|\^/| 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(-0.5)*cos(c(2.0)*c(x) + c(3.0)) + c(2.0)/c(3.0)*sin(c(1.5)*c(x)-c(2.0))); > end; exact_soln_y := proc(x) return c(-0.5)*cos(c(2.0)*c(x) + c(3.0)) + c(2.0)*sin(c(1.5)*c(x) - c(2.0))/c(3.0) end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if (rad_given < glob_least_given_sing) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])* (array_x[1] - array_given_rad_poles[1, 1]) + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if rad_given < glob_least_given_sing then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if array_rad_test_poles[1, 1] < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if array_rad_test_poles[1, 2] < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if array_rad_test_poles[1, 3] < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > array_const_1D5, #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_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7_g, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_const_1D5, 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_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7_g, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > array_const_1D5, #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_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7_g, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_const_1D5, 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_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7_g, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > array_const_1D5, #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_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7_g, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_const_1D5, 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_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7_g, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > array_const_1D5, #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_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7_g, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_const_1D5, 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_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7_g, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > array_const_1D5, #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_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7_g, > array_tmp7, > array_tmp8, > 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)*30*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 6 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 5; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > array_est_rel_error[1] := est_rel_err; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," "); > omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," "); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_const_1D5, 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_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7_g, array_tmp7, array_tmp8, 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)*30*ATS_MAX_TERMS/float_abs(numeric_val)) ; if glob_prec < evalf(est_rel_err) then glob_est_digits := -int_trunc(log10(est_rel_err)) + 3 else glob_est_digits := Digits end if else relerr := glob__m1; glob_est_digits := -16 end if; array_est_digits[1] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; array_est_rel_error[1] := est_rel_err; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4, " "); omniout_int(INFO, "Estimated correct digits ", 32, glob_est_digits, 4, " "); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > array_const_1D5, #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_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7_g, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr((glob_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr((left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_const_1D5, 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_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7_g, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(glob_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(left_sec); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > array_const_1D5, #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_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7_g, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_const_1D5, 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_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7_g, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > array_const_1D5, #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_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7_g, > array_tmp7, > array_tmp8, > 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_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; > #emit pre sin 1 $eq_no = 1 > array_tmp3[1] := sin(array_tmp2[1]); > array_tmp3_g[1] := cos(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 mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := array_const_1D5[1] * array_x[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp6[1] := array_tmp5[1] - array_const_2D0[1]; > #emit pre cos 1 $eq_no = 1 > array_tmp7[1] := cos(array_tmp6[1]); > array_tmp7_g[1] := sin(array_tmp6[1]); > #emit pre add FULL FULL $eq_no = 1 i = 1 > array_tmp8[1] := array_tmp4[1] + array_tmp7[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_tmp8[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_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp3[2] := array_tmp3_g[1] * array_tmp2[2] / c(1); > array_tmp3_g[2] := neg(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 mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp5[2] := array_const_1D5[1] * array_x[2]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp6[2] := array_tmp5[2]; > #emit pre cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp7[2] := neg(array_tmp7_g[1]) * array_tmp6[2] / c(1); > array_tmp7_g[2] := array_tmp7[1] * array_tmp6[2] / c(1); > #emit pre add FULL FULL $eq_no = 1 i = 2 > array_tmp8[2] := array_tmp4[2] + array_tmp7[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_tmp8[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 sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := array_tmp3_g[2] * array_tmp2[2] / c(2); > array_tmp3_g[3] := neg(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 cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp7[3] := neg(array_tmp7_g[2]) * array_tmp6[2] / c(2); > array_tmp7_g[3] := array_tmp7[2] * array_tmp6[2] / c(2); > #emit pre add FULL FULL $eq_no = 1 i = 3 > array_tmp8[3] := array_tmp4[3] + array_tmp7[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_tmp8[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 sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := array_tmp3_g[3] * array_tmp2[2] / c(3); > array_tmp3_g[4] := neg(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 cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp7[4] := neg(array_tmp7_g[3]) * array_tmp6[2] / c(3); > array_tmp7_g[4] := array_tmp7[3] * array_tmp6[2] / c(3); > #emit pre add FULL FULL $eq_no = 1 i = 4 > array_tmp8[4] := array_tmp4[4] + array_tmp7[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_tmp8[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 sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := array_tmp3_g[4] * array_tmp2[2] / c(4); > array_tmp3_g[5] := neg(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 cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp7[5] := neg(array_tmp7_g[4]) * array_tmp6[2] / c(4); > array_tmp7_g[5] := array_tmp7[4] * array_tmp6[2] / c(4); > #emit pre add FULL FULL $eq_no = 1 i = 5 > array_tmp8[5] := array_tmp4[5] + array_tmp7[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_tmp8[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 sin LINEAR $eq_no = 1 > array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_tmp2[2] / c(kkk - 1); > array_tmp3_g[kkk] := neg(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 cos LINEAR $eq_no = 1 > array_tmp7[kkk] := neg(array_tmp7_g[kkk - 1]) * array_tmp6[2] / c(kkk - 1); > array_tmp7_g[kkk] := array_tmp7[kkk - 1] * array_tmp6[2] / c(kkk - 1); > #emit FULL - FULL add $eq_no = 1 > array_tmp8[kkk] := array_tmp4[kkk] + array_tmp7[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_tmp8[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_const_1D5, 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_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7_g, array_tmp7, array_tmp8, 