] (closed_form) = 20.421435173290268224081404664595 y[1] (numeric) = 20.421435173290268224081404664575 absolute error = 2.0e-29 relative error = 9.7936309717147233788362365929273e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.15 y[1] (closed_form) = 20.441866822585568729660523509357 y[1] (numeric) = 20.441866822585568729660523509338 absolute error = 1.9e-29 relative error = 9.2946501241302991370292762386584e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.16 y[1] (closed_form) = 20.462318913749395309767037109779 y[1] (numeric) = 20.46231891374939530976703710976 absolute error = 1.9e-29 relative error = 9.2853601197825097486660940746021e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1158.1MB, alloc=44.3MB, time=12.42 TOP MAIN SOLVE Loop x[1] = 5.17 y[1] (closed_form) = 20.482791467233840832568512702623 y[1] (numeric) = 20.482791467233840832568512702604 absolute error = 1.9e-29 relative error = 9.2760794007956139228484351199121e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.18 y[1] (closed_form) = 20.503284503511460488556653661363 y[1] (numeric) = 20.503284503511460488556653661345 absolute error = 1.8e-29 relative error = 8.7790812232631607466931357707914e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.19 y[1] (closed_form) = 20.523798043075292263104196034213 y[1] (numeric) = 20.523798043075292263104196034196 absolute error = 1.7e-29 relative error = 8.2830672784444894724674523297347e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.2 y[1] (closed_form) = 20.544332106438877429504601670086 y[1] (numeric) = 20.544332106438877429504601670069 absolute error = 1.7e-29 relative error = 8.2747883513195180509548500159255e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.21 y[1] (closed_form) = 20.564886714136281062515040973882 y[1] (numeric) = 20.564886714136281062515040973865 absolute error = 1.7e-29 relative error = 8.2665176989835875146792274737465e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.22 y[1] (closed_form) = 20.585461886722112572423178835812 y[1] (numeric) = 20.585461886722112572423178835795 absolute error = 1.7e-29 relative error = 8.2582553131660448384889974593280e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.23 y[1] (closed_form) = 20.606057644771546259658297803231 y[1] (numeric) = 20.606057644771546259658297803214 absolute error = 1.7e-29 relative error = 8.2500011856045035163093093694785e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.24 y[1] (closed_form) = 20.626674008880341889967313107838 y[1] (numeric) = 20.62667400888034188996731310782 absolute error = 1.8e-29 relative error = 8.7265644438121785516227872601654e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.25 y[1] (closed_form) = 20.647310999664865290176254725963 y[1] (numeric) = 20.647310999664865290176254725944 absolute error = 1.9e-29 relative error = 9.2021668101518868730010388410262e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.26 y[1] (closed_form) = 20.66796863776210896455781223514 y[1] (numeric) = 20.667968637762108964557812235122 absolute error = 1.8e-29 relative error = 8.7091287564238379437812363437649e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.27 y[1] (closed_form) = 20.688646943829712731825558836229 y[1] (numeric) = 20.68864694382971273182555883621 absolute error = 1.9e-29 relative error = 9.1837808686017799809396222212137e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.28 y[1] (closed_form) = 20.709345938545984382775491537031 y[1] (numeric) = 20.709345938545984382775491537012 absolute error = 1.9e-29 relative error = 9.1746016780933649380991476703864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.29 y[1] (closed_form) = 20.730065642609920358595545140656 y[1] (numeric) = 20.730065642609920358595545140637 absolute error = 1.9e-29 relative error = 9.1654316621873925387889373375688e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.3 y[1] (closed_form) = 20.750806076741226449863758349892 y[1] (numeric) = 20.750806076741226449863758349872 absolute error = 2.0e-29 relative error = 9.6381798018040485398616571325432e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.31 y[1] (closed_form) = 20.771567261680338516255790987445 y[1] (numeric) = 20.771567261680338516255790987424 absolute error = 2.1e-29 relative error = 1.0109973761460492783743969514588e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1199.4MB, alloc=44.3MB, time=12.86 TOP MAIN SOLVE Loop x[1] = 5.32 y[1] (closed_form) = 20.79234921818844322698251204131 y[1] (numeric) = 20.792349218188443226982512041289 absolute error = 2.1e-29 relative error = 1.0099868841001338558967521085991e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.33 y[1] (closed_form) = 20.813151967047498821978398974595 y[1] (numeric) = 20.813151967047498821978398974575 absolute error = 2.0e-29 relative error = 9.6093085908684447536137494554155e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.34 y[1] (closed_form) = 20.833975529060255893861509489898 y[1] (numeric) = 20.83397552906025589386150948988 absolute error = 1.8e-29 relative error = 8.6397336767976485571583476036796e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.35 y[1] (closed_form) = 20.854819925050278190685807709983 y[1] (numeric) = 20.854819925050278190685807709965 absolute error = 1.8e-29 relative error = 8.6310982615480936115432769205208e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.36 y[1] (closed_form) = 20.875685175861963439506647528774 y[1] (numeric) = 20.875685175861963439506647528755 absolute error = 1.9e-29 relative error = 9.1014976705862705540250473615472e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.37 y[1] (closed_form) = 20.896571302360564190780236699911 y[1] (numeric) = 20.896571302360564190780236699893 absolute error = 1.8e-29 relative error = 8.6138533157191412697584405407447e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.38 y[1] (closed_form) = 20.917478325432208683617926064067 y[1] (numeric) = 20.917478325432208683617926064048 absolute error = 1.9e-29 relative error = 9.0833128661111741968662141927064e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.39 y[1] (closed_form) = 20.938406265983921731916189171036 y[1] (numeric) = 20.938406265983921731916189171017 absolute error = 1.9e-29 relative error = 9.0742340933879889962590120371028e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.4 y[1] (closed_form) = 20.959355144943645631383178428338 y[1] (numeric) = 20.959355144943645631383178428318 absolute error = 2.0e-29 relative error = 9.5422783104206877577268014166942e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.41 y[1] (closed_form) = 20.980324983260261087482764804619 y[1] (numeric) = 20.980324983260261087482764804599 absolute error = 2.0e-29 relative error = 9.5327408016594400773333717321220e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.42 y[1] (closed_form) = 21.001315801903608164316989033638 y[1] (numeric) = 21.001315801903608164316989033618 absolute error = 2.0e-29 relative error = 9.5232128256397884514733041702946e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.43 y[1] (closed_form) = 21.022327621864507254467873203041 y[1] (numeric) = 21.022327621864507254467873203019 absolute error = 2.2e-29 relative error = 1.0465063810117131673146639243599e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.44 y[1] (closed_form) = 21.043360464154780069819562571469 y[1] (numeric) = 21.043360464154780069819562571446 absolute error = 2.3e-29 relative error = 1.0929813248781322721642603843170e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.45 y[1] (closed_form) = 21.06441434980727065338178843791 y[1] (numeric) = 21.064414349807270653381788437887 absolute error = 2.3e-29 relative error = 1.0918888898617985565937535216794e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.46 y[1] (closed_form) = 21.085489299875866412135663888488 y[1] (numeric) = 21.085489299875866412135663888467 absolute error = 2.1e-29 relative error = 9.9594558614884172021212260764727e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1240.6MB, alloc=44.3MB, time=13.30 TOP MAIN SOLVE Loop x[1] = 5.47 y[1] (closed_form) = 21.106585335435519170922845268254 y[1] (numeric) = 21.106585335435519170922845268233 absolute error = 2.1e-29 relative error = 9.9495013836953651132255634840524e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.48 y[1] (closed_form) = 21.127702477582266247399113268886 y[1] (numeric) = 21.127702477582266247399113268866 absolute error = 2.0e-29 relative error = 9.4662446241947865188932948272623e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.49 y[1] (closed_form) = 21.148840747433251548073448587638 y[1] (numeric) = 21.148840747433251548073448587617 absolute error = 2.1e-29 relative error = 9.9296222666713702774084274156252e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.5 y[1] (closed_form) = 21.170000166126746685453698198371 y[1] (numeric) = 21.170000166126746685453698198348 absolute error = 2.3e-29 relative error = 1.0864430713043338264175070671695e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.51 y[1] (closed_form) = 21.191180754822172116319949382093 y[1] (numeric) = 21.19118075482217211631994938207 absolute error = 2.3e-29 relative error = 1.0853571712735365589497346173326e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.52 y[1] (closed_form) = 21.212382534700118301146749792143 y[1] (numeric) = 21.21238253470011830114674979212 absolute error = 2.3e-29 relative error = 1.0842723566000010114524754596954e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.53 y[1] (closed_form) = 21.233605526962366884695332978007 y[1] (numeric) = 21.233605526962366884695332977984 absolute error = 2.3e-29 relative error = 1.0831886261989124199889562889955e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.54 y[1] (closed_form) = 21.254849752831911897797029961738 y[1] (numeric) = 21.254849752831911897797029961716 absolute error = 2.2e-29 relative error = 1.0350578929436472369353804011878e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.55 y[1] (closed_form) = 21.276115233552980980349068652192 y[1] (numeric) = 21.276115233552980980349068652169 absolute error = 2.3e-29 relative error = 1.0810244138802373283720233470116e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.56 y[1] (closed_form) = 21.297401990391056625543984094612 y[1] (numeric) = 21.297401990391056625543984094589 absolute error = 2.3e-29 relative error = 1.0799439297984383291924853908358e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.57 y[1] (closed_form) = 21.318710044632897445353883786764 y[1] (numeric) = 21.318710044632897445353883786741 absolute error = 2.3e-29 relative error = 1.0788645256606591237817596746426e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.58 y[1] (closed_form) = 21.340039417586559457290833547657 y[1] (numeric) = 21.340039417586559457290833547633 absolute error = 2.4e-29 relative error = 1.1246464699695605054716100602721e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.59 y[1] (closed_form) = 21.361390130581417392464650701002 y[1] (numeric) = 21.361390130581417392464650700976 absolute error = 2.6e-29 relative error = 1.2171492511050510108436561226036e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.6 y[1] (closed_form) = 21.38276220496818602495941263298 y[1] (numeric) = 21.382762204968186024959412632955 absolute error = 2.5e-29 relative error = 1.1691660675247730848574217128414e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.61 y[1] (closed_form) = 21.404155662118941522550010102614 y[1] (numeric) = 21.404155662118941522550010102589 absolute error = 2.5e-29 relative error = 1.1679974858454697684163644516807e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.62 y[1] (closed_form) = 21.425570523427142818780096023063 y[1] (numeric) = 21.425570523427142818780096023039 absolute error = 2.4e-29 relative error = 1.1201568692771996453492548802084e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1281.8MB, alloc=44.3MB, time=13.75 TOP MAIN SOLVE Loop x[1] = 5.63 y[1] (closed_form) = 21.447006810307653006422801793583 y[1] (numeric) = 21.447006810307653006422801793559 absolute error = 2.4e-29 relative error = 1.1190372722997109366273298829433e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.64 y[1] (closed_form) = 21.468464544196760752345614644636 y[1] (numeric) = 21.468464544196760752345614644613 absolute error = 2.3e-29 relative error = 1.0713388445946049565285801372657e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.65 y[1] (closed_form) = 21.489943746552201733800830862832 y[1] (numeric) = 21.48994374655220173380083086281 absolute error = 2.2e-29 relative error = 1.0237346481434894656211996574127e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.66 y[1] (closed_form) = 21.511444438853180096163021187921 y[1] (numeric) = 21.5114444388531800961630211879 absolute error = 2.1e-29 relative error = 9.7622454222881342391353364982564e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.67 y[1] (closed_form) = 21.532966642600389932134966121103 y[1] (numeric) = 21.532966642600389932134966121083 absolute error = 2.0e-29 relative error = 9.2880838632018314515581637272212e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.68 y[1] (closed_form) = 21.554510379316036782443540352376 y[1] (numeric) = 21.554510379316036782443540352357 absolute error = 1.9e-29 relative error = 8.8148604007412874614320993112391e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.69 y[1] (closed_form) = 21.5760756705438591580470470046 y[1] (numeric) = 21.576075670543859158047047004581 absolute error = 1.9e-29 relative error = 8.8060499463019703568959520114450e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.7 y[1] (closed_form) = 21.5976625378491500838755239034 y[1] (numeric) = 21.59766253784915008387552390338 absolute error = 2.0e-29 relative error = 9.2602613662245614651054189706180e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.71 y[1] (closed_form) = 21.619271002818778664125565615019 y[1] (numeric) = 21.619271002818778664125565614997 absolute error = 2.2e-29 relative error = 1.0176106306790631777479682815561e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.72 y[1] (closed_form) = 21.640901087061211669131226548728 y[1] (numeric) = 21.640901087061211669131226548706 absolute error = 2.2e-29 relative error = 1.0165935286841400742862348424907e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.73 y[1] (closed_form) = 21.662552812206535143832591996506 y[1] (numeric) = 21.662552812206535143832591996484 absolute error = 2.2e-29 relative error = 1.0155774432828303710947899056299e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.74 y[1] (closed_form) = 21.684226199906476037863625580358 y[1] (numeric) = 21.684226199906476037863625580335 