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_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; array_tmp3[1] := sin(array_tmp2[1]); array_tmp3_g[1] := cos(array_tmp2[1]); array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; array_tmp5[1] := array_const_1D5[1]*array_x[1]; array_tmp6[1] := array_tmp5[1] - array_const_2D0[1]; array_tmp7[1] := cos(array_tmp6[1]); array_tmp7_g[1] := sin(array_tmp6[1]); array_tmp8[1] := array_tmp4[1] + array_tmp7[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp3_g[1]*array_tmp2[2]/c(1); array_tmp3_g[2] := neg(array_tmp3[1])*array_tmp2[2]/c(1); array_tmp4[2] := array_tmp3[2]; array_tmp5[2] := array_const_1D5[1]*array_x[2]; array_tmp6[2] := array_tmp5[2]; array_tmp7[2] := neg(array_tmp7_g[1])*array_tmp6[2]/c(1); array_tmp7_g[2] := array_tmp7[1]*array_tmp6[2]/c(1); array_tmp8[2] := array_tmp4[2] + array_tmp7[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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_g[2]*array_tmp2[2]/c(2); array_tmp3_g[3] := neg(array_tmp3[2])*array_tmp2[2]/c(2); array_tmp4[3] := array_tmp3[3]; array_tmp7[3] := neg(array_tmp7_g[2])*array_tmp6[2]/c(2); array_tmp7_g[3] := array_tmp7[2]*array_tmp6[2]/c(2); array_tmp8[3] := array_tmp4[3] + array_tmp7[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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_g[3]*array_tmp2[2]/c(3); array_tmp3_g[4] := neg(array_tmp3[3])*array_tmp2[2]/c(3); array_tmp4[4] := array_tmp3[4]; array_tmp7[4] := neg(array_tmp7_g[3])*array_tmp6[2]/c(3); array_tmp7_g[4] := array_tmp7[3]*array_tmp6[2]/c(3); array_tmp8[4] := array_tmp4[4] + array_tmp7[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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_g[4]*array_tmp2[2]/c(4); array_tmp3_g[5] := neg(array_tmp3[4])*array_tmp2[2]/c(4); array_tmp4[5] := array_tmp3[5]; array_tmp7[5] := neg(array_tmp7_g[4])*array_tmp6[2]/c(4); array_tmp7_g[5] := array_tmp7[4]*array_tmp6[2]/c(4); array_tmp8[5] := array_tmp4[5] + array_tmp7[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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_g[kkk - 1]*array_tmp2[2]/c(kkk - 1); array_tmp3_g[kkk] := neg(array_tmp3[kkk - 1])*array_tmp2[2]/c(kkk - 1); array_tmp4[kkk] := array_tmp3[kkk]; array_tmp7[kkk] := neg(array_tmp7_g[kkk - 1])*array_tmp6[2]/c(kkk - 1); array_tmp7_g[kkk] := array_tmp7[kkk - 1]*array_tmp6[2]/c(kkk - 1); array_tmp8[kkk] := array_tmp4[kkk] + array_tmp7[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_tmp8[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > array_const_1D5, > #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_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7_g, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3_g:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_tmp5:= Array(0..(30),[]); > array_tmp6:= Array(0..(30),[]); > array_tmp7_g:= Array(0..(30),[]); > array_tmp7:= Array(0..(30),[]); > array_tmp8:= 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_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp6[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp7_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp7[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp8[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_g); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_tmp6); > zero_ats_ar(array_tmp7_g); > zero_ats_ar(array_tmp7); > zero_ats_ar(array_tmp8); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_2D0); > array_const_2D0[1] := c(2.0); > zero_ats_ar(array_const_3D0); > array_const_3D0[1] := c(3.0); > zero_ats_ar(array_const_1D5); > array_const_1D5[1] := c(1.5); > 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_sin_cospostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(0.1);"); > omniout_str(ALWAYS,"x_end := c(5.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 3;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=100000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#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(-0.5)*cos(c(2.0)*c(x) + c(3.0)) + c(2.0)/c(3.0)*sin(c(1.5)*c(x)-c(2.0)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(0.1); > x_end := c(5.0) ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_type_given_pole := 3; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=100000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > 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 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; "); > 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,"2015-05-01T22:08:30-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"lin_sin_cos") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; ") > ; > 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_sin_cos diffeq.mxt") > ; > logitem_str(html_log_file,"lin_sin_cos 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_2D0, array_const_3D0, array_const_1D5, 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_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7_g, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 32; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3_g := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_tmp5 := Array(0 .. 30, []); array_tmp6 := Array(0 .. 30, []); array_tmp7_g := Array(0 .. 30, []); array_tmp7 := Array(0 .. 30, []); array_tmp8 := 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_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp7_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp7[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp8[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_g); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_tmp6); zero_ats_ar(array_tmp7_g); zero_ats_ar(array_tmp7); zero_ats_ar(array_tmp8); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_2D0); array_const_2D0[1] := c(2.0); zero_ats_ar(array_const_3D0); array_const_3D0[1] := c(3.0); zero_ats_ar(array_const_1D5); array_const_1D5[1] := c(1.5); 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_sin_cospostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( 2.0 * x \ + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(0.1);"); omniout_str(ALWAYS, "x_end := c(5.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 3;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=100000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#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(-0.5)*cos(c(2.0)*c(x) + c(3.0)) + c(2.0\ )/c(3.0)*sin(c(1.5)*c(x)-c(2.0)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(0.1); x_end := c(5.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 3; glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 100000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); 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 ) = sin ( 2.0 * x\ + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; "); 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, "2015-05-01T22:08:30-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "lin_sin_cos"); logitem_str(html_log_file, "diff ( y , x , 1 ) = si\ n ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) \ ; "); 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_sin_cos diffeq.mxt"); logitem_str(html_log_file, "lin_sin_cos 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_sin_cospostode.ode################# diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(0.1); x_end := c(5.0) ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 3; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=100000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); 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(-0.5)*cos(c(2.0)*c(x) + c(3.0)) + c(2.0)/c(3.0)*sin(c(1.5)*c(x)-c(2.0))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = -0.1417027474194900776774757512823 y[1] (numeric) = -0.1417027474194900776774757512823 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=4.1MB, alloc=40.3MB, time=0.14 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = -0.14506998092304834169597241580393 y[1] (numeric) = -0.14506998092304834169597241580393 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] = 0.12 y[1] (closed_form) = -0.14849180092505574930206495712746 y[1] (numeric) = -0.14849180092505574930206495712747 absolute error = 1e-32 relative error = 6.7343785567305696214864669805355e-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] = 0.13 y[1] (closed_form) = -0.15196728302967060681000425470327 y[1] (numeric) = -0.15196728302967060681000425470327 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] = 0.14 y[1] (closed_form) = -0.15549545593961291722726108067322 y[1] (numeric) = -0.15549545593961291722726108067323 absolute error = 1e-32 relative error = 6.4310560971527857177697371189492e-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] = 0.15 y[1] (closed_form) = -0.15907530175043103369378437754139 y[1] (numeric) = -0.15907530175043103369378437754139 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] = 0.16 y[1] (closed_form) = -0.16270575626915505166216727393838 y[1] (numeric) = -0.16270575626915505166216727393839 absolute error = 1e-32 relative error = 6.1460640540937950099404926102674e-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] = 0.17 y[1] (closed_form) = -0.16638570935722939367090435220731 y[1] (numeric) = -0.16638570935722939367090435220733 absolute error = 2e-32 relative error = 1.2020263084649948551204866058559e-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] = 0.18 y[1] (closed_form) = -0.17011400529760603224336913025888 y[1] (numeric) = -0.17011400529760603224336913025891 absolute error = 3e-32 relative error = 1.7635232294669968466694701530275e-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] = 0.19 y[1] (closed_form) = -0.17388944318586883135772225224932 y[1] (numeric) = -0.17388944318586883135772225224934 absolute error = 2e-32 relative error = 1.1501560781135047622302278685793e-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] = 0.2 y[1] (closed_form) = -0.17771077734524856975632149588242 y[1] (numeric) = -0.17771077734524856975632149588243 absolute error = 1e-32 relative error = 5.6271207348175885498384079738129e-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] = 0.21 y[1] (closed_form) = -0.18157671776537734475770015310277 y[1] (numeric) = -0.18157671776537734475770015310278 absolute error = 1e-32 relative error = 5.5073140009730797874725211329923e-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 memory used=45.0MB, alloc=44.3MB, time=0.58 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = -0.18548593056462024783994899120326 y[1] (numeric) = -0.18548593056462024783994899120327 absolute error = 1e-32 relative error = 5.3912444839131151528701882145672e-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] = 0.23 y[1] (closed_form) = -0.18943703847581145769937758801889 y[1] (numeric) = -0.18943703847581145769937758801891 absolute error = 2e-32 relative error = 1.0557597479836937448924384096877e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = -0.19342862135521121734658890922082 y[1] (numeric) = -0.19342862135521121734658890922084 absolute error = 2e-32 relative error = 1.0339731452292220000857405937757e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = -0.19745921671448955365156484039438 y[1] (numeric) = -0.19745921671448955365156484039439 absolute error = 1e-32 relative error = 5.0643369129024809840183025783871e-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] = 0.26 y[1] (closed_form) = -0.20152732027553206513016717576008 y[1] (numeric) = -0.20152732027553206513016717576009 absolute error = 1e-32 relative error = 4.9621063716461896284075258386059e-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] = 0.27 y[1] (closed_form) = -0.20563138654785265118701154256297 y[1] (numeric) = -0.20563138654785265118701154256297 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] = 0.28 y[1] (closed_form) = -0.20976982942838768797276918161599 y[1] (numeric) = -0.20976982942838768797276918161599 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] = 0.29 y[1] (closed_form) = -0.21394102282343587692292823200953 y[1] (numeric) = -0.21394102282343587692292823200954 absolute error = 1e-32 relative error = 4.6741853750287687548433774935132e-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] = 0.3 y[1] (closed_form) = -0.21814330129249780632992836912335 y[1] (numeric) = -0.21814330129249780632992836912336 absolute error = 1e-32 relative error = 4.5841425983516603431180379996071e-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] = 0.31 y[1] (closed_form) = -0.22237496071375917833425675413321 y[1] (numeric) = -0.22237496071375917833425675413323 absolute error = 2e-32 relative error = 8.9938183398912342092457870969261e-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] = 0.32 y[1] (closed_form) = -0.22663425897095166783648964067753 y[1] (numeric) = -0.22663425897095166783648964067753 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 memory used=85.8MB, alloc=44.3MB, time=0.98 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (closed_form) = -0.2309194166613155003245561961451 y[1] (numeric) = -0.23091941666131550032455619614512 absolute error = 2e-32 relative error = 8.6610300204133835100480338961057e-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] = 0.34 y[1] (closed_form) = -0.23522861782437806672932137709439 y[1] (numeric) = -0.23522861782437806672932137709441 absolute error = 2e-32 relative error = 8.5023668399616329923367257109417e-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] = 0.35 y[1] (closed_form) = -0.23956001069125323937325653540896 y[1] (numeric) = -0.23956001069125323937325653540898 absolute error = 2e-32 relative error = 8.3486387992260326991877743283890e-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] = 0.36 y[1] (closed_form) = -0.24391170845415651802175482275518 y[1] (numeric) = -0.2439117084541565180217548227552 absolute error = 2e-32 relative error = 8.1996883736145133278135495880334e-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] = 0.37 y[1] (closed_form) = -0.24828179005582172309702864507736 y[1] (numeric) = -0.24828179005582172309702864507737 absolute error = 1e-32 relative error = 4.0276816103797538773278014662029e-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] = 0.38 y[1] (closed_form) = -0.25266830099849566833347176153968 y[1] (numeric) = -0.25266830099849566833347176153968 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] = 0.39 y[1] (closed_form) = -0.25706925417217809155265835906017 y[1] (numeric) = -0.25706925417217809155265835906019 absolute error = 2e-32 relative error = 7.7800046778851804747174280511671e-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] = 0.4 y[1] (closed_form) = -0.26148263070176510377469896536204 y[1] (numeric) = -0.26148263070176510377469896536205 absolute error = 1e-32 relative error = 3.8243457980983577154902108055312e-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] = 0.41 y[1] (closed_form) = -0.26590638081274553746487548647272 y[1] (numeric) = -0.26590638081274553746487548647272 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] = 0.42 y[1] (closed_form) = -0.27033842471509083818858719980412 y[1] (numeric) = -0.27033842471509083818858719980413 absolute error = 1e-32 relative error = 3.6990672008757102719881110295235e-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] = 0.43 y[1] (closed_form) = -0.27477665350497055410415758300266 y[1] (numeric) = -0.27477665350497055410415758300268 absolute error = 2e-32 relative error = 7.2786387580188690675958350941044e-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=126.6MB, alloc=44.3MB, time=1.41 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (closed_form) = -0.27921893008391703829314619353906 y[1] (numeric) = -0.27921893008391703829314619353907 absolute error = 1e-32 relative error = 3.5814190667497290353191994724982e-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] = 0.45 y[1] (closed_form) = -0.28366309009505469358175574788811 y[1] (numeric) = -0.28366309009505469358175574788813 absolute error = 2e-32 relative error = 7.0506176863891798409802588926016e-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] = 0.46 y[1] (closed_form) = -0.2881069428760009618525705784787 y[1] (numeric) = -0.28810694287600096185257057847874 absolute error = 4e-32 relative error = 1.3883733450052849277227745082952e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (closed_form) = -0.29254827242803829342712125102832 y[1] (numeric) = -0.29254827242803829342712125102834 absolute error = 2e-32 relative error = 6.8364785865962160690605539006734e-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] = 0.48 y[1] (closed_form) = -0.29698483840114853039513433506444 y[1] (numeric) = -0.29698483840114853039513433506447 absolute error = 3e-32 relative error = 1.0101525775358901589670401741204e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (closed_form) = -0.3014143770944935041874126612847 y[1] (numeric) = -0.30141437709449350418741266128476 absolute error = 6e-32 relative error = 1.9906150654913843309254725621233e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = -0.30583460247191818557940980647516 y[1] (numeric) = -0.3058346024719181855794098064752 absolute error = 4e-32 relative error = 1.3078964798848361386101467817074e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (closed_form) = -0.3102432071920454379453138424972 y[1] (numeric) = -0.31024320719204543794531384249725 absolute error = 5e-32 relative error = 1.6116388317585052385861389262315e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = -0.31463786365252431516035689167258 y[1] (numeric) = -0.31463786365252431516035689167262 absolute error = 4e-32 relative error = 1.2713028093838916168374128062315e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = -0.31901622504798691720220687862681 y[1] (numeric) = -0.31901622504798691720220687862686 absolute error = 5e-32 relative error = 1.5673184018298417944789365237985e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = -0.32337592644126207228701856527782 