absolute error = 2.3e-29 relative error = 1.0606788449799144268351505607117e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.75 y[1] (closed_form) = 21.705921271834423857280923196915 y[1] (numeric) = 21.705921271834423857280923196891 absolute error = 2.4e-29 relative error = 1.1056890743975179627651128690353e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.76 y[1] (closed_form) = 21.727638049685452337955025189881 y[1] (numeric) = 21.727638049685452337955025189856 absolute error = 2.5e-29 relative error = 1.1506082687327314503409401542836e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.77 y[1] (closed_form) = 21.749376555176341140645960143449 y[1] (numeric) = 21.749376555176341140645960143426 absolute error = 2.3e-29 relative error = 1.0575015767302999350605743175385e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1323.0MB, alloc=44.3MB, time=14.19 TOP MAIN SOLVE Loop x[1] = 5.78 y[1] (closed_form) = 21.771136810045597567784715374027 y[1] (numeric) = 21.771136810045597567784715374003 absolute error = 2.4e-29 relative error = 1.1023769778032888256435656867519e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.79 y[1] (closed_form) = 21.792918836053478301982350903559 y[1] (numeric) = 21.792918836053478301982350903535 absolute error = 2.4e-29 relative error = 1.1012751518302908653509179876853e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.8 y[1] (closed_form) = 21.81472265498201116628849542537 y[1] (numeric) = 21.814722654982011166288495425346 absolute error = 2.4e-29 relative error = 1.1001744271325365082815139281407e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.81 y[1] (closed_form) = 21.836548288635016906220984522842 y[1] (numeric) = 21.836548288635016906220984522819 absolute error = 2.3e-29 relative error = 1.0532800191672467580808546001595e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.82 y[1] (closed_form) = 21.85839575883813099358842317237 y[1] (numeric) = 21.858395758838130993588423172347 absolute error = 2.3e-29 relative error = 1.0522272656125863029765394818185e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.83 y[1] (closed_form) = 21.880265087438825452127476354985 y[1] (numeric) = 21.880265087438825452127476354962 absolute error = 2.3e-29 relative error = 1.0511755642852791460669179091101e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.84 y[1] (closed_form) = 21.902156296306430704976713415748 y[1] (numeric) = 21.902156296306430704976713415726 absolute error = 2.2e-29 relative error = 1.0044673091712923996898765677964e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.85 y[1] (closed_form) = 21.924069407332157444008853646581 y[1] (numeric) = 21.92406940733215744400885364656 absolute error = 2.1e-29 relative error = 9.5785137374984239557761965522233e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.86 y[1] (closed_form) = 21.946004442429118521043282426608 y[1] (numeric) = 21.946004442429118521043282426586 absolute error = 2.2e-29 relative error = 1.0024603821489477890176652232153e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.87 y[1] (closed_form) = 21.967961423532350860960729134333 y[1] (numeric) = 21.967961423532350860960729134311 absolute error = 2.2e-29 relative error = 1.0014584228299549461745292307821e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.88 y[1] (closed_form) = 21.989940372598837396742019948181 y[1] (numeric) = 21.98994037259883739674201994816 absolute error = 2.1e-29 relative error = 9.5498212565267437051415902275621e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.89 y[1] (closed_form) = 22.011941311607529026452840575957 y[1] (numeric) = 22.011941311607529026452840575937 absolute error = 2.0e-29 relative error = 9.0859773415139106460675718856536e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.9 y[1] (closed_form) = 22.03396426255936659219646589984 y[1] (numeric) = 22.033964262559366592196465899818 absolute error = 2.2e-29 relative error = 9.9845854962118280863575329256927e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.91 y[1] (closed_form) = 22.056009247477302881056435491449 y[1] (numeric) = 22.056009247477302881056435491426 absolute error = 2.3e-29 relative error = 1.0427997078678531937355541311516e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.92 y[1] (closed_form) = 22.078076288406324648051175941515 y[1] (numeric) = 22.078076288406324648051175941492 absolute error = 2.3e-29 relative error = 1.0417574293860827644563849668746e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1364.1MB, alloc=44.3MB, time=14.64 TOP MAIN SOLVE Loop x[1] = 5.93 y[1] (closed_form) = 22.100165407413474661122592960596 y[1] (numeric) = 22.100165407413474661122592960574 absolute error = 2.2e-29 relative error = 9.9546766254609685897407694802207e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.94 y[1] (closed_form) = 22.122276626587873768180678241275 y[1] (numeric) = 22.122276626587873768180678241253 absolute error = 2.2e-29 relative error = 9.9447269245151222759760751092219e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.95 y[1] (closed_form) = 22.144409968040742986226198128284 y[1] (numeric) = 22.144409968040742986226198128263 absolute error = 2.1e-29 relative error = 9.4832059333744369680320364338728e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.96 y[1] (closed_form) = 22.166565453905425612573553221084 y[1] (numeric) = 22.166565453905425612573553221063 absolute error = 2.1e-29 relative error = 9.4737274674638899506204259802035e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.97 y[1] (closed_form) = 22.188743106337409358195920133598 y[1] (numeric) = 22.188743106337409358195920133576 absolute error = 2.2e-29 relative error = 9.9149374502950093922432772565212e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.98 y[1] (closed_form) = 22.210942947514348503214808758097 y[1] (numeric) = 22.210942947514348503214808758076 absolute error = 2.1e-29 relative error = 9.4547989473585737680400862702848e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.99 y[1] (closed_form) = 22.233164999636086074556190524624 y[1] (numeric) = 22.233164999636086074556190524604 absolute error = 2.0e-29 relative error = 8.9955703564145551620747108680545e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6 y[1] (closed_form) = 22.255409284924676045795375313951 y[1] (numeric) = 22.255409284924676045795375313931 absolute error = 2.0e-29 relative error = 8.9865792823444318286020477003112e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.01 y[1] (closed_form) = 22.277675825624405559212836870774 y[1] (numeric) = 22.277675825624405559212836870754 absolute error = 2.0e-29 relative error = 8.9775971948543397211930378912761e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.02 y[1] (closed_form) = 22.299964644001817170083208774851 y[1] (numeric) = 22.299964644001817170083208774832 absolute error = 1.9e-29 relative error = 8.5201928807140810711858453286524e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.03 y[1] (closed_form) = 22.322275762345731113219695260907 y[1] (numeric) = 22.322275762345731113219695260886 absolute error = 2.1e-29 relative error = 9.4076429408796175203023765093327e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.04 y[1] (closed_form) = 22.344609202967267591796163433588 y[1] (numeric) = 22.344609202967267591796163433567 absolute error = 2.1e-29 relative error = 9.3982400001926597591828078117495e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.05 y[1] (closed_form) = 22.366964988199869088469205701403 y[1] (numeric) = 22.366964988199869088469205701382 absolute error = 2.1e-29 relative error = 9.3888464577464853774157872413100e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.06 y[1] (closed_form) = 22.389343140399322698822483553591 y[1] (numeric) = 22.38934314039932269882248355357 absolute error = 2.1e-29 relative error = 9.3794623041475511460317030899543e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.07 y[1] (closed_form) = 22.4117436819437824871556861261 y[1] (numeric) = 22.411743681943782487155686126079 absolute error = 2.1e-29 relative error = 9.3700875300117026840834979953181e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1405.2MB, alloc=44.3MB, time=15.08 TOP MAIN SOLVE Loop x[1] = 6.08 y[1] (closed_form) = 22.434166635233791864640459347508 y[1] (numeric) = 22.434166635233791864640459347486 absolute error = 2.2e-29 relative error = 9.8064707986291253161339586465368e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.09 y[1] (closed_form) = 22.456612022692305989865683822685 y[1] (numeric) = 22.456612022692305989865683822664 absolute error = 2.1e-29 relative error = 9.3513660826395334892677541445511e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.1 y[1] (closed_form) = 22.479079866764714191794502001334 y[1] (numeric) = 22.479079866764714191794502001312 absolute error = 2.2e-29 relative error = 9.7868774569047049585917996603276e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.11 y[1] (closed_form) = 22.501570189918862415155517590301 y[1] (numeric) = 22.501570189918862415155517590279 absolute error = 2.2e-29 relative error = 9.7770954712557901681852194957280e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.12 y[1] (closed_form) = 22.524083014645075688290612602742 y[1] (numeric) = 22.52408301464507568829061260272 absolute error = 2.2e-29 relative error = 9.7673232627031613915519040978781e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.13 y[1] (closed_form) = 22.546618363456180613481849893817 y[1] (numeric) = 22.546618363456180613481849893795 absolute error = 2.2e-29 relative error = 9.7575608214746092617123369693733e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.14 y[1] (closed_form) = 22.569176258887527879779951511698 y[1] (numeric) = 22.569176258887527879779951511676 absolute error = 2.2e-29 relative error = 9.7478081378076917365775921067435e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.15 y[1] (closed_form) = 22.591756723497014798356865694248 y[1] (numeric) = 22.591756723497014798356865694228 absolute error = 2.0e-29 relative error = 8.8527865472270221240967985224194e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.16 y[1] (closed_form) = 22.614359779865107860404957865805 y[1] (numeric) = 22.614359779865107860404957865786 absolute error = 1.9e-29 relative error = 8.4017412763180744291265770763341e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.17 y[1] (closed_form) = 22.636985450594865317605383535152 y[1] (numeric) = 22.636985450594865317605383535133 absolute error = 1.9e-29 relative error = 8.3933437345124543035653226931114e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.18 y[1] (closed_form) = 22.659633758311959785188223564922 y[1] (numeric) = 22.659633758311959785188223564904 absolute error = 1.8e-29 relative error = 7.9436411867854119181195857699727e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.19 y[1] (closed_form) = 22.682304725664700867606984874462 y[1] (numeric) = 22.682304725664700867606984874445 absolute error = 1.7e-29 relative error = 7.4948292096458544744192536105242e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.2 y[1] (closed_form) = 22.704998375324057806850092252533 y[1] (numeric) = 22.704998375324057806850092252517 absolute error = 1.6e-29 relative error = 7.0469064720959882008172508070478e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.21 y[1] (closed_form) = 22.727714729983682153412019593238 y[1] (numeric) = 22.727714729983682153412019593223 absolute error = 1.5e-29 relative error = 6.5998716449090038227966612207977e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.22 y[1] (closed_form) = 22.750453812359930459946731528186 y[1] (numeric) = 22.750453812359930459946731528172 absolute error = 1.4e-29 relative error = 6.1537234006268660319428448007032e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1446.4MB, alloc=44.3MB, time=15.52 TOP MAIN SOLVE Loop x[1] = 6.23 y[1] (closed_form) = 22.773215645191886997626129110234 y[1] (numeric) = 22.773215645191886997626129110221 absolute error = 1.3e-29 relative error = 5.7084604135581056045532705353252e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.24 y[1] (closed_form) = 22.796000251241386495226215909137 y[1] (numeric) = 22.796000251241386495226215909124 absolute error = 1.3e-29 relative error = 5.7027548064235820140298240335007e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.25 y[1] (closed_form) = 22.818807653293036900963723607183 y[1] (numeric) = 22.818807653293036900963723607168 absolute error = 1.5e-29 relative error = 6.5735248869742385500055013606045e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.26 y[1] (closed_form) = 22.841637874154242167105958933306 y[1] (numeric) = 22.841637874154242167105958933292 absolute error = 1.4e-29 relative error = 6.1291576712374345488782800372467e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.27 y[1] (closed_form) = 22.864490936655225057376656547464 y[1] (numeric) = 22.864490936655225057376656547451 absolute error = 1.3e-29 relative error = 5.6856721787577788003654407949367e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.28 y[1] (closed_form) = 22.887366863649049977180645282991 y[1] (numeric) = 22.887366863649049977180645282978 absolute error = 1.3e-29 relative error = 5.6799893484677352262962547935495e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.29 y[1] (closed_form) = 22.91026567801164582667015797353 y[1] (numeric) = 22.910265678011645826670157973517 absolute error = 1.3e-29 relative error = 5.6743121981675134524237784814911e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.3 y[1] (closed_form) = 22.933187402641828876675637932731 y[1] (numeric) = 22.933187402641828876675637932719 absolute error = 1.2e-29 relative error = 5.2325914358584271127049512596389e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.31 y[1] (closed_form) = 22.956132060461325667523918019455 y[1] (numeric) = 22.956132060461325667523918019443 absolute error = 1.2e-29 relative error = 5.2273614598464060232082300610695e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.32 y[1] (closed_form) = 22.979099674414795930766671108543 y[1] (numeric) = 22.97909967441479593076667110853 absolute error = 1.3e-29 relative error = 5.6573147704626370930526263633234e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.33 y[1] (closed_form) = 23.002090267469855533842053697532 y[1] (numeric) = 23.002090267469855533842053697517 absolute error = 1.5e-29 relative error = 6.5211464808541264229000190727739e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.34 y[1] (closed_form) = 23.025103862617099447692487312864 y[1] (numeric) = 23.025103862617099447692487312849 absolute error = 1.5e-29 relative error = 6.5146285938599266368341802022174e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.35 