y[1] (numeric) = -0.32337592644126207228701856527789 absolute error = 7e-32 relative error = 2.1646632997807517265063503608850e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=167.5MB, alloc=44.3MB, time=1.83 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = -0.32771458584738755727333274158048 y[1] (numeric) = -0.32771458584738755727333274158054 absolute error = 6e-32 relative error = 1.8308614444137443346084566636482e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (closed_form) = -0.33202980532995620098253697486991 y[1] (numeric) = -0.33202980532995620098253697486996 absolute error = 5e-32 relative error = 1.5058889050732135862932250735669e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (closed_form) = -0.3363191721093250408455461857403 y[1] (numeric) = -0.33631917210932504084554618574035 absolute error = 5e-32 relative error = 1.4866830126397561389059883977754e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (closed_form) = -0.34058025968221072464052590958633 y[1] (numeric) = -0.34058025968221072464052590958636 absolute error = 3e-32 relative error = 8.8084964254805774593630014782830e-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] = 0.59 y[1] (closed_form) = -0.34481062895218856870479431334328 y[1] (numeric) = -0.34481062895218856870479431334332 absolute error = 4e-32 relative error = 1.1600570470101836327140790899936e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = -0.34900782937060710447342927789258 y[1] (numeric) = -0.34900782937060710447342927789261 absolute error = 3e-32 relative error = 8.5957957029506551381238845842542e-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] = 0.61 y[1] (closed_form) = -0.35316940008742456902340485495794 y[1] (numeric) = -0.35316940008742456902340485495798 absolute error = 4e-32 relative error = 1.1326009555215793032692792697305e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (closed_form) = -0.35729287111146862490795623699825 y[1] (numeric) = -0.35729287111146862490795623699829 absolute error = 4e-32 relative error = 1.1195297537162658860039357820750e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (closed_form) = -0.36137576447961563228980116526333 y[1] (numeric) = -0.36137576447961563228980116526337 absolute error = 4e-32 relative error = 1.1068810897598615004663120369108e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (closed_form) = -0.3654155954343810444771174263261 y[1] (numeric) = -0.36541559543438104447711742632614 absolute error = 4e-32 relative error = 1.0946440299695128855439296789829e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (closed_form) = -0.36940987360940795859992990390861 y[1] (numeric) = -0.36940987360940795859992990390867 absolute error = 6e-32 relative error = 1.6242121363393885188882924546371e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=208.4MB, alloc=44.3MB, time=2.25 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (closed_form) = -0.37335610422233652841685911013964 y[1] (numeric) = -0.37335610422233652841685911013971 absolute error = 7e-32 relative error = 1.8748856442511635879899527947993e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (closed_form) = -0.37725178927453283810512068365934 y[1] (numeric) = -0.37725178927453283810512068365943 absolute error = 9e-32 relative error = 2.3856745695778635250383847026682e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (closed_form) = -0.38109442875715194626351257499772 y[1] (numeric) = -0.3810944287571519462635125749978 absolute error = 8e-32 relative error = 2.0992172533432411428519228279934e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (closed_form) = -0.38488152186300614006251040718414 y[1] (numeric) = -0.38488152186300614006251040718424 absolute error = 1.0e-31 relative error = 2.5982021562363748454536858429711e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = -0.38861056820370599223071153029285 y[1] (numeric) = -0.38861056820370599223071153029294 absolute error = 9e-32 relative error = 2.3159431925902449827443763655785e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (closed_form) = -0.39227906903153859000475042501559 y[1] (numeric) = -0.3922790690315385900047504250157 absolute error = 1.1e-31 relative error = 2.8041261612955490487240475699811e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (closed_form) = -0.39588452846554430683059455690605 y[1] (numeric) = -0.39588452846554430683059455690617 absolute error = 1.2e-31 relative error = 3.0311869085948420590062602073112e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (closed_form) = -0.39942445472125071593540664992447 y[1] (numeric) = -0.39942445472125071593540664992459 absolute error = 1.2e-31 relative error = 3.0043228095221481425147752954768e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (closed_form) = -0.40289636134351970124532177189104 y[1] (numeric) = -0.40289636134351970124532177189114 absolute error = 1.0e-31 relative error = 2.4820278760159229275055418241344e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (closed_form) = -0.40629776844196150676614273230611 y[1] (numeric) = -0.40629776844196150676614273230623 absolute error = 1.2e-31 relative error = 2.9534988700569656812821168329475e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (closed_form) = -0.40962620392836738163736526058633 y[1] (numeric) = -0.40962620392836738163736526058644 absolute error = 1.1e-31 relative error = 2.6853750796478841676860759457864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=249.2MB, alloc=52.3MB, time=2.69 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (closed_form) = -0.4128792047556106256864978742343 y[1] (numeric) = -0.41287920475561062568649787423442 absolute error = 1.2e-31 relative error = 2.9064190837857720186688184862254e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (closed_form) = -0.41605431815746422042638325445377 y[1] (numeric) = -0.4160543181574642204263832544539 absolute error = 1.3e-31 relative error = 3.1245920142282685174031605269619e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (closed_form) = -0.41914910288878184393340838848293 y[1] (numeric) = -0.41914910288878184393340838848305 absolute error = 1.2e-31 relative error = 2.8629430236867553168022722395920e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (closed_form) = -0.42216113046548791570316249643966 y[1] (numeric) = -0.42216113046548791570316249643979 absolute error = 1.3e-31 relative error = 3.0793929288719210219764964198653e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (closed_form) = -0.42508798640382140008975509419525 y[1] (numeric) = -0.42508798640382140008975509419537 absolute error = 1.2e-31 relative error = 2.8229449864057894198243924381774e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (closed_form) = -0.42792727145827741488624322258808 y[1] (numeric) = -0.42792727145827741488624322258821 absolute error = 1.3e-31 relative error = 3.0378993971800393099411861062872e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (closed_form) = -0.43067660285769024548986363254434 y[1] (numeric) = -0.43067660285769024548986363254447 absolute error = 1.3e-31 relative error = 3.0185062094714322748041220848423e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (closed_form) = -0.43333361553890115531302725443317 y[1] (numeric) = -0.43333361553890115531302725443329 absolute error = 1.2e-31 relative error = 2.7692289657880783400810134640545e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (closed_form) = -0.43589596337745440994768491311814 y[1] (numeric) = -0.43589596337745440994768491311826 absolute error = 1.2e-31 relative error = 2.7529504763063995211870540605477e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (closed_form) = -0.43836132041476519626729330848922 y[1] (numeric) = -0.43836132041476519626729330848934 absolute error = 1.2e-31 relative error = 2.7374678013666753948335473268569e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (closed_form) = -0.44072738208120361825985233752365 y[1] (numeric) = -0.44072738208120361825985233752377 absolute error = 1.2e-31 relative error = 2.7227716016494321068775635547976e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=290.1MB, alloc=52.3MB, time=3.11 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (closed_form) = -0.44299186641453968893198981648543 y[1] (numeric) = -0.44299186641453968893198981648556 absolute error = 1.3e-31 relative error = 2.9345911258413388284451110434643e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (closed_form) = -0.44515251527319521201441790169517 y[1] (numeric) = -0.44515251527319521201441790169532 absolute error = 1.5e-31 relative error = 3.3696316397975034910339221131093e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (closed_form) = -0.44720709554374965824178874789537 y[1] (numeric) = -0.44720709554374965824178874789554 absolute error = 1.7e-31 relative error = 3.8013708121804416363890066121634e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (closed_form) = -0.44915340034214858838551032687904 y[1] (numeric) = -0.4491534003421485883855103268792 absolute error = 1.6e-31 relative error = 3.5622573463346346203450553756028e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (closed_form) = -0.45098925020806485859895735658782 y[1] (numeric) = -0.45098925020806485859895735658798 absolute error = 1.6e-31 relative error = 3.5477564027564660703485288877253e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (closed_form) = -0.45271249429186476250538473614837 y[1] (numeric) = -0.45271249429186476250538473614853 absolute error = 1.6e-31 relative error = 3.5342519152309421443246492869049e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (closed_form) = -0.45432101153363341823667862609966 y[1] (numeric) = -0.45432101153363341823667862609983 absolute error = 1.7e-31 relative error = 3.7418476294137870260090351334925e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (closed_form) = -0.45581271183371609663531104547175 y[1] (numeric) = -0.45581271183371609663531104547192 absolute error = 1.7e-31 relative error = 3.7296019963132857469400928370717e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (closed_form) = -0.45718553721423480828466758114724 y[1] (numeric) = -0.45718553721423480828466758114742 absolute error = 1.8e-31 relative error = 3.9371324188598056877162760886760e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (closed_form) = -0.458437462971042321059458056364 y[1] (numeric) = -0.45843746297104232105945805636418 absolute error = 1.8e-31 relative error = 3.9263806852401564557160319257435e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (closed_form) = -0.45956649881557886551666469311172 y[1] (numeric) = -0.4595664988155788655166646931119 absolute error = 1.8e-31 relative error = 3.9167345849600943945839186716215e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=330.9MB, alloc=52.3MB, time=3.53 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (closed_form) = -0.46057069000610010161055405036359 y[1] (numeric) = -0.46057069000610010161055405036377 absolute error = 1.8e-31 relative error = 3.9081948527296854567200196696658e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = -0.46144811846774846574884487590049 y[1] (numeric) = -0.46144811846774846574884487590067 absolute error = 1.8e-31 relative error = 3.9007635484070255434080973140540e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = -0.46219690390094379085182438580794 y[1] (numeric) = -0.46219690390094379085182438580812 absolute error = 1.8e-31 relative error = 3.8944440882402987020454103153488e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = -0.46281520487757309247762215321149 y[1] (numeric) = -0.46281520487757309247762215321166 absolute error = 1.7e-31 relative error = 3.6731723203642264259208795924675e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = -0.46330121992446363978601375318772 y[1] (numeric) = -0.46330121992446363978601375318789 absolute error = 1.7e-31 relative error = 3.6693190669283517249955609562060e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = -0.46365318859362787958705938027213 y[1] (numeric) = -0.4636531885936278795870593802723 absolute error = 1.7e-31 relative error = 3.6665336113755858114458338906705e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = -0.46386939251877345332318747333403 y[1] (numeric) = -0.46386939251877345332318747333421 absolute error = 1.8e-31 relative error = 3.8804026069194712879958388652273e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (closed_form) = -0.46394815645757643883481172153153 y[1] (numeric) = -0.46394815645757643883481172153171 absolute error = 1.8e-31 relative error = 3.8797438354830332209971323151450e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = -0.46388784931922105933888387953762 y[1] (numeric) = -0.46388784931922105933888387953779 absolute error = 1.7e-31 relative error = 3.6646788711858614097978327123850e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = -0.46368688517671442929415525534937 y[1] (numeric) = -0.46368688517671442929415525534953 absolute error = 1.6e-31 relative error = 3.4506043866007303939638992873338e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (closed_form) = -0.46334372426349044873286121036096 y[1] (numeric) = -0.4633437242634904487328612103611 absolute error = 1.4e-31 relative error = 3.0215149719042264705411156810018e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = -0.46285687395382271211263690124941 y[1] (numeric) = -0.46285687395382271211263690124956 absolute error = 1.5e-31 relative error = 3.2407426234954192450731461628959e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=371.7MB, alloc=52.3MB, time=3.95 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (closed_form) = -0.4622248897265722626021764848283 y[1] (numeric) = -0.46222488972657226260217648482845 absolute error = 1.5e-31 relative error = 3.2451735796558261268632421277329e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = -0.46144637611180219568864227953801 y[1] (numeric) = -0.46144637611180219568864227953816 absolute error = 1.5e-31 relative error = 3.2506485642799161415483144756050e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = -0.46051998761979749472590001387666 y[1] (numeric) = -0.46051998761979749472590001387683 absolute error = 1.7e-31 relative error = 3.6914792966673786953204080161132e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = -0.45944442965203506308560958426016 y[1] (numeric) = -0.45944442965203506308560958426033 absolute error = 1.7e-31 relative error = 3.7001210381144731335694099478481e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = -0.45821845939365570039782302567727 y[1] (numeric) = -0.45821845939365570039782302567742 absolute error = 1.5e-31 relative error = 3.2735477352547014556054869790058e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = -0.45684088668699675135928402969179 y[1] (numeric) = -0.45684088668699675135928402969194 absolute error = 1.5e-31 relative error = 3.2834188964082822587289714399480e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = -0.45531057488575133204782746549644 y[1] (numeric) = -0.45531057488575133204782746549661 absolute error = 1.7e-31 relative error = 3.7337151688747224563294141940201e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = -0.45362644168932740782943199646506 y[1] (numeric) = -0.45362644168932740782943199646522 absolute error = 1.6e-31 relative error = 3.5271312537283331678482857603110e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (closed_form) = -0.45178745995698755591851299633441 y[1] (numeric) = -0.45178745995698755591851299633456 absolute error = 1.5e-31 relative error = 3.3201452739365708887484617324524e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = -0.44979265850135799150965100423596 y[1] (numeric) = -0.44979265850135799150965100423611 absolute error = 1.5e-31 relative error = 3.3348699042749522222008520346866e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = -0.44764112286090336611875147095508 y[1] (numeric) = -0.44764112286090336611875147095522 absolute error = 1.4e-31 relative error = 3.1275053351946520440018241468571e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=412.7MB, alloc=52.3MB, time=4.38 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = -0.44533199605097195725435842038206 y[1] (numeric) = -0.44533199605097195725435842038222 absolute error = 1.6e-31 relative error = 3.5928251600786992846525339064571e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (closed_form) = -0.44286447929302415660957043551177 y[1] (numeric) = -0.44286447929302415660957043551192 absolute error = 1.5e-31 relative error = 3.3870406639849642717303737402355e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = -0.44023783272166562637039830141275 y[1] (numeric) = -0.44023783272166562637039830141289 absolute error = 1.4e-31 relative error = 3.1800992462297781021908078243351e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (closed_form) = -0.43745137606911512665200572980433 y[1] (numeric) = -0.43745137606911512665200572980446 absolute error = 1.3e-31 relative error = 2.9717588539362749894081370034900e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (closed_form) = -0.43450448932674581810183046388225 y[1] (numeric) = -0.4345044893267458181018304638824 absolute error = 1.5e-31 relative error = 3.4522082897790392635005131213433e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (closed_form) = -0.4313966133833478088783787958957 y[1] (numeric) = -0.43139661338334780887837879589585 absolute error = 1.5e-31 relative error = 3.4770787564506666106279300884343e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (closed_form) = -0.42812725063976884098672812628836 y[1] (numeric) = -0.42812725063976884098672812628851 absolute error = 1.5e-31 relative error = 