y[1] (closed_form) = 23.048140482870124737361545335286 y[1] (numeric) = 23.048140482870124737361545335272 absolute error = 1.4e-29 relative error = 6.0742427400618726900006140605500e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.36 y[1] (closed_form) = 23.071200151265553575592935843244 y[1] (numeric) = 23.071200151265553575592935843232 absolute error = 1.2e-29 relative error = 5.2012898857980515152061954164315e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.37 y[1] (closed_form) = 23.094282890863056279454594075168 y[1] (numeric) = 23.094282890863056279454594075154 absolute error = 1.4e-29 relative error = 6.0621063949722866241852516056980e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.38 y[1] (closed_form) = 23.117388724745374370010921136662 y[1] (numeric) = 23.117388724745374370010921136649 absolute error = 1.3e-29 relative error = 5.6234725101475266311949158370875e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1487.7MB, alloc=44.3MB, time=15.97 TOP MAIN SOLVE Loop x[1] = 6.39 y[1] (closed_form) = 23.140517676018343655066228626768 y[1] (numeric) = 23.140517676018343655066228626756 absolute error = 1.2e-29 relative error = 5.1857093985568827918177629896125e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.4 y[1] (closed_form) = 23.163669767810917335002471928655 y[1] (numeric) = 23.163669767810917335002471928644 absolute error = 1.1e-29 relative error = 4.7488157577198766227486104895826e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.41 y[1] (closed_form) = 23.186845023275189131734378004407 y[1] (numeric) = 23.186845023275189131734378004396 absolute error = 1.1e-29 relative error = 4.7440693155787641408672287988008e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.42 y[1] (closed_form) = 23.210043465586416440805096650958 y[1] (numeric) = 23.210043465586416440805096650945 absolute error = 1.3e-29 relative error = 5.6010235479632466817587606930248e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.43 y[1] (closed_form) = 23.233265117943043506645527314753 y[1] (numeric) = 23.23326511794304350664552731474 absolute error = 1.3e-29 relative error = 5.5954253239937868213535486885339e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.44 y[1] (closed_form) = 23.256510003566724621020496726403 y[1] (numeric) = 23.25651000356672462102049672639 absolute error = 1.3e-29 relative error = 5.5898326954501172401943670348932e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.45 y[1] (closed_form) = 23.279778145702347344684985803432 y[1] (numeric) = 23.279778145702347344684985803417 absolute error = 1.5e-29 relative error = 6.4433603731610872252606619985112e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.46 y[1] (closed_form) = 23.303069567618055752273627479285 y[1] (numeric) = 23.303069567618055752273627479271 absolute error = 1.4e-29 relative error = 6.0077922178348552265343041406078e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.47 y[1] (closed_form) = 23.326384292605273700446720350032 y[1] (numeric) = 23.326384292605273700446720350019 absolute error = 1.3e-29 relative error = 5.5730883264755036560690540120835e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.48 y[1] (closed_form) = 23.349722343978728119316026286723 y[1] (numeric) = 23.34972234397872811931602628671 absolute error = 1.3e-29 relative error = 5.5675180237645755013311687700969e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.49 y[1] (closed_form) = 23.37308374507647232717364344112 y[1] (numeric) = 23.373083745076472327173643441107 absolute error = 1.3e-29 relative error = 5.5619532885721350710195639020239e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.5 y[1] (closed_form) = 23.396468519259909368547269375638 y[1] (numeric) = 23.396468519259909368547269375626 absolute error = 1.2e-29 relative error = 5.1289791833847200390454100941166e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.51 y[1] (closed_form) = 23.419876689913815375605192374698 y[1] (numeric) = 23.419876689913815375605192374685 absolute error = 1.3e-29 relative error = 5.5508404984893367132172458166891e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.52 y[1] (closed_form) = 23.443308280446362952934372344421 y[1] (numeric) = 23.443308280446362952934372344408 absolute error = 1.3e-29 relative error = 5.5452924324861877768623036950505e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.53 y[1] (closed_form) = 23.466763314289144585714996080705 y[1] (numeric) = 23.466763314289144585714996080692 absolute error = 1.3e-29 relative error = 5.5397499117759334344132492083954e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1528.9MB, alloc=44.3MB, time=16.41 TOP MAIN SOLVE Loop x[1] = 6.54 y[1] (closed_form) = 23.490241814897196071314915082181 y[1] (numeric) = 23.490241814897196071314915082167 absolute error = 1.4e-29 relative error = 5.9599216178019027071035370155002e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.55 y[1] (closed_form) = 23.513743805749019974327397504452 y[1] (numeric) = 23.513743805749019974327397504438 absolute error = 1.4e-29 relative error = 5.9539646751518377161238079965368e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.56 y[1] (closed_form) = 23.5372693103466091050756492953 y[1] (numeric) = 23.537269310346609105075649295285 absolute error = 1.5e-29 relative error = 6.3728718069288686150584962988402e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.57 y[1] (closed_form) = 23.560818352215470021607583017364 y[1] (numeric) = 23.560818352215470021607583017348 absolute error = 1.6e-29 relative error = 6.7909355951956942858131279867809e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.58 y[1] (closed_form) = 23.584390954904646555204336354993 y[1] (numeric) = 23.584390954904646555204336354977 absolute error = 1.6e-29 relative error = 6.7841480539367564892432757527743e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.59 y[1] (closed_form) = 23.607987141986743359426065815772 y[1] (numeric) = 23.607987141986743359426065815757 absolute error = 1.5e-29 relative error = 6.3537818407747856016749240760556e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.6 y[1] (closed_form) = 23.631606937057949482718564674462 y[1] (numeric) = 23.631606937057949482718564674446 absolute error = 1.6e-29 relative error = 6.7705933170839810680614322864997e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.61 y[1] (closed_form) = 23.655250363738061964604277767948 y[1] (numeric) = 23.655250363738061964604277767933 absolute error = 1.5e-29 relative error = 6.3410869761894426197930417084901e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.62 y[1] (closed_form) = 23.678917445670509455481309334171 y[1] (numeric) = 23.678917445670509455481309334157 absolute error = 1.4e-29 relative error = 5.9124324547868137615431798907316e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.63 y[1] (closed_form) = 23.702608206522375860054043696015 y[1] (numeric) = 23.702608206522375860054043696001 absolute error = 1.4e-29 relative error = 5.9065229775630952341476047216445e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.64 y[1] (closed_form) = 23.726322669984424004419022222751 y[1] (numeric) = 23.726322669984424004419022222737 absolute error = 1.4e-29 relative error = 5.9006194068628464801118009666625e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.65 y[1] (closed_form) = 23.750060859771119326829743656881 y[1] (numeric) = 23.750060859771119326829743656865 absolute error = 1.6e-29 relative error = 6.7368248420371386368260264805077e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.66 y[1] (closed_form) = 23.773822799620653592164078573154 y[1] (numeric) = 23.773822799620653592164078573138 absolute error = 1.6e-29 relative error = 6.7300913844849990213232289893681e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.67 y[1] (closed_form) = 23.79760851329496863011801243915 y[1] (numeric) = 23.797608513294968630118012439133 absolute error = 1.7e-29 relative error = 7.1435749480888550275235330160416e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.68 y[1] (closed_form) = 23.82141802457978009714945547315 y[1] (numeric) = 23.821418024579780097149455473133 absolute error = 1.7e-29 relative error = 7.1364349437379419816783467564308e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1570.1MB, alloc=44.3MB, time=16.84 TOP MAIN SOLVE Loop x[1] = 6.69 y[1] (closed_form) = 23.845251357284601262195881245086 y[1] (numeric) = 23.84525135728460126219588124507 absolute error = 1.6e-29 relative error = 6.7099313654800634133712411931780e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.7 y[1] (closed_form) = 23.869108535242766816189579740184 y[1] (numeric) = 23.869108535242766816189579740166 absolute error = 1.8e-29 relative error = 7.5411278864575016853483949240890e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.71 y[1] (closed_form) = 23.892989582311456705394334402544 y[1] (numeric) = 23.892989582311456705394334402525 absolute error = 1.9e-29 relative error = 7.9521233349828050774729061067004e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.72 y[1] (closed_form) = 23.916894522371719988587356497323 y[1] (numeric) = 23.916894522371719988587356497304 absolute error = 1.9e-29 relative error = 7.9441751863844671468498106209607e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.73 y[1] (closed_form) = 23.940823379328498718110333975428 y[1] (numeric) = 23.940823379328498718110333975411 absolute error = 1.7e-29 relative error = 7.1008418259659799715974477203536e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.74 y[1] (closed_form) = 23.964776177110651844813475893779 y[1] (numeric) = 23.964776177110651844813475893763 absolute error = 1.6e-29 relative error = 6.6764654431790580199533493149484e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.75 y[1] (closed_form) = 23.988752939670979146916457337163 y[1] (numeric) = 23.988752939670979146916457337146 absolute error = 1.7e-29 relative error = 7.0866543345346428439500520997187e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.76 y[1] (closed_form) = 24.012753690986245182810193704622 y[1] (numeric) = 24.012753690986245182810193704604 absolute error = 1.8e-29 relative error = 7.4960165883668417268247879841025e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.77 y[1] (closed_form) = 24.03677845505720326782339716415 y[1] (numeric) = 24.036778455057203267823397164131 absolute error = 1.9e-29 relative error = 7.9045534473453977554716844802968e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.78 y[1] (closed_form) = 24.060827255908619474977892044249 y[1] (numeric) = 24.06082725590861947497789204423 absolute error = 1.9e-29 relative error = 7.8966528448576797463908618810618e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.79 y[1] (closed_form) = 24.084900117589296659756689919656 y[1] (numeric) = 24.084900117589296659756689919638 absolute error = 1.8e-29 relative error = 7.4735622369695980889199084882794e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.8 y[1] (closed_form) = 24.108997064172098508908849161329 y[1] (numeric) = 24.108997064172098508908849161311 absolute error = 1.8e-29 relative error = 7.4660924102684646056256669149862e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.81 y[1] (closed_form) = 24.133118119753973613315167757546 y[1] (numeric) = 24.133118119753973613315167757528 absolute error = 1.8e-29 relative error = 7.4586300496603635651842924853646e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.82 y[1] (closed_form) = 24.157263308455979564938782273816 y[1] (numeric) = 24.157263308455979564938782273799 absolute error = 1.7e-29 relative error = 7.0372209728116596410962655752386e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.83 y[1] (closed_form) = 24.181432654423307077884769904222 y[1] (numeric) = 24.181432654423307077884769904205 absolute error = 1.7e-29 relative error = 7.0301872692767573840565114852527e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.84 y[1] (closed_form) = 24.205626181825304133592874675782 y[1] (numeric) = 24.205626181825304133592874675766 absolute error = 1.6e-29 relative error = 6.6100335020514920025720246085140e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1611.5MB, alloc=44.3MB, time=17.30 TOP MAIN SOLVE Loop x[1] = 6.85 y[1] (closed_form) = 24.2298439148555001501875030006 y[1] (numeric) = 24.229843914855500150187503000585 absolute error = 1.5e-29 relative error = 6.1907125991857449834015851143398e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.86 y[1] (closed_form) = 24.254085877731630176009157927788 y[1] (numeric) = 24.254085877731630176009157927773 absolute error = 1.5e-29 relative error = 6.1845249809113312928706757960583e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.87 y[1] (closed_form) = 24.278352094695659107351505628623 y[1] (numeric) = 24.278352094695659107351505628609 absolute error = 1.4e-29 relative error = 5.7664539773515862980519824493748e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.88 y[1] (closed_form) = 24.302642590013805930428291854023 y[1] (numeric) = 24.302642590013805930428291854008 absolute error = 1.5e-29 relative error = 6.1721682917575585130626029656464e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.89 y[1] (closed_form) = 24.326957387976567987594350333277 y[1] (numeric) = 24.32695738797656798759435033326 absolute error = 1.7e-29 relative error = 6.9881324363243771389936663967171e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.9 y[1] (closed_form) = 24.351296512898745267844969337052 y[1] (numeric) = 24.351296512898745267844969337036 absolute error = 1.6e-29 relative error = 6.5704920440375278104620802542430e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.91 y[1] (closed_form) = 24.375659989119464721617906906091 y[1] (numeric) = 24.375659989119464721617906906076 absolute error = 1.5e-29 relative error = 6.1536795338856600092182446998621e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.92 y[1] (closed_form) = 24.400047841002204599922369549609 y[1] (numeric) = 24.400047841002204599922369549594 absolute error = 1.5e-29 relative error = 6.1475289301661843884332157391829e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.93 y[1] (closed_form) = 24.424460092934818817819293544427 y[1] (numeric) = 24.424460092934818817819293544411 absolute error = 1.6e-29 relative error = 6.5508101055745613097889765653054e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.94 y[1] (closed_form) = 24.448896769329561342277292317131 y[1] (numeric) = 24.448896769329561342277292317113 absolute error = 1.8e-29 relative error = 7.3622953910053245907546807945848e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.95 y[1] (closed_form) = 24.473357894623110604428657767256 