3.5036312165564932326515821278848e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (closed_form) = -0.4246959655995992937179910649383 y[1] (numeric) = -0.42469596559959929371799106493846 absolute error = 1.6e-31 relative error = 3.7674009870592225405457472825551e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = -0.42110238543557711802448149830897 y[1] (numeric) = -0.42110238543557711802448149830912 absolute error = 1.5e-31 relative error = 3.5620790854662099759357751896651e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = -0.41734620053139790132359000878467 y[1] (numeric) = -0.41734620053139790132359000878484 absolute error = 1.7e-31 relative error = 4.0733568386040815146362845472234e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (closed_form) = -0.41342716499862499365564539418202 y[1] (numeric) = -0.41342716499862499365564539418219 absolute error = 1.7e-31 relative error = 4.1119697589432808182944178093890e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=453.4MB, alloc=52.3MB, time=4.80 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = -0.40934509716840449945575940856764 y[1] (numeric) = -0.40934509716840449945575940856782 absolute error = 1.8e-31 relative error = 4.3972677636822417425562703853726e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (closed_form) = -0.4050998800576999505070400877571 y[1] (numeric) = -0.40509988005769995050704008775725 absolute error = 1.5e-31 relative error = 3.7027905310323695223545748628161e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = -0.40069146180977162093316772906555 y[1] (numeric) = -0.40069146180977162093316772906571 absolute error = 1.6e-31 relative error = 3.9930973142612168500561477537248e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (closed_form) = -0.39611985610863572031463746090582 y[1] (numeric) = -0.39611985610863572031463746090597 absolute error = 1.5e-31 relative error = 3.7867326690854536937298392947129e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (closed_form) = -0.39138514256724910207100876051531 y[1] (numeric) = -0.39138514256724910207100876051545 absolute error = 1.4e-31 relative error = 3.5770392069991449030452510600825e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -0.38648746708917564698247554511874 y[1] (numeric) = -0.38648746708917564698247554511887 absolute error = 1.3e-31 relative error = 3.3636278293599784753397037521232e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (closed_form) = -0.38142704220350112191603887582572 y[1] (numeric) = -0.38142704220350112191603887582586 absolute error = 1.4e-31 relative error = 3.6704267005092524313883919924201e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = -0.37620414737277406721111958527366 y[1] (numeric) = -0.37620414737277406721111958527378 absolute error = 1.2e-31 relative error = 3.1897574983694720513425008964585e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (closed_form) = -0.37081912927376112845342237627477 y[1] (numeric) = -0.37081912927376112845342237627489 absolute error = 1.2e-31 relative error = 3.2360790079793520010429153504498e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = -0.36527240205081621516305654197562 y[1] (numeric) = -0.36527240205081621516305654197573 absolute error = 1.1e-31 relative error = 3.0114511630883338669080900046913e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = -0.35956444754167393583584824585281 y[1] (numeric) = -0.35956444754167393583584824585296 absolute error = 1.5e-31 relative error = 4.1717138895556359560302232369619e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=494.1MB, alloc=52.3MB, time=5.22 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (closed_form) = -0.35369581547548892135344614420701 y[1] (numeric) = -0.35369581547548892135344614420715 absolute error = 1.4e-31 relative error = 3.9582034582962710687352232903347e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = -0.34766712364295390252349741204862 y[1] (numeric) = -0.34766712364295390252349741204876 absolute error = 1.4e-31 relative error = 4.0268403446676414253782476672369e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (closed_form) = -0.34147905803834074789020137510524 y[1] (numeric) = -0.3414790580383407478902013751054 absolute error = 1.6e-31 relative error = 4.6854996297323581112748640840498e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = -0.33513237297332009039317635767707 y[1] (numeric) = -0.33513237297332009039317635767721 absolute error = 1.4e-31 relative error = 4.1774537851389668325900312500734e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (closed_form) = -0.32862789116242667133678096325755 y[1] (numeric) = -0.32862789116242667133678096325767 absolute error = 1.2e-31 relative error = 3.6515464215631395373978324542097e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (closed_form) = -0.32196650378004910281538274709266 y[1] (numeric) = -0.32196650378004910281538274709278 absolute error = 1.2e-31 relative error = 3.7270957876406238283239641298716e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = -0.31514917048883439054159367906187 y[1] (numeric) = -0.315149170488834390541593679062 absolute error = 1.3e-31 relative error = 4.1250306893828821982623300479090e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (closed_form) = -0.30817691943940926323156515806094 y[1] (numeric) = -0.30817691943940926323156515806107 absolute error = 1.3e-31 relative error = 4.2183561389502217618559979044471e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = -0.30105084724133211757166920890053 y[1] (numeric) = -0.30105084724133211757166920890069 absolute error = 1.6e-31 relative error = 5.3147168149883602112738840515535e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (closed_form) = -0.2937721189052012045540523943724 y[1] (numeric) = -0.29377211890520120455405239437257 absolute error = 1.7e-31 relative error = 5.7867983058956711575735336212020e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = -0.28634196775585654882847508429222 y[1] (numeric) = -0.2863419677558565488284750842924 absolute error = 1.8e-31 relative error = 6.2861899501044573009928402016895e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (closed_form) = -0.2787616953166250028543899290909 y[1] (numeric) = -0.27876169531662500285438992909109 absolute error = 1.9e-31 relative error = 6.8158575296434794967849446230327e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=534.8MB, alloc=52.3MB, time=5.64 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (closed_form) = -0.27103267116456978720817192840804 y[1] (numeric) = -0.27103267116456978720817192840823 absolute error = 1.9e-31 relative error = 7.0102249733808983045047467538557e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (closed_form) = -0.26315633275671785254349838924558 y[1] (numeric) = -0.26315633275671785254349838924578 absolute error = 2.0e-31 relative error = 7.6000451102537414335714077813176e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (closed_form) = -0.25513418522725041253767158176514 y[1] (numeric) = -0.25513418522725041253767158176535 absolute error = 2.1e-31 relative error = 8.2309628485477565348025546304650e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = -0.24696780115565403578660415541985 y[1] (numeric) = -0.24696780115565403578660415542006 absolute error = 2.1e-31 relative error = 8.5031327572797761984370085955189e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = -0.23865882030584174312549347407082 y[1] (numeric) = -0.23865882030584174312549347407104 absolute error = 2.2e-31 relative error = 9.2181801501436054801379498482313e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (closed_form) = -0.2302089493362656303279497496672 y[1] (numeric) = -0.23020894933626563032794974966742 absolute error = 2.2e-31 relative error = 9.5565355141188084812176504123349e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = -0.22161996148105461964036721213839 y[1] (numeric) = -0.22161996148105461964036721213861 absolute error = 2.2e-31 relative error = 9.9269036295183589094461807026037e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (closed_form) = -0.21289369620222303219928636314861 y[1] (numeric) = -0.21289369620222303219928636314883 absolute error = 2.2e-31 relative error = 1.0333795876747184020308903614291e-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] = 1.64 y[1] (closed_form) = -0.20403205881300776210983403973773 y[1] (numeric) = -0.20403205881300776210983403973796 absolute error = 2.3e-31 relative error = 1.1272738281330163699304090945309e-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] = 1.65 y[1] (closed_form) = -0.19503702007240391688129279697245 y[1] (numeric) = -0.19503702007240391688129279697269 absolute error = 2.4e-31 relative error = 1.2305356178581092010385063566537e-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] = 1.66 y[1] (closed_form) = -0.18591061575098086306749589293821 y[1] (numeric) = -0.18591061575098086306749589293845 absolute error = 2.4e-31 relative error = 1.2909429568103281468014867972957e-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=575.4MB, alloc=52.3MB, time=6.06 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (closed_form) = -0.17665494616807267539093909452584 y[1] (numeric) = -0.17665494616807267539093909452609 absolute error = 2.5e-31 relative error = 1.4151882266695523405378618335173e-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] = 1.68 y[1] (closed_form) = -0.16727217570044902738794169888164 y[1] (numeric) = -0.16727217570044902738794169888189 absolute error = 2.5e-31 relative error = 1.4945701456511209656693825899968e-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] = 1.69 y[1] (closed_form) = -0.15776453226258457674940838478106 y[1] (numeric) = -0.1577645322625845767494083847813 absolute error = 2.4e-31 relative error = 1.5212544705583257377538868955662e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = -0.14813430675865688410511747749788 y[1] (numeric) = -0.14813430675865688410511747749814 absolute error = 2.6e-31 relative error = 1.7551639838811730815087802358027e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = -0.13838385250641485507421928894642 y[1] (numeric) = -0.13838385250641485507421928894666 absolute error = 2.4e-31 relative error = 1.7343063923507598246607405248345e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (closed_form) = -0.12851558463307160705585789259504 y[1] (numeric) = -0.12851558463307160705585789259529 absolute error = 2.5e-31 relative error = 1.9452893648173635940245394957031e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (closed_form) = -0.11853197944338752954847911530709 y[1] (numeric) = -0.11853197944338752954847911530734 absolute error = 2.5e-31 relative error = 2.1091354516643617550958375330447e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (closed_form) = -0.10843557376012112486526395450696 y[1] (numeric) = -0.10843557376012112486526395450721 absolute error = 2.5e-31 relative error = 2.3055164585843820468902744815739e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = -0.09822896423703698007289041753865 y[1] (numeric) = -0.0982289642370369800728904175389 absolute error = 2.50e-31 relative error = 2.5450741738121487647783972382137e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (closed_form) = -0.08791480664467192595597979928083 y[1] (numeric) = -0.087914806644671925955979799281089 absolute error = 2.59e-31 relative error = 2.9460338921839247054039784514527e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (closed_form) = -0.07749581512907207995445119205798 y[1] (numeric) = -0.077495815129072079954451192058237 absolute error = 2.57e-31 relative error = 3.3163081073727299314368433125127e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=616.0MB, alloc=52.3MB, time=6.47 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = -0.06697476144372504251171481484572 y[1] (numeric) = -0.066974761443725042511714814845978 absolute error = 2.58e-31 relative error = 3.8521973716439773111509885609374e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (closed_form) = -0.0563544741549230153080707302616 y[1] (numeric) = -0.05635447415492301530807073026186 absolute error = 2.60e-31 relative error = 4.6136531996596922317648106357978e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -0.04563783782080403066145929323495 y[1] (numeric) = -0.045637837820804030661459293235206 absolute error = 2.56e-31 relative error = 5.6093805540301533514403956275373e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = -0.03482779214432981921012132945143 y[1] (numeric) = -0.034827792144329819210121329451684 absolute error = 2.54e-31 relative error = 7.2930261828656507863696717672553e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (closed_form) = -0.02392733110047009313166993154122 y[1] (numeric) = -0.023927331100470093131669931541475 absolute error = 2.55e-31 relative error = 1.0657268833254457331395688117457e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = -0.0129395020378741799149922680897 y[1] (numeric) = -0.012939502037874179914992268089956 absolute error = 2.56e-31 relative error = 1.9784378042577133687927949582200e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (closed_form) = -0.00186740475532200243318526381416 y[1] (numeric) = -0.0018674047553220024331852638144132 absolute error = 2.532e-31 relative error = 1.3558924452687276859193563209698e-26 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (closed_form) = 0.0092858094467426398493609381956 y[1] (numeric) = 0.0092858094467426398493609381953323 absolute error = 2.677e-31 relative error = 2.8828935327108852650414344089815e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (closed_form) = 0.02051693873928268084407828189804 y[1] (numeric) = 0.02051693873928268084407828189777 absolute error = 2.70e-31 relative error = 1.3159857980325568697316138834586e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (closed_form) = 0.03182273176201773919608239518866 y[1] (numeric) = 0.03182273176201773919608239518841 absolute error = 2.50e-31 relative error = 7.8560194602271505810509844489755e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = 0.04319988864471823442365344253482 y[1] (numeric) = 0.043199888644718234423653442534563 absolute error = 2.57e-31 relative error = 5.9490894088548002692663693935292e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=656.5MB, alloc=52.3MB, time=6.89 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (closed_form) = 0.05464506205209798412721171199396 y[1] (numeric) = 0.054645062052097984127211711993691 absolute error = 2.69e-31 relative error = 4.9226771806670919758169281822958e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 0.06615485825194921558723536290051 y[1] (numeric) = 0.066154858251949215587235362900253 absolute error = 2.57e-31 relative error = 3.8848242863921130077743609679545e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = 0.07772583820615367060212948747714 y[1] (numeric) = 0.077725838206153670602129487476883 absolute error = 2.57e-31 relative error = 3.3064937726159243461890278357526e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (closed_form) = 0.08935451868419336076576158598553 y[1] (numeric) = 0.089354518684193360765761585985276 absolute error = 2.54e-31 relative error = 2.8426094588200395309096109778201e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (closed_form) = 0.10103737339877454581734196321672 y[1] (numeric) = 0.10103737339877454581734196321647 absolute error = 2.5e-31 relative error = 2.4743319386708461328976764289552e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (closed_form) = 0.11277083416316866442886449922903 y[1] (numeric) = 0.11277083416316866442886449922876 absolute error = 2.7e-31 relative error = 2.3942360806636909007049328433016e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = 0.12455129206986424898921670270821 y[1] (numeric) = 0.12455129206986424898921670270793 absolute error = 2.8e-31 relative error = 2.2480698140244124546524684892613e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (closed_form) = 0.13637509869011430770585259953813 y[1] (numeric) = 0.13637509869011430770585259953786 absolute error = 2.7e-31 relative error = 1.9798335810082315678314323225120e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (closed_form) = 0.14823856729395426272419047047154 y[1] (numeric) = 0.14823856729395426272419047047126 absolute error = 2.8e-31 relative error = 1.8888471813463045646459989481970e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (closed_form) = 0.16013797409025629595262868083917 y[1] (numeric) = 0.1601379740902562959526286808389 absolute error = 2.7e-31 relative error = 1.6860460583060937686882573408690e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = 0.17206955948637687880798329504642 y[1] (numeric) = 0.17206955948637687880798329504615 absolute error = 2.7e-31 relative error = 1.5691328600244163879462271118539e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=697.2MB, alloc=52.3MB, time=7.31 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 0.18402952936694535203106945356061 y[1] (numeric) = 0.18402952936694535203106945356034 absolute error = 2.7e-31 relative error = 1.4671558468295269141328804468700e-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] = 2.01 y[1] (closed_form) = 0.19601405639133268087041418600295 y[1] (numeric) = 0.19601405639133268087041418600268 absolute error = 2.7e-31 relative error = 1.3774522346548347749182878343633e-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] = 2.02 y[1] (closed_form) = 0.20801928130933094303397557171088 y[1] (numeric) = 0.20801928130933094303397557171061 absolute error = 2.7e-31 relative error = 1.2979566043135292808291136349786e-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] = 2.03 y[1] (closed_form) = 