y[1] (numeric) = 24.473357894623110604428657767236 absolute error = 2.0e-29 relative error = 8.1721519728169691532863573768445e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.96 y[1] (closed_form) = 24.49784349327659393624982778951 y[1] (numeric) = 24.49784349327659393624982778949 absolute error = 2.0e-29 relative error = 8.1639839055584537020571023271560e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.97 y[1] (closed_form) = 24.522353589775612031690756677561 y[1] (numeric) = 24.522353589775612031690756677542 absolute error = 1.9e-29 relative error = 7.7480328021702979342315390922281e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.98 y[1] (closed_form) = 24.546888208630263432277649540782 y[1] (numeric) = 24.546888208630263432277649540762 absolute error = 2.0e-29 relative error = 8.1476722548352765170825982916652e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.99 y[1] (closed_form) = 24.571447374375169037213546338735 y[1] (numeric) = 24.571447374375169037213546338717 absolute error = 1.8e-29 relative error = 7.3255757895530664307703028808068e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1652.8MB, alloc=44.3MB, time=17.73 TOP MAIN SOLVE Loop x[1] = 7 y[1] (closed_form) = 24.596031111569496638001265636025 y[1] (numeric) = 24.596031111569496638001265636006 absolute error = 1.9e-29 relative error = 7.7248235350713831257856305532668e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.01 y[1] (closed_form) = 24.620639444796985477613242702496 y[1] (numeric) = 24.620639444796985477613242702478 absolute error = 1.8e-29 relative error = 7.3109392793629867823280030306300e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.02 y[1] (closed_form) = 24.645272398665970834232821130679 y[1] (numeric) = 24.64527239866597083423282113066 absolute error = 1.9e-29 relative error = 7.7093893273536936119620264426920e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.03 y[1] (closed_form) = 24.669929997809408629591581713805 y[1] (numeric) = 24.669929997809408629591581713785 absolute error = 2.0e-29 relative error = 8.1070355699330805624130064143324e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.04 y[1] (closed_form) = 24.694612266884900061927316923782 y[1] (numeric) = 24.694612266884900061927316923761 absolute error = 2.1e-29 relative error = 8.5038792158566024579535736535319e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.05 y[1] (closed_form) = 24.719319230574716263587283949159 y[1] (numeric) = 24.719319230574716263587283949137 absolute error = 2.2e-29 relative error = 8.8999214722664136404390295008427e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.06 y[1] (closed_form) = 24.744050913585822983301393898375 y[1] (numeric) = 24.744050913585822983301393898353 absolute error = 2.2e-29 relative error = 8.8910259992719338705353664855398e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.07 y[1] (closed_form) = 24.768807340649905293150019443555 y[1] (numeric) = 24.768807340649905293150019443532 absolute error = 2.3e-29 relative error = 9.2858730271816576683064323235353e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.08 y[1] (closed_form) = 24.793588536523392320251127874703 y[1] (numeric) = 24.793588536523392320251127874681 absolute error = 2.2e-29 relative error = 8.8732617174766121948154608207467e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.09 y[1] (closed_form) = 24.818394525987482003191471253503 y[1] (numeric) = 24.818394525987482003191471253483 absolute error = 2.0e-29 relative error = 8.0585389917377154666551607539244e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.1 y[1] (closed_form) = 24.843225333848165873226590099968 y[1] (numeric) = 24.843225333848165873226590099948 absolute error = 2.0e-29 relative error = 8.0504844806727194934046412998546e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.11 y[1] (closed_form) = 24.868080984936253860274411814005 y[1] (numeric) = 24.868080984936253860274411813986 absolute error = 1.9e-29 relative error = 7.6403161190882313132725654126238e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.12 y[1] (closed_form) = 24.892961504107399123727249827578 y[1] (numeric) = 24.892961504107399123727249827561 absolute error = 1.7e-29 relative error = 6.8292396616589627954865312478910e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.13 y[1] (closed_form) = 24.917866916242122908107034301518 y[1] (numeric) = 24.917866916242122908107034301502 absolute error = 1.6e-29 relative error = 6.4210953745686706321389844428550e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.14 y[1] (closed_form) = 24.942797246245839423588630024294 y[1] (numeric) = 24.942797246245839423588630024277 absolute error = 1.7e-29 relative error = 6.8155948317138663115265984251069e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1694.1MB, alloc=44.3MB, time=18.17 TOP MAIN SOLVE Loop x[1] = 7.15 y[1] (closed_form) = 24.967752519048880751416122038129 y[1] (numeric) = 24.967752519048880751416122038111 absolute error = 1.8e-29 relative error = 7.2092992696347385657342014035387e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.16 y[1] (closed_form) = 24.992732759606521774236974410829 y[1] (numeric) = 24.992732759606521774236974410812 absolute error = 1.7e-29 relative error = 6.8019772641571841440191915870947e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.17 y[1] (closed_form) = 25.017737992899005131378992489557 y[1] (numeric) = 25.017737992899005131378992489539 absolute error = 1.8e-29 relative error = 7.1948950800864136095741411921291e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.18 y[1] (closed_form) = 25.042768243931566199095043915592 y[1] (numeric) = 25.042768243931566199095043915575 absolute error = 1.7e-29 relative error = 6.7883869045186279094764775602653e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.19 y[1] (closed_form) = 25.067823537734458095800518646885 y[1] (numeric) = 25.067823537734458095800518646868 absolute error = 1.7e-29 relative error = 6.7816019106764465163550755429502e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.2 y[1] (closed_form) = 25.092903899362976712328533227943 y[1] (numeric) = 25.092903899362976712328533227926 absolute error = 1.7e-29 relative error = 6.7748236984367409331915840346750e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.21 y[1] (closed_form) = 25.118009353897485767227909564335 y[1] (numeric) = 25.118009353897485767227909564319 absolute error = 1.6e-29 relative error = 6.3699315397847513933452998288149e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.22 y[1] (closed_form) = 25.143139926443441887128983501903 y[1] (numeric) = 25.143139926443441887128983501886 absolute error = 1.7e-29 relative error = 6.7612875916586808033394187846390e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.23 y[1] (closed_form) = 25.168295642131419712202323578543 y[1] (numeric) = 25.168295642131419712202323578526 absolute error = 1.7e-29 relative error = 6.7545296835842183505816794187380e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.24 y[1] (closed_form) = 25.193476526117137026735465409403 y[1] (numeric) = 25.193476526117137026735465409388 absolute error = 1.5e-29 relative error = 5.9539222323882373760600163842663e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.25 y[1] (closed_form) = 25.218682603581479914852792284304 y[1] (numeric) = 25.218682603581479914852792284289 absolute error = 1.5e-29 relative error = 5.9479712861248929912232038971166e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.26 y[1] (closed_form) = 25.243913899730527941403717699362 y[1] (numeric) = 25.243913899730527941403717699347 absolute error = 1.5e-29 relative error = 5.9420262878333303955697485170098e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.27 y[1] (closed_form) = 25.269170439795579358044350713106 y[1] (numeric) = 25.269170439795579358044350713091 absolute error = 1.5e-29 relative error = 5.9360872315685508021205137797234e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.28 y[1] (closed_form) = 25.294452249033176334537850210844 y[1] (numeric) = 25.294452249033176334537850210831 absolute error = 1.3e-29 relative error = 5.1394668965392977910179297616318e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.29 y[1] (closed_form) = 25.319759352725130215298699379741 y[1] (numeric) = 25.319759352725130215298699379728 absolute error = 1.3e-29 relative error = 5.1343299985198430484181931707718e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1735.3MB, alloc=44.3MB, time=18.62 TOP MAIN SOLVE Loop x[1] = 7.3 y[1] (closed_form) = 25.345091776178546801206156940979 y[1] (numeric) = 25.345091776178546801206156940967 absolute error = 1.2e-29 relative error = 4.7346445244592135567775172428192e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.31 y[1] (closed_form) = 25.370449544725851656712166954577 y[1] (numeric) = 25.370449544725851656712166954566 absolute error = 1.1e-29 relative error = 4.3357528925957641903664801096407e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.32 y[1] (closed_form) = 25.395832683724815442269034306862 y[1] (numeric) = 25.39583268372481544226903430685 absolute error = 1.2e-29 relative error = 4.7251846983896398496772943837562e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.33 y[1] (closed_form) = 25.421241218558579272102198310405 y[1] (numeric) = 25.421241218558579272102198310394 absolute error = 1.1e-29 relative error = 4.3270900525382433428326916160991e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.34 y[1] (closed_form) = 25.446675174635680097353462191288 y[1] (numeric) = 25.446675174635680097353462191276 absolute error = 1.2e-29 relative error = 4.7157437730651599482410226489419e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.35 y[1] (closed_form) = 25.472134577390076114620061609054 y[1] (numeric) = 25.472134577390076114620061609042 absolute error = 1.2e-29 relative error = 4.7110303863782204753944574034685e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.36 y[1] (closed_form) = 25.497619452281172199914980750537 y[1] (numeric) = 25.497619452281172199914980750526 absolute error = 1.1e-29 relative error = 4.3141282348285549694264031610286e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.37 y[1] (closed_form) = 25.523129824793845368073949959983 y[1] (numeric) = 25.523129824793845368073949959972 absolute error = 1.1e-29 relative error = 4.3098162629390021756610758646169e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.38 y[1] (closed_form) = 25.548665720438470257634584314605 y[1] (numeric) = 25.548665720438470257634584314594 absolute error = 1.1e-29 relative error = 4.3055086008660714722651408581845e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.39 y[1] (closed_form) = 25.574227164750944641213148026824 y[1] (numeric) = 25.574227164750944641213148026813 absolute error = 1.1e-29 relative error = 4.3012052443021004273360433691759e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.4 y[1] (closed_form) = 25.599814183292714961404455052082 y[1] (numeric) = 25.599814183292714961404455052071 absolute error = 1.1e-29 relative error = 4.2969061889437321182896795171382e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.41 y[1] (closed_form) = 25.625426801650801892230441804265 y[1] (numeric) = 25.625426801650801892230441804256 absolute error = 9e-30 relative error = 3.5121366249479270415025487317047e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.42 y[1] (closed_form) = 25.651065045437825926162973429434 y[1] (numeric) = 25.651065045437825926162973429425 absolute error = 9e-30 relative error = 3.5086262438060817940296906538269e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.43 y[1] (closed_form) = 25.676728940292032986746470662803 y[1] (numeric) = 25.676728940292032986746470662795 absolute error = 8e-30 relative error = 3.1156616633695757672610577451618e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.44 y[1] (closed_form) = 25.702418511877320066845969893721 y[1] (numeric) = 25.702418511877320066845969893713 absolute error = 8e-30 relative error = 3.1125475590178907256632042507354e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.45 y[1] (closed_form) = 25.728133785883260892546254688867 y[1] (numeric) = 25.728133785883260892546254688859 absolute error = 8e-30 relative error = 3.1094365672140240809279738760032e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1776.5MB, alloc=44.3MB, time=19.06 TOP MAIN SOLVE Loop x[1] = 7.46 y[1] (closed_form) = 25.753874788025131612727722674912 y[1] (numeric) = 25.753874788025131612727722674905 absolute error = 7e-30 relative error = 2.7180375992411107986969717233032e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.47 y[1] (closed_form) = 25.77964154404393651434467735867 y[1] (numeric) = 25.779641544043936514344677358663 absolute error = 7e-30 relative error = 2.7153209202077762708335851992190e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.48 y[1] (closed_form) = 25.80543407970643376343176016516 y[1] (numeric) = 25.805434079706433763431760165152 absolute error = 8e-30 relative error = 3.1001222359949579742827002457017e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.49 y[1] (closed_form) = 25.83125242080516117186426370217 y[1] (numeric) = 25.831252420805161171864263702162 absolute error = 8e-30 relative error = 3.0970236633035231203846979580176e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.5 y[1] (closed_form) = 25.857096593158461989898093013769 y[1] (numeric) = 25.857096593158461989898093013763 absolute error = 6e-30 relative error = 2.3204461407270072414927706442158e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.51 y[1] (closed_form) = 25.88296662261051072451516736489 y[1] (numeric) = 25.882966622610510724515167364885 absolute error = 5e-30 relative error = 1.9317723786855885335186935392765e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.52 y[1] (closed_form) = 25.908862535031338983600080904531 y[1] (numeric) = 25.908862535031338983600080904525 absolute error = 6e-30 relative error = 2.3158098862454528389026418727106e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.53 y[1] (closed_form) = 25.934784356316861345973866386383 y[1] (numeric) = 25.934784356316861345973866386378 absolute error = 5e-30 relative error = 1.9279126948985655559994252727965e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.54 y[1] (closed_form) = 25.960732112388901257310731982824 y[1] (numeric) = 25.960732112388901257310731982819 absolute error = 5e-30 relative error = 1.9259857458387759708754685113593e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.55 y[1] (closed_form) = 25.986705829195216951963667111146 y[1] (numeric) = 25.986705829195216951963667111141 absolute error = 5e-30 relative error = 1.9240607227648927233449858172222e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.56 y[1] (closed_form) = 26.012705532709527400724839099806 y[1] (numeric) = 26.012705532709527400724839099803 absolute error = 3e-30 relative error = 1.1532825742511355474636808934073e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.57 y[1] (closed_form) = 26.038731248931538284546728457248 y[1] (numeric) = 26.038731248931538284546728457246 absolute error = 2e-30 relative error = 7.6808657875067054596020594503636e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.58 y[1] (closed_form) = 26.064783003886967994249976466592 y[1] (numeric) = 26.064783003886967994249976466589 absolute error = 3e-30 relative error = 1.1509783141308402272483000766309e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.59 y[1] (closed_form) = 26.090860823627573656243944816215 y[1] (numeric) = 26.090860823627573656243944816213 absolute error = 2e-30 relative error = 7.6655194074272312083948436626695e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.6 y[1] (closed_form) = 26.116964734231177184286012988948 y[1] (numeric) = 26.116964734231177184286012988946 absolute error = 2e-30 relative error = 7.6578577195022404556708072550891e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1817.5MB, alloc=44.3MB, time=19.52 TOP MAIN SOLVE Loop x[1] = 7.61 y[1] (closed_form) = 26.14309476180169135730566517135 y[1] (numeric) = 26.143094761801691357305665171347 absolute error = 3e-30 relative error = 1.1475305534153411040027685298599e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.62 y[1] (closed_form) = 26.169250932469145923319444509332 y[1] (numeric) = 26.169250932469145923319444509329 absolute error = 3e-30 relative error = 1.1463835964359951825453255042444e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.63 y[1] (closed_form) = 26.195433272389713729462878627251 y[1] (numeric) = 26.195433272389713729462878627248 absolute error = 3e-30 relative error = 1.1452377858403412290526190891556e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.64 y[1] (closed_form) = 26.221641807745736878165506444582 y[1] (numeric) = 26.22164180774573687816550644458 absolute error = 2e-30 relative error = 7.6272874698837903492431753638897e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.65 y[1] (closed_form) = 26.247876564745752909495162467371 y[1] (numeric) = 26.247876564745752909495162467369 absolute error = 2e-30 relative error = 7.6196639947867446625695832691303e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.66 y[1] (closed_form) = 26.274137569624521009697700900936 y[1] (numeric) = 26.274137569624521009697700900933 absolute error = 3e-30 relative error = 1.1418072209031493101992077559559e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.67 y[1] (closed_form) = 26.300424848643048245958368125726 y[1] (numeric) = 26.300424848643048245958368125724 absolute error = 2e-30 relative error = 7.6044398959706864984480122442709e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.68 y[1] (closed_form) = 26.326738428088615827411058299901 y[1] (numeric) = 26.326738428088615827411058299898 absolute error = 3e-30 relative error = 1.1395258885541360904400388347883e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.69 y[1] (closed_form) = 26.353078334274805392421713100058 y[1] (numeric) = 26.353078334274805392421713100057 absolute error = 1e-30 relative error = 3.7946231074621757358094815579866e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.7 y[1] (closed_form) = 26.379444593541525322172152885726 y[1] (numeric) = 26.379444593541525322172152885724 absolute error = 2e-30 relative error = 7.5816607620679763685281305548054e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.71 y[1] (closed_form) = 26.405837232255037080570652873613 y[1] (numeric) = 26.405837232255037080570652873612 absolute error = 1e-30 relative error = 3.7870414454364975692491161778128e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.72 y[1] (closed_form) = 26.432256276807981580515604234421 y[1] (numeric) = 26.43225627680798158051560423442 absolute error = 1e-30 relative error = 3.7832562968807679775293755952282e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.73 y[1] (closed_form) = 26.458701753619405576538626378044 y[1] (numeric) = 26.458701753619405576538626378044 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.74 y[1] (closed_form) = 26.485173689134788083853523072498 y[1] (numeric) = 26.485173689134788083853523072498 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.75 y[1] (closed_form) = 26.51167210982606682383750144771 y[1] (numeric) = 26.511672109826066823837501447711 absolute error = 1e-30 relative error = 3.7719235356315691338261078131295e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1858.7MB, alloc=44.3MB, time=19.95 TOP MAIN SOLVE Loop x[1] = 7.76 y[1] (closed_form) = 26.538197042191664695971099367612 y[1] (numeric) = 26.538197042191664695971099367614 absolute error = 2e-30 relative error = 7.5363069948584171798495606311357e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.77 y[1] (closed_form) = 26.564748512756516276263293112661 y[1] (numeric) = 26.564748512756516276263293112662 absolute error = 1e-30 relative error = 3.7643872273806594880339622700709e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.78 y[1] (closed_form) = 26.591326548072094342188283800101 y[1] (numeric) = 26.591326548072094342188283800102 absolute error = 1e-30 relative error = 3.7606247217196514657487039448675e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.79 y[1] (closed_form) = 26.617931174716436424160487480972 y[1] (numeric) = 26.617931174716436424160487480973 absolute error = 1e-30 relative error = 3.7568659766836785485188341859594e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.8 y[1] (closed_form) = 26.644562419294171383574280391061 y[1] (numeric) = 26.644562419294171383574280391063 absolute error = 2e-30 relative error = 7.5062219770279907742853446495499e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.81 y[1] (closed_form) = 26.671220308436546017435077397755 y[1] (numeric) = 26.671220308436546017435077397757 absolute error = 2e-30 relative error = 7.4987195069112269980427314953984e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.82 y[1] (closed_form) = 26.697904868801451689608348276095 y[1] (numeric) = 26.697904868801451689608348276098 absolute error = 3e-30 relative error = 1.1236836803271892539510283144513e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.83 y[1] (closed_form) = 26.724616127073450988713203065274 y[1] (numeric) = 26.724616127073450988713203065277 absolute error = 3e-30 relative error = 1.1225605583014684256947161316711e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.84 y[1] (closed_form) = 26.751354109963804412687204401361 y[1] (numeric) = 26.751354109963804412687204401364 absolute error = 3e-30 relative error = 1.1214385588363994456231396564714e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.85 y[1] (closed_form) = 26.778118844210497080049091393319 y[1] (numeric) = 26.778118844210497080049091393322 absolute error = 3e-30 relative error = 1.1203176808099827551673602781952e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.86 y[1] (closed_form) = 26.804910356578265467886126307243 y[1] (numeric) = 26.804910356578265467886126307246 absolute error = 3e-30 relative error = 1.1191979231013402345041822261223e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.87 y[1] (closed_form) = 26.831728673858624176592802048403 y[1] (numeric) = 26.831728673858624176592802048405 absolute error = 2e-30 relative error = 7.4538618972714272111862622650647e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.88 y[1] (closed_form) = 26.858573822869892721387675182026 y[1] (numeric) = 26.858573822869892721387675182028 absolute error = 2e-30 relative error = 7.4464117610631046189506653334842e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.89 y[1] (closed_form) = 26.885445830457222350635116011892 y[1] (numeric) = 26.885445830457222350635116011892 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.9 y[1] (closed_form) = 26.91234472349262289099879404071 y[1] (numeric) = 26.912344723492622890998794040711 absolute error = 1e-30 relative error = 3.7157669102204569053152411990820e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1899.9MB, alloc=44.3MB, time=20.41 TOP MAIN SOLVE Loop x[1] = 7.91 y[1] (closed_form) = 26.939270528874989619453743968019 y[1] (numeric) = 26.939270528874989619453743968019 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.92 y[1] (closed_form) = 26.966223273530130162183884239901 y[1] (numeric) = 26.966223273530130162183884239901 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.93 y[1] (closed_form) = 26.993202984410791420391887050278 y[1] (numeric) = 26.993202984410791420391887050278 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.94 y[1] (closed_form) = 27.0202096884966865230483256059 y[1] (numeric) = 27.020209688496686523048325605901 absolute error = 1e-30 relative error = 3.7009335291196129592889120266310e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.95 y[1] (closed_form) = 27.047243412794521806607051406423 y[1] (numeric) = 27.047243412794521806607051406422 absolute error = 1e-30 relative error = 3.6972344454405898260105739582920e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.96 y[1] (closed_form) = 27.074304184338023821713781257191 y[1] (numeric) = 27.074304184338023821713781257191 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.97 y[1] (closed_form) = 27.10139203018796636693490072558 y[1] (numeric) = 27.10139203018796636693490072558 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.98 y[1] (closed_form) = 27.128506977432197549533517771941 y[1] (numeric) = 27.128506977432197549533517771942 absolute error = 1e-30 relative error = 3.6861593630341882177995611821936e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.99 y[1] (closed_form) = 27.155649053185666873319827333453 y[1] (numeric) = 27.155649053185666873319827333454 absolute error = 1e-30 relative error = 3.6824750461366292120974231515422e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8 y[1] (closed_form) = 27.182818284590452353602874713527 y[1] (numeric) = 27.182818284590452353602874713529 absolute error = 2e-30 relative error = 7.3575888234288464319104754032291e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.01 y[1] (closed_form) = 27.210014698815787659270832730755 y[1] (numeric) = 27.210014698815787659270832730758 absolute error = 3e-30 relative error = 1.1025352368260806501342389847223e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.02 y[1] (closed_form) = 27.237238323058089282026934709967 y[1] (numeric) = 27.237238323058089282026934709972 absolute error = 5e-30 relative error = 1.8357220877886050658367026075358e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.03 y[1] (closed_form) = 27.26448918454098373280823255358 y[1] (numeric) = 27.264489184540983732808232553585 absolute error = 5e-30 relative error = 1.8338872832559831469004876891053e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.04 y[1] (closed_form) = 27.291767310515334765414376314268 y[1] (numeric) = 27.291767310515334765414376314273 absolute error = 5e-30 relative error = 1.8320543126107973078927851345247e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.05 y[1] (closed_form) = 27.319072728259270627373638900002 y[1] (numeric) = 27.319072728259270627373638900006 absolute error = 4e-30 relative error = 1.4641785392160614007041576632158e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.06 y[1] (closed_form) = 27.346405465078211338073436779749 y[1] (numeric) = 27.346405465078211338073436779752 absolute error = 3e-30 relative error = 1.0970363193916096395283673180758e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1941.2MB, alloc=44.3MB, time=20.84 TOP MAIN SOLVE Loop x[1] = 8.07 y[1] (closed_form) = 27.373765548304895994182624822638 y[1] (numeric) = 27.37376554830489599418262482264 absolute error = 2e-30 relative error = 7.3062655427172269322305724960500e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.08 y[1] (closed_form) = 27.401153005299410102392870695142 y[1] (numeric) = 27.401153005299410102392870695146 absolute error = 4e-30 relative error = 1.4597925858179749013962300107008e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.09 y[1] (closed_form) = 27.428567863449212939506441559956 y[1] (numeric) = 27.428567863449212939506441559959 absolute error = 3e-30 relative error = 1.0937501421639089127805900468556e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.1 y[1] (closed_form) = 27.456010150169164939897763166604 y[1] (numeric) = 27.456010150169164939897763166607 absolute error = 3e-30 relative error = 1.0926569387145699592711388869120e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.11 y[1] (closed_form) = 27.48347989290155511037613879765 y[1] (numeric) = 27.483479892901555110376138797653 absolute error = 3e-30 relative error = 1.0915648279222607750795750371546e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.12 y[1] (closed_form) = 27.510977119116128472477042935493 y[1] (numeric) = 27.510977119116128472477042935497 absolute error = 4e-30 relative error = 1.4539650782598273025166381065950e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.13 y[1] (closed_form) = 27.538501856310113532209431943337 y[1] (numeric) = 27.538501856310113532209431943339 absolute error = 2e-30 relative error = 7.2625591996091983092418622892664e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.14 y[1] (closed_form) = 27.566054132008249777286541509929 y[1] (numeric) = 27.566054132008249777286541509932 absolute error = 3e-30 relative error = 1.0882950405718597392578476744791e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.15 y[1] (closed_form) = 27.593633973762815201867668091167 y[1] (numeric) = 27.59363397376281520186766809117 absolute error = 3e-30 relative error = 1.0872072894974709952455592935609e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.16 y[1] (closed_form) = 27.621241409153653858838459092636 y[1] (numeric) = 27.621241409153653858838459092639 absolute error = 3e-30 relative error = 1.0861206256304623493147443010875e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.17 y[1] (closed_form) = 27.648876465788203439657264075669 y[1] (numeric) = 27.648876465788203439657264075674 absolute error = 5e-30 relative error = 1.8083917464736164065023858283543e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.18 y[1] (closed_form) = 27.676539171301522881795126835586 y[1] (numeric) = 27.676539171301522881795126835591 absolute error = 5e-30 relative error = 1.8065842586216927370805004358123e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.19 y[1] (closed_form) = 27.704229553356320003797025794385 y[1] (numeric) = 27.70422955335632000379702579439 absolute error = 5e-30 relative error = 1.8047785773541782380445888878624e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.2 y[1] (closed_form) = 27.731947639642979167991997771454 y[1] (numeric) = 27.73194763964297916799199777146 absolute error = 6e-30 relative error = 2.1635696410384697896880498079241e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.21 y[1] (closed_form) = 27.759693457879588970879807844716 y[1] (numeric) = 27.759693457879588970879807844722 absolute error = 6e-30 relative error = 2.1614071528217470296684790933891e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1982.5MB, alloc=44.3MB, time=21.28 TOP MAIN SOLVE Loop x[1] = 8.22 y[1] (closed_form) = 27.787467035811969961221855691182 y[1] (numeric) = 27.787467035811969961221855691187 absolute error = 5e-30 relative error = 1.7993723550102976738872309181534e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.23 y[1] (closed_form) = 27.815268401213702385864036500145 y[1] (numeric) = 27.815268401213702385864036500149 absolute error = 4e-30 relative error = 1.4380591056333155581730551417205e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.24 y[1] (closed_form) = 27.84309758188615396331930228417 y[1] (numeric) = 27.843097581886153963319302284174 absolute error = 4e-30 relative error = 1.4366217653176184488146811069680e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.25 y[1] (closed_form) = 27.87095460565850768513769717277 y[1] (numeric) = 27.870954605658507685137697172775 absolute error = 5e-30 relative error = 1.7939823270297579694489870473167e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.26 y[1] (closed_form) = 27.898839500387789645091668061106 y[1] (numeric) = 27.898839500387789645091668061112 absolute error = 6e-30 relative error = 2.1506270896739632874037935088864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.27 y[1] (closed_form) = 27.926752293958896896204479801354 y[1] (numeric) = 27.926752293958896896204479801359 absolute error = 5e-30 relative error = 1.7903979479495715869685028549762e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.28 y[1] (closed_form) = 27.95469301428462533564959196747 y[1] (numeric) = 27.954693014284625335649591967474 absolute error = 4e-30 relative error = 1.4308867559218167337381871037901e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.29 y[1] (closed_form) = 27.982661689305697617548882095049 y[1] (numeric) = 27.982661689305697617548882095053 absolute error = 4e-30 relative error = 1.4294565843708513602852738320182e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.3 y[1] (closed_form) = 28.010658346990791093697628196836 y[1] (numeric) = 28.01065834699079109369762819684 absolute error = 4e-30 relative error = 1.4280278422765894790697224626054e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.31 y[1] (closed_form) = 28.038683015336565782244191281195 y[1] (numeric) = 28.0386830153365657822441912812 absolute error = 5e-30 relative error = 1.7832506602628610959597582784777e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.32 y[1] (closed_form) = 28.066735722367692364352366555551 y[1] (numeric) = 28.066735722367692364352366555555 absolute error = 4e-30 relative error = 1.4251746407446353681360811874877e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.33 y[1] (closed_form) = 28.094816496136880208874399979479 y[1] (numeric) = 28.094816496136880208874399979484 absolute error = 5e-30 relative error = 1.7796877230671767108713476163405e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.34 y[1] (closed_form) = 28.122925364724905425062694842819 y[1] (numeric) = 28.122925364724905425062694842825 absolute error = 6e-30 relative error = 2.1334907098697167032774045537900e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.35 y[1] (closed_form) = 28.151062356240638943348261082825 y[1] (numeric) = 28.151062356240638943348261082833 absolute error = 8e-30 relative error = 2.8418110473996120188324143354978e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.36 y[1] (closed_form) = 28.179227498821074624213988121168 y[1] (numeric) = 28.179227498821074624213988121176 absolute error = 8e-30 relative error = 2.8389706567842193171688186524085e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2023.7MB, alloc=44.3MB, time=21.73 TOP MAIN SOLVE Loop x[1] = 8.37 y[1] (closed_form) = 28.20742082063135739519085009639 y[1] (numeric) = 28.207420820631357395190850096398 absolute error = 8e-30 relative error = 2.8361331051397199806204915194907e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.38 y[1] (closed_form) = 28.235642349864811416005180490368 y[1] (numeric) = 28.235642349864811416005180490377 absolute error = 9e-30 relative error = 3.1874606883321323942536328978075e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.39 y[1] (closed_form) = 28.263892114742968271905181298406 y[1] (numeric) = 28.263892114742968271905181298416 absolute error = 1.0e-29 relative error = 3.5380831342700375157494320279400e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.4 y[1] (closed_form) = 28.292170143515595195194860071813 y[1] (numeric) = 28.292170143515595195194860071823 absolute error = 1.0e-29 relative error = 3.5345468195878014815255826530896e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.41 y[1] (closed_form) = 28.32047646446072331500361636926 y[1] (numeric) = 28.32047646446072331500361636927 absolute error = 1.0e-29 relative error = 3.5310140394526795806813319730639e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.42 y[1] (closed_form) = 28.34881110588467593531972738885 y[1] (numeric) = 28.348811105884675935319727388859 absolute error = 9e-30 relative error = 3.1747363112987022453267822631580e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.43 y[1] (closed_form) = 28.377174096122096841316010816751 y[1] (numeric) = 28.37717409612209684131601081676 absolute error = 9e-30 relative error = 3.1715631618265687281107046813278e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.44 y[1] (closed_form) = 28.405565463535978633995971220407 y[1] (numeric) = 28.405565463535978633995971220416 absolute error = 9e-30 relative error = 3.1683931839178613344023173220922e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.45 y[1] (closed_form) = 28.43398523651769109318876463484 y[1] (numeric) = 28.433985236517691093188764634849 absolute error = 9e-30 relative error = 3.1652263744026018913293919459530e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.46 y[1] (closed_form) = 28.462433443487009568921344339362 y[1] (numeric) = 28.462433443487009568921344339372 absolute error = 1.0e-29 relative error = 3.5134030334599784663685374944499e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.47 y[1] (closed_form) = 28.490910112892143401196179199226 y[1] (numeric) = 28.490910112892143401196179199235 absolute error = 9e-30 relative error = 3.1589022478883529673508882818659e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.48 y[1] (closed_form) = 28.519415273209764368202964352279 y[1] (numeric) = 28.519415273209764368202964352288 absolute error = 9e-30 relative error = 3.1557449245652364451858255943189e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.49 y[1] (closed_form) = 28.547948952945035162992772454722 y[1] (numeric) = 28.547948952945035162992772454733 absolute error = 1.1e-29 relative error = 3.8531664807622646819007295584887e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.5 y[1] (closed_form) = 28.576511180631637898643122162488 y[1] (numeric) = 28.576511180631637898643122162498 absolute error = 1.0e-29 relative error = 3.4993774911115535467179887357681e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.51 y[1] (closed_form) = 28.605101984831802641942469015675 y[1] (numeric) = 28.605101984831802641942469015686 absolute error = 1.1e-29 relative error = 3.8454678489987141198684581515888e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2064.9MB, alloc=44.3MB, time=22.17 TOP MAIN SOLVE Loop x[1] = 8.52 y[1] (closed_form) = 28.633721394136335975622652412928 y[1] (numeric) = 28.633721394136335975622652412941 absolute error = 1.3e-29 relative error = 4.5401014492870503914034706699388e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.53 y[1] (closed_form) = 28.662369437164649589167860910568 y[1] (numeric) = 28.66236943716464958916786091058 absolute error = 1.2e-29 relative error = 4.1866741081218401932817853980622e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.54 y[1] (closed_form) = 28.691046142564788898228706657838 y[1] (numeric) = 28.69104614256478889822870665785 absolute error = 1.2e-29 relative error = 4.1824895266531678058596617249007e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.55 y[1] (closed_form) = 28.719751539013461692670028384709 y[1] (numeric) = 28.719751539013461692670028384722 absolute error = 1.3e-29 relative error = 4.5265015549805681634450871772262e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.56 y[1] (closed_form) = 28.748485655216066813281070992449 y[1] (numeric) = 28.748485655216066813281070992461 absolute error = 1.2e-29 relative error = 4.1741329070050492857715627020609e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.57 y[1] (closed_form) = 28.777248519906722857176718459518 y[1] (numeric) = 28.777248519906722857176718459532 absolute error = 1.4e-29 relative error = 4.8649543372138132767024189373922e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.58 y[1] (closed_form) = 28.806040161848296911918485466416 y[1] (numeric) = 28.80604016184829691191848546643 absolute error = 1.4e-29 relative error = 4.8600918145431450133595730048610e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.59 y[1] (closed_form) = 28.834860609832433318384001862864 y[1] (numeric) = 28.834860609832433318384001862877 absolute error = 1.3e-29 relative error = 4.5084317125386465650531345719402e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.6 y[1] (closed_form) = 28.863709892679582462413752849215 y[1] (numeric) = 28.863709892679582462413752849228 absolute error = 1.3e-29 relative error = 4.5039255342907467161456085251717e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.61 y[1] (closed_form) = 28.892588039239029595263866521213 y[1] (numeric) = 28.892588039239029595263866521225 absolute error = 1.2e-29 relative error = 4.1533143322788521401155388529755e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.62 y[1] (closed_form) = 28.921495078388923682893769233309 y[1] (numeric) = 28.921495078388923682893769233319 absolute error = 1.0e-29 relative error = 3.4576359115930778268169537776797e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.63 y[1] (closed_form) = 28.950431039036306284117558070577 y[1] (numeric) = 28.950431039036306284117558070588 absolute error = 1.1e-29 relative error = 3.7995980043156431262461248919251e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.64 y[1] (closed_form) = 28.979395950117140457647968583027 y[1] (numeric) = 28.979395950117140457647968583038 absolute error = 1.1e-29 relative error = 3.7958003054772215918143076172107e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.65 y[1] (closed_form) = 29.008389840596339698061844828672 y[1] (numeric) = 29.008389840596339698061844828681 absolute error = 9e-30 relative error = 3.1025506929049815147055220306146e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.66 y[1] (closed_form) = 29.037412739467796900716047693244 y[1] (numeric) = 29.037412739467796900716047693252 absolute error = 8e-30 relative error = 2.7550663937515204005564450591926e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.67 y[1] (closed_form) = 29.066464675754413355642766404877 y[1] (numeric) = 29.066464675754413355642766404887 absolute error = 1.0e-29 relative error = 3.4403908805398784938777264069348e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2106.2MB, alloc=44.3MB, time=22.63 TOP MAIN SOLVE Loop x[1] = 8.68 y[1] (closed_form) = 29.095545678508127770453227141486 y[1] (numeric) = 29.095545678508127770453227141496 absolute error = 1.0e-29 relative error = 3.4369522092815237261879919989852e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.69 y[1] (closed_form) = 29.124655776809945322278821636965 y[1] (numeric) = 29.124655776809945322278821636975 absolute error = 1.0e-29 relative error = 3.4335169749756646527156376623121e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.7 y[1] (closed_form) = 29.153794999769966738778707729755 y[1] (numeric) = 29.153794999769966738778707729766 absolute error = 1.1e-29 relative error = 3.7730936916057733494652603833863e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.71 y[1] (closed_form) = 29.182963376527417408242962863816 y[1] (numeric) = 29.182963376527417408242962863827 absolute error = 1.1e-29 relative error = 3.7693224838323216112014501005993e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.72 y[1] (closed_form) = 29.212160936250676518820400647562 y[1] (numeric) = 29.212160936250676518820400647572 absolute error = 1.0e-29 relative error = 3.4232318594378798322515521695300e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.73 y[1] (closed_form) = 29.241387708137306226900189701024 y[1] (numeric) = 29.241387708137306226900189701034 absolute error = 1.0e-29 relative error = 3.4198103386239756342582016636712e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.74 y[1] (closed_form) = 29.270643721414080854676443175278 y[1] (numeric) = 29.270643721414080854676443175288 absolute error = 1.0e-29 relative error = 3.4163922376206950444448702206494e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.75 y[1] (closed_form) = 29.299929005337016116924976511169 y[1] (numeric) = 29.299929005337016116924976511181 absolute error = 1.2e-29 relative error = 4.0955730636119241296270499108306e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.76 y[1] (closed_form) = 29.329243589191398377021460216515 y[1] (numeric) = 29.329243589191398377021460216526 absolute error = 1.1e-29 relative error = 3.7505229095147175226434742055178e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.77 y[1] (closed_form) = 29.358587502291813932230223682388 y[1] (numeric) = 29.358587502291813932230223682401 absolute error = 1.3e-29 relative error = 4.4280059451038587698748353424674e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.78 y[1] (closed_form) = 29.38796077398217832829299532972 y[1] (numeric) = 29.387960773982178328292995329734 absolute error = 1.4e-29 relative error = 4.7638555487642117767327079922954e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.79 y[1] (closed_form) = 29.417363433635765703346893677405 y[1] (numeric) = 29.41736343363576570334689367742 absolute error = 1.5e-29 relative error = 5.0990293653744047963109065835063e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.8 y[1] (closed_form) = 29.446795510655238161201013252344 y[1] (numeric) = 29.446795510655238161201013252359 absolute error = 1.5e-29 relative error = 5.0939328846740872682266532287147e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.81 y[1] (closed_form) = 29.476257034472675174000978620467 y[1] (numeric) = 29.476257034472675174000978620482 absolute error = 1.5e-29 relative error = 5.0888414979070789086508740883365e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.82 y[1] (closed_form) = 29.505748034549603014310869205724 y[1] (numeric) = 29.505748034549603014310869205737 absolute error = 1.3e-29 relative error = 4.4059211733177268561205695451787e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2147.4MB, alloc=44.3MB, time=23.06 TOP MAIN SOLVE Loop x[1] = 8.83 y[1] (closed_form) = 29.535268540377024216641946981439 y[1] (numeric) = 29.535268540377024216641946981451 absolute error = 1.2e-29 relative error = 4.0629391886500238177666949062316e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.84 y[1] (closed_form) = 29.564818581475447068457648565196 y[1] (numeric) = 29.564818581475447068457648565209 absolute error = 1.3e-29 relative error = 4.3971181369418125796998293414289e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.85 y[1] (closed_form) = 29.594398187394915130684332724717 y[1] (numeric) = 29.59439818739491513068433272473 absolute error = 1.3e-29 relative error = 4.3927232166312693918219449359164e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.86 y[1] (closed_form) = 29.624007387715036787757303807931 y[1] (numeric) = 29.624007387715036787757303807945 absolute error = 1.4e-29 relative error = 4.7258967420477172720701459647679e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.87 y[1] (closed_form) = 29.653646212045014827231661145728 y[1] (numeric) = 29.653646212045014827231661145741 absolute error = 1.3e-29 relative error = 4.3839465497904031378773079980102e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.88 y[1] (closed_form) = 29.683314690023676048987554040703 y[1] (numeric) = 29.683314690023676048987554040716 absolute error = 1.3e-29 relative error = 4.3795647944834124995553737358280e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.89 y[1] (closed_form) = 29.713012851319500904059451549626 y[1] (numeric) = 29.713012851319500904059451549639 absolute error = 1.3e-29 relative error = 4.3751874187415813083909781047074e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.9 y[1] (closed_form) = 29.742740725630653163119065891359 y[1] (numeric) = 29.742740725630653163119065891372 absolute error = 1.3e-29 relative error = 4.3708144181875334577716059616097e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.91 y[1] (closed_form) = 29.772498342685009614641597965635 y[1] (numeric) = 29.772498342685009614641597965647 absolute error = 1.2e-29 relative error = 4.0305653431830166423686292639549e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.92 y[1] (closed_form) = 29.802285732240189792785003151405 y[1] (numeric) = 29.802285732240189792785003151418 absolute error = 1.3e-29 relative error = 4.3620815251551549194562863816058e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.93 y[1] (closed_form) = 29.832102924083585735012005266506 y[1] (numeric) = 29.832102924083585735012005266519 absolute error = 1.3e-29 relative error = 4.3577216239439304716406903397986e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.94 y[1] (closed_form) = 29.861949948032391769484616313138 y[1] (numeric) = 29.86194994803239176948461631315 absolute error = 1.2e-29 relative error = 4.0184917665735628719104609680546e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.95 y[1] (closed_form) = 29.891826833933634332260949406148 y[1] (numeric) = 29.89182683393363433226094940616 absolute error = 1.2e-29 relative error = 4.0144752833832913717328156020164e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.96 y[1] (closed_form) = 29.921733611664201814324142083434 y[1] (numeric) = 29.921733611664201814324142083447 absolute error = 1.3e-29 relative error = 4.3446680492243576106700287215756e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.97 y[1] (closed_form) = 29.951670311130874438473237029863 y[1] (numeric) = 29.951670311130874438473237029875 absolute error = 1.2e-29 relative error = 4.0064543564171330910799585508038e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2188.6MB, alloc=44.3MB, time=23.50 TOP MAIN SOLVE Loop x[1] = 8.98 y[1] (closed_form) = 29.981636962270354166105897108083 y[1] (numeric) = 29.981636962270354166105897108096 absolute error = 1.3e-29 relative error = 4.3359873966720118990388520374981e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.99 y[1] (closed_form) = 30.011633595049294633922861481429 y[1] (numeric) = 30.011633595049294633922861481442 absolute error = 1.3e-29 relative error = 4.3316535765465542870480817611194e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9 y[1] (closed_form) = 30.041660239464331120584079535887 y[1] (numeric) = 30.0416602394643311205840795359 absolute error = 1.3e-29 relative error = 4.3273240880750341927550097836071e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.01 y[1] (closed_form) = 30.071716925542110543346489259728 y[1] (numeric) = 30.071716925542110543346489259741 absolute error = 1.3e-29 relative error = 4.3229989269279627838488238255245e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.02 y[1] (closed_form) = 30.101803683339321484713436721111 y[1] (numeric) = 30.101803683339321484713436721124 absolute error = 1.3e-29 relative error = 4.3186780887801785528280073770647e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.03 y[1] (closed_form) = 30.131920542942724249125763295557 y[1] (numeric) = 30.131920542942724249125763295569 absolute error = 1.2e-29 relative error = 3.9824876024407781463124354766740e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.04 y[1] (closed_form) = 30.162067534469180949724617336901 y[1] (numeric) = 30.162067534469180949724617336912 absolute error = 1.1e-29 relative error = 3.6469648466336768453985823532762e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.05 y[1] (closed_form) = 30.192244688065685625216077057034 y[1] (numeric) = 30.192244688065685625216077057043 absolute error = 9e-30 relative error = 2.9808979401778289488104225130981e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.06 y[1] (closed_form) = 30.222452033909394386867701481565 y[1] (numeric) = 30.222452033909394386867701481574 absolute error = 9e-30 relative error = 2.9779185321899290646572791237061e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.07 y[1] (closed_form) = 30.252689602207655595667156480479 y[1] (numeric) = 30.252689602207655595667156480487 absolute error = 8e-30 relative error = 2.6443929796629418047281376726689e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.08 y[1] (closed_form) = 30.282957423198040069673093034912 y[1] (numeric) = 30.282957423198040069673093034919 absolute error = 7e-30 relative error = 2.3115311698842533556094085128553e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.09 y[1] (closed_form) = 30.313255527148371321588485093454 y[1] (numeric) = 30.313255527148371321588485093462 absolute error = 8e-30 relative error = 2.6391094789654801645016725097271e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.1 y[1] (closed_form) = 30.343583944356755826586664593838 y[1] (numeric) = 30.343583944356755826586664593844 absolute error = 6e-30 relative error = 1.9773537664511343961167869028967e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.11 y[1] (closed_form) = 30.373942705151613320420321478555 y[1] (numeric) = 30.373942705151613320420321478563 absolute error = 8e-30 relative error = 2.6338365347094531993036610456900e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.12 y[1] (closed_form) = 30.404331839891707127843766815947 y[1] (numeric) = 30.404331839891707127843766815957 absolute error = 1.0e-29 relative error = 3.2890050183176850828625177395904e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2229.8MB, alloc=44.3MB, time=23.94 TOP MAIN SOLVE Loop x[1] = 9.13 y[1] (closed_form) = 30.434751378966174521378787451541 y[1] (numeric) = 30.43475137896617452137878745155 absolute error = 9e-30 relative error = 2.9571458915284614612370841702013e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.14 y[1] (closed_form) = 30.465201352794557110454450958028 y[1] (numeric) = 30.465201352794557110454450958036 absolute error = 8e-30 relative error = 2.6259468655263504935038861729781e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.15 y[1] (closed_form) = 30.495681791826831260951250026217 y[1] (numeric) = 30.495681791826831260951250026226 absolute error = 9e-30 relative error = 2.9512375100962970488178140903313e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.16 y[1] (closed_form) = 30.52619272654343854518000584364 y[1] (numeric) = 30.526192726543438545180005843649 absolute error = 9e-30 relative error = 2.9482877477132058252081776274160e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.17 y[1] (closed_form) = 30.556734187455316222325980442257 y[1] (numeric) = 30.556734187455316222325980442265 absolute error = 8e-30 relative error = 2.6180808298827626715183989583688e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.18 y[1] (closed_form) = 30.58730620510392774938867846191 y[1] (numeric) = 30.587306205103927749388678461919 absolute error = 9e-30 relative error = 2.9423970648641892489022084988524e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.19 y[1] (closed_form) = 30.617908810061293322647849271863 y[1] (numeric) = 30.617908810061293322647849271873 absolute error = 1.0e-29 relative error = 3.2660623761195339514433841624207e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.2 y[1] (closed_form) = 30.648542032930020449686230918988 y[1] (numeric) = 30.648542032930020449686230918998 absolute error = 1.0e-29 relative error = 3.2627979462303948066253482374258e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.21 y[1] (closed_form) = 30.679205904343334551999607927883 y[1] (numeric) = 30.679205904343334551999607927893 absolute error = 1.0e-29 relative error = 3.2595367791394737920400347984698e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.22 y[1] (closed_form) = 30.709900454965109598224785565521 y[1] (numeric) = 30.70990045496510959822478556553 absolute error = 9e-30 relative error = 2.9306509844270431905022463622215e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.23 y[1] (closed_form) = 30.740625715489898768016113800976 y[1] (numeric) = 30.740625715489898768016113800985 absolute error = 9e-30 relative error = 2.9277217982797886161351615256568e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.24 y[1] (closed_form) = 30.771381716642965146601224839288 y[1] (numeric) = 30.771381716642965146601224839297 absolute error = 9e-30 relative error = 2.9247955398545762983813487006676e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.25 y[1] (closed_form) = 30.80216848918031245004667878777 y[1] (numeric) = 30.80216848918031245004667878778 absolute error = 1.0e-29 relative error = 3.2465246735834972979706813747248e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.26 y[1] (closed_form) = 30.832986063888715781264242722967 y[1] (numeric) = 30.832986063888715781264242722976 absolute error = 9e-30 relative error = 2.9189517944681685524720810215764e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.27 y[1] (closed_form) = 30.863834471585752416788559167095 y[1] (numeric) = 30.863834471585752416788559167103 absolute error = 8e-30 relative error = 2.5920304903673131119378505110531e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.28 y[1] (closed_form) = 30.894713743119832624356990754214 y[1] (numeric) = 30.894713743119832624356990754221 absolute error = 7e-30 relative error = 2.2657597860277571453748154584270e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2271.1MB, alloc=44.3MB, time=24.39 TOP MAIN SOLVE Loop x[1] = 9.29 y[1] (closed_form) = 30.925623909370230511322458668527 y[1] (numeric) = 30.925623909370230511322458668534 absolute error = 7e-30 relative error = 2.2634951587440901588829531848893e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.3 y[1] (closed_form) = 30.956565001247114903930123270235 y[1] (numeric) = 30.956565001247114903930123270243 absolute error = 8e-30 relative error = 2.5842660513780234755246849011227e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.31 y[1] (closed_form) = 30.987537049691580257488786188181 y[1] (numeric) = 30.987537049691580257488786188189 absolute error = 8e-30 relative error = 2.5816830770290677887180731345221e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.32 y[1] (closed_form) = 31.018540085675677597467924053276 y[1] (numeric) = 31.018540085675677597467924053284 absolute error = 8e-30 relative error = 2.5791026843634042712428405169858e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.33 y[1] (closed_form) = 31.049574140202445491551294972316 y[1] (numeric) = 31.049574140202445491551294972323 absolute error = 7e-30 relative error = 2.2544592619505600371023977335349e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.34 y[1] (closed_form) = 31.080639244305941052678089798371 y[1] (numeric) = 31.080639244305941052678089798378 absolute error = 7e-30 relative error = 2.2522059295425911590387720507253e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.35 y[1] (closed_form) = 31.111735429051270973102631241492 y[1] (numeric) = 31.111735429051270973102631241499 absolute error = 7e-30 relative error = 2.2499548493407395074000234169781e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.36 y[1] (closed_form) = 31.142862725534622589503654882003 y[1] (numeric) = 31.142862725534622589503654882011 absolute error = 8e-30 relative error = 2.5688068789644853631365452795122e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.37 y[1] (closed_form) = 31.174021164883294979174237198279 y[1] (numeric) = 31.174021164883294979174237198287 absolute error = 8e-30 relative error = 2.5662393560609328924054762152136e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.38 y[1] (closed_form) = 31.20521077825573008732346680149 y[1] (numeric) = 31.205210778255730087323466801497 absolute error = 7e-30 relative error = 2.2432150994723315439073372756343e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.39 y[1] (closed_form) = 31.236431596841543885520986181606 y[1] (numeric) = 31.236431596841543885520986181614 absolute error = 8e-30 relative error = 2.5611120064075808158734635631481e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.4 y[1] (closed_form) = 31.267683651861557561315562411795 y[1] (numeric) = 31.267683651861557561315562411803 absolute error = 8e-30 relative error = 2.5585521745304311294412914213906e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.41 y[1] (closed_form) = 31.298966974567828739058876432372 y[1] (numeric) = 31.29896697456782873905887643238 absolute error = 8e-30 relative error = 2.5559949012056691861285666796859e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.42 y[1] (closed_form) = 31.330281596243682731965751740702 y[1] (numeric) = 31.330281596243682731965751740711 absolute error = 9e-30 relative error = 2.8726202068605241290756320905614e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.43 y[1] (closed_form) = 31.361627548203743825442074549888 y[1] (numeric) = 31.361627548203743825442074549898 absolute error = 1.0e-29 relative error = 3.1886100249834629658955262442625e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2312.4MB, alloc=44.3MB, time=24.83 TOP MAIN SOLVE Loop x[1] = 9.44 y[1] (closed_form) = 31.393004861793966591711688746769 y[1] (numeric) = 31.393004861793966591711688746779 absolute error = 1.0e-29 relative error = 3.1854230087321898226809219333465e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.45 y[1] (closed_form) = 31.424413568391667235773580278727 y[1] (numeric) = 31.424413568391667235773580278736 absolute error = 9e-30 relative error = 2.8640152601137717772241447449180e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.46 y[1] (closed_form) = 31.455853699405554972720696929117 y[1] (numeric) = 31.455853699405554972720696929128 absolute error = 1.1e-29 relative error = 3.4969643822471984948098765833417e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.47 y[1] (closed_form) = 31.487325286275763436451780802733 y[1] (numeric) = 31.487325286275763436451780802744 absolute error = 1.1e-29 relative error = 3.4934691657644607005858610116589e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.48 y[1] (closed_form) = 31.518828360473882119807622235773 y[1] (numeric) = 31.518828360473882119807622235785 absolute error = 1.2e-29 relative error = 3.8072481193649234108320696131834e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.49 y[1] (closed_form) = 31.550362953502987846163175269177 y[1] (numeric) = 31.550362953502987846163175269189 absolute error = 1.2e-29 relative error = 3.8034427742352354202719820241990e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.5 y[1] (closed_form) = 31.581929096897676272507006280068 y[1] (numeric) = 31.58192909689767627250700628008 absolute error = 1.2e-29 relative error = 3.7996412325486386185223994291543e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.51 y[1] (closed_form) = 31.613526822224093424039578853379 y[1] (numeric) = 31.613526822224093424039578853391 absolute error = 1.2e-29 relative error = 3.7958434905035910021913689688951e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.52 y[1] (closed_form) = 31.645156161079967260321909494573 y[1] (numeric) = 31.645156161079967260321909494586 absolute error = 1.3e-29 relative error = 4.1080536729942127272321566765674e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.53 y[1] (closed_form) = 31.676817145094639273006160334744 y[1] (numeric) = 31.676817145094639273006160334756 absolute error = 1.2e-29 relative error = 3.7882593901509697238035861358051e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.54 y[1] (closed_form) = 31.708509805929096115179766561321 y[1] (numeric) = 31.708509805929096115179766561334 absolute error = 1.3e-29 relative error = 4.0998457762809030002102692222898e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.55 y[1] (closed_form) = 31.740234175276001262354727921153 y[1] (numeric) = 31.740234175276001262354727921166 absolute error = 1.3e-29 relative error = 4.0957479797443734010290655436696e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.56 y[1] (closed_form) = 31.77199028485972670513372528788 y[1] (numeric) = 31.771990284859726705133725287892 absolute error = 1.2e-29 relative error = 3.7769116421133829463670326182981e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.57 y[1] (closed_form) = 31.803778166436384673584754962368 y[1] (numeric) = 31.803778166436384673584754962381 absolute error = 1.3e-29 relative error = 4.0875646698225762434656424138667e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.58 y[1] (closed_form) = 31.835597851793859393356005083486 y[1] (numeric) = 31.835597851793859393356005083499 absolute error = 1.3e-29 relative error = 4.0834791482539980813437491847476e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2353.6MB, alloc=44.3MB, time=25.28 TOP MAIN SOLVE Loop x[1] = 9.59 y[1] (closed_form) = 31.867449372751838873562730266726 y[1] (numeric) = 31.86744937275183887356273026674 absolute error = 1.4e-29 relative error = 4.3931975340237475757110938840072e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.6 y[1] (closed_form) = 31.899332761161846726477912360218 y[1] (numeric) = 31.899332761161846726477912360233 absolute error = 1.5e-29 relative error = 4.7022927132390795688913411221649e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.61 y[1] (closed_form) = 31.931248048907274019058527011435 y[1] (numeric) = 31.931248048907274019058527011451 absolute error = 1.6e-29 relative error = 5.0107656222812560494288320132746e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.62 y[1] (closed_form) = 31.963195267903411156339267573512 y[1] (numeric) = 31.963195267903411156339267573528 absolute error = 1.6e-29 relative error = 5.0057573612068670704453918233864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.63 y[1] (closed_form) = 31.99517445009747979672560974756 y[1] (numeric) = 31.995174450097479796725609747575 absolute error = 1.5e-29 relative error = 4.6882069742721154169903383121436e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.64 y[1] (closed_form) = 32.027185627468664799218132256705 y[1] (numeric) = 32.027185627468664799218132256719 absolute error = 1.4e-29 relative error = 4.3712863699121473840490119702775e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.65 y[1] (closed_form) = 32.059228832028146202600040778825 y[1] (numeric) = 32.05922883202814620260004077884 absolute error = 1.5e-29 relative error = 4.6788399304897013195686364709327e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.66 y[1] (closed_form) = 32.091304095819131236619874328181 y[1] (numeric) = 32.091304095819131236619874328197 absolute error = 1.6e-29 relative error = 4.9857743244795361287445822324194e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.67 y[1] (closed_form) = 32.123411450916886365201405271318 y[1] (numeric) = 32.123411450916886365201405271334 absolute error = 1.6e-29 relative error = 4.9807910422114641440263036418077e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.68 y[1] (closed_form) = 32.155550929428769361712776189791 y[1] (numeric) = 32.155550929428769361712776189808 absolute error = 1.7e-29 relative error = 5.2868010370307775265003257031669e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.69 y[1] (closed_form) = 32.187722563494261416326948861554 y[1] (numeric) = 32.187722563494261416326948861571 absolute error = 1.7e-29 relative error = 5.2815168785133519975180017440643e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.7 y[1] (closed_form) = 32.219926385284999275505572724101 y[1] (numeric) = 32.219926385284999275505572724117 absolute error = 1.6e-29 relative error = 4.9658710602477601019377778473192e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.71 y[1] (closed_form) = 32.252162427004807413638412305939 y[1] (numeric) = 32.252162427004807413638412305955 absolute error = 1.6e-29 relative error = 4.9609076712956041589267452339481e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.72 y[1] (closed_form) = 32.284430720889730236870505268483 y[1] (numeric) = 32.2844307208897302368705052685 absolute error = 1.7e-29 relative error = 5.2656960709547537280379010520225e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.73 y[1] (closed_form) = 32.316731299208064319149254888211 y[1] (numeric) = 32.316731299208064319149254888228 absolute error = 1.7e-29 relative error = 5.2604330068544377999904031608119e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop memory used=2394.9MB, alloc=44.3MB, time=25.72 x[1] = 9.74 y[1] (closed_form) = 32.349064194260390670523693028876 y[1] (numeric) = 32.349064194260390670523693028893 absolute error = 1.7e-29 relative error = 5.2551752031875670958125554439901e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.75 y[1] (closed_form) = 32.381429438379607037728181905713 y[1] (numeric) = 32.381429438379607037728181905729 absolute error = 1.6e-29 relative error = 4.9411036750083176569254903963671e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.76 y[1] (closed_form) = 32.413827063930960237082855228031 y[1] (numeric) = 32.413827063930960237082855228049 absolute error = 1.8e-29 relative error = 5.5531856711945648277113964125242e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.77 y[1] (closed_form) = 32.446257103312078519743131623343 y[1] (numeric) = 32.446257103312078519743131623359 absolute error = 1.6e-29 relative error = 4.9312313432808055568306390254484e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.78 y[1] (closed_form) = 32.478719588953003969330665595226 y[1] (numeric) = 32.478719588953003969330665595241 absolute error = 1.5e-29 relative error = 4.6184086656858093075146962524564e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.79 y[1] (closed_form) = 32.511214553316224931978133648575 y[1] (numeric) = 32.51121455331622493197813364859 absolute error = 1.5e-29 relative error = 4.6137925654549139587116119972160e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.8 y[1] (closed_form) = 32.543742028896708478820285629729 y[1] (numeric) = 32.543742028896708478820285629743 absolute error = 1.4e-29 relative error = 4.3019023404158373110458177568545e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.81 y[1] (closed_form) = 32.576302048221932900963723775236 y[1] (numeric) = 32.57630204822193290096372377525 absolute error = 1.4e-29 relative error = 4.2976025883097871683384264108380e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.82 y[1] (closed_form) = 32.608894643851920236967904441737 y[1] (numeric) = 32.608894643851920236967904441751 absolute error = 1.4e-29 relative error = 4.2933071338066834689791670040257e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.83 y[1] (closed_form) = 32.641519848379268832869890000679 y[1] (numeric) = 32.641519848379268832869890000693 absolute error = 1.4e-29 relative error = 4.2890159726110713519097863200321e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.84 y[1] (closed_form) = 32.674177694429185934785410925333 y[1] (numeric) = 32.674177694429185934785410925347 absolute error = 1.4e-29 relative error = 4.2847291004317892639213890685742e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.85 y[1] (closed_form) = 32.706868214659520314118830673888 y[1] (numeric) = 32.706868214659520314118830673901 absolute error = 1.3e-29 relative error = 3.9747003334832529064573465740709e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.86 y[1] (closed_form) = 32.739591441760794925414638581296 y[1] (numeric) = 32.73959144176079492541463858131 absolute error = 1.4e-29 relative error = 4.2761682059790097589163055432944e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.87 y[1] (closed_form) = 32.772347408456239596883128614104 y[1] (numeric) = 32.772347408456239596883128614119 absolute error = 1.5e-29 relative error = 4.5770294733692326882630922348224e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.88 y[1] (closed_form) = 32.805136147501823753632954516656 y[1] (numeric) = 32.805136147501823753632954516672 absolute error = 1.6e-29 relative error = 4.8772850470911494037924999218425e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.89 y[1] (closed_form) = 32.837957691686289173643284583956 y[1] (numeric) = 32.837957691686289173643284583974 absolute error = 1.8e-29 relative error = 5.4814614748581421556488997202222e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2436.3MB, alloc=44.3MB, time=26.16 TOP MAIN SOLVE Loop x[1] = 9.9 y[1] (closed_form) = 32.870812073831182776508312036078 y[1] (numeric) = 32.870812073831182776508312036097 absolute error = 1.9e-29 relative error = 5.7802040172673769274584603122602e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.91 y[1] (closed_form) = 32.903699326790889444986909741357 y[1] (numeric) = 32.903699326790889444986909741377 absolute error = 2.0e-29 relative error = 6.0783438972515701491388936889383e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.92 y[1] (closed_form) = 32.936619483452664879390250840762 y[1] (numeric) = 32.936619483452664879390250840781 absolute error = 1.9e-29 relative error = 5.7686551619377899471383185357681e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.93 y[1] (closed_form) = 32.969572576736668484840249663801 y[1] (numeric) = 32.969572576736668484840249663818 absolute error = 1.7e-29 relative error = 5.1562694543377855525416115305849e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.94 y[1] (closed_form) = 33.002558639595996291431710197145 y[1] (numeric) = 33.002558639595996291431710197163 absolute error = 1.8e-29 relative error = 5.4541225716977768771552410748097e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.95 y[1] (closed_form) = 33.035577705016713907331102270859 y[1] (numeric) = 33.035577705016713907331102270879 absolute error = 2.0e-29 relative error = 6.0540790836428574780154833295458e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.96 y[1] (closed_form) = 33.068629806017889504844918563765 y[1] (numeric) = 33.068629806017889504844918563784 absolute error = 1.9e-29 relative error = 5.7456266290604956910013657415201e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.97 y[1] (closed_form) = 33.101714975651626839490598499039 y[1] (numeric) = 33.101714975651626839490598499057 absolute error = 1.8e-29 relative error = 5.4377847230091012384809322033784e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.98 y[1] (closed_form) = 33.134833247003098302103038103722 y[1] (numeric) = 33.13483324700309830210303810374 absolute error = 1.8e-29 relative error = 5.4323496562723827170143577260281e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.99 y[1] (closed_form) = 33.167984653190578004009737941409 y[1] (numeric) = 33.167984653190578004009737941428 absolute error = 1.9e-29 relative error = 5.7284155786572050061808505713925e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; Iterations = 9000 Total Elapsed Time = 26 Seconds Elapsed Time(since restart) = 26 Seconds Time to Timeout = 2 Minutes 33 Seconds Percent Done = 100 % > quit memory used=2465.9MB, alloc=44.3MB, time=26.47