0.2200413142945657155379096546969 y[1] (numeric) = 0.22004131429456571553790965469665 absolute error = 2.5e-31 relative error = 1.1361502761491829709193713903114e-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] = 2.04 y[1] (closed_form) = 0.23207623629515531554338867341538 y[1] (numeric) = 0.23207623629515531554338867341513 absolute error = 2.5e-31 relative error = 1.0772322233029028582552742611544e-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] = 2.05 y[1] (closed_form) = 0.2441201004011228230031088520085 y[1] (numeric) = 0.24412010040112282300310885200825 absolute error = 2.5e-31 relative error = 1.0240860936449546560029661489078e-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] = 2.06 y[1] (closed_form) = 0.25616893322805897290319966226248 y[1] (numeric) = 0.25616893322805897290319966226223 absolute error = 2.5e-31 relative error = 9.7591849585223915578671211619437e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = 0.26821873631652635547597211497181 y[1] (numeric) = 0.26821873631652635547597211497156 absolute error = 2.5e-31 relative error = 9.3207507959091147169939744175776e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = 0.28026548754668790729256634636374 y[1] (numeric) = 0.2802654875466879072925663463635 absolute error = 2.4e-31 relative error = 8.5633091002694258550440725046002e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = 0.29230514256763541786497022636972 y[1] (numeric) = 0.29230514256763541786497022636948 absolute error = 2.4e-31 relative error = 8.2105979351515267225747312240093e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 0.30433363624088671846026346028893 y[1] (numeric) = 0.30433363624088671846026346028869 absolute error = 2.4e-31 relative error = 7.8860819646644237314054882280638e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=737.8MB, alloc=52.3MB, time=7.73 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = 0.31634688409751336534444344859611 y[1] (numeric) = 0.31634688409751336534444344859587 absolute error = 2.4e-31 relative error = 7.5866086269406853434846112729158e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = 0.32834078380835398163762815367018 y[1] (numeric) = 0.32834078380835398163762815366994 absolute error = 2.4e-31 relative error = 7.3094788048043173011516473999156e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = 0.34031121666676198330503233001022 y[1] (numeric) = 0.34031121666676198330503233000997 absolute error = 2.5e-31 relative error = 7.3462168672742830544477781123971e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = 0.35225404908333018837527663244243 y[1] (numeric) = 0.35225404908333018837527663244216 absolute error = 2.7e-31 relative error = 7.6649225382254741974811699911997e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = 0.36416513409202879703268974370806 y[1] (numeric) = 0.36416513409202879703268974370779 absolute error = 2.7e-31 relative error = 7.4142188453375614995764153589479e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = 0.37604031286718743645248595851966 y[1] (numeric) = 0.37604031286718743645248595851939 absolute error = 2.7e-31 relative error = 7.1800812508993018453619296844651e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = 0.38787541625074639073090416536288 y[1] (numeric) = 0.38787541625074639073090416536259 absolute error = 2.9e-31 relative error = 7.4766274904240454412731145115607e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = 0.3996662662891967855140140556632 y[1] (numeric) = 0.39966626628919678551401405566292 absolute error = 2.8e-31 relative error = 7.0058452168037922006947977103303e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (closed_form) = 0.41140867777962437136887696148002 y[1] (numeric) = 0.41140867777962437136887696147975 absolute error = 2.7e-31 relative error = 6.5628173294056888964286912088646e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 0.42309845982426665190051651900953 y[1] (numeric) = 0.42309845982426665190051651900927 absolute error = 2.6e-31 relative error = 6.1451417267742036456286608484451e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = 0.43473141739298843433961633653102 y[1] (numeric) = 0.43473141739298843433961633653074 absolute error = 2.8e-31 relative error = 6.4407583348613989543410074448726e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=778.6MB, alloc=52.3MB, time=8.16 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = 0.44630335289307644396044903949761 y[1] (numeric) = 0.44630335289307644396044903949733 absolute error = 2.8e-31 relative error = 6.2737597238504562599864716198529e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = 0.45781006774574944129628308310702 y[1] (numeric) = 0.45781006774574944129628308310673 absolute error = 2.9e-31 relative error = 6.3345046435513326123142741721633e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = 0.46924736396877631466815052786358 y[1] (numeric) = 0.4692473639687763146681505278633 absolute error = 2.8e-31 relative error = 5.9670020867422747963074971203156e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = 0.48061104576459089190698927611876 y[1] (numeric) = 0.48061104576459089190698927611849 absolute error = 2.7e-31 relative error = 5.6178484115042430463696644649532e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = 0.49189692111328872610943989363256 y[1] (numeric) = 0.4918969211132887261094398936323 absolute error = 2.6e-31 relative error = 5.2856602438485161494375163482171e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = 0.50310080336988786250988972187633 y[1] (numeric) = 0.50310080336988786250988972187606 absolute error = 2.7e-31 relative error = 5.3667177271726919728294678394475e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = 0.51421851286523258866615229519327 y[1] (numeric) = 0.514218512865232588666152295193 absolute error = 2.7e-31 relative error = 5.2506861041535884453529680011190e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = 0.52524587850991640963771031009802 y[1] (numeric) = 0.52524587850991640963771031009775 absolute error = 2.7e-31 relative error = 5.1404496645641460190994175915393e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 0.53617873940059797508115971487278 y[1] (numeric) = 0.53617873940059797508115971487251 absolute error = 2.7e-31 relative error = 5.0356342047772527107174359663672e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = 0.54701294642808141749733209218734 y[1] (numeric) = 0.54701294642808141749733209218707 absolute error = 2.7e-31 relative error = 4.9358978021098496492455035821910e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = 0.55774436388653054144045448792256 y[1] (numeric) = 0.55774436388653054144045448792226 absolute error = 3.0e-31 relative error = 5.3788082753451731207435734621270e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=819.2MB, alloc=52.3MB, time=8.58 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = 0.56836887108318453344494609162956 y[1] (numeric) = 0.56836887108318453344494609162925 absolute error = 3.1e-31 relative error = 5.4542044044250526016308376134400e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = 0.57888236394794134274426158339482 y[1] (numeric) = 0.57888236394794134274426158339452 absolute error = 3.0e-31 relative error = 5.1824000640478810453040256336233e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = 0.58928075664217361445321108478224 y[1] (numeric) = 0.58928075664217361445321108478194 absolute error = 3.0e-31 relative error = 5.0909519209392356330790020511801e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = 0.59955998316614104056505509599747 y[1] (numeric) = 0.59955998316614104056505509599719 absolute error = 2.8e-31 relative error = 4.6700915314825241320774433343606e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = 0.60971599896436223058163849232852 y[1] (numeric) = 0.60971599896436223058163849232825 absolute error = 2.7e-31 relative error = 4.4282912119513111564731589962458e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = 0.61974478252830869345240115279732 y[1] (numeric) = 0.61974478252830869345240115279705 absolute error = 2.7e-31 relative error = 4.3566320784260405419499274614686e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = 0.62964233699578326624874783391537 y[1] (numeric) = 0.62964233699578326624874783391511 absolute error = 2.6e-31 relative error = 4.1293284254127471077940600640015e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 0.63940469174634532304512526055458 y[1] (numeric) = 0.63940469174634532304512526055433 absolute error = 2.5e-31 relative error = 3.9098868561192245480410592812830e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = 0.64902790399214535011684626157972 y[1] (numeric) = 0.64902790399214535011684626157945 absolute error = 2.7e-31 relative error = 4.1600676694983454440722117610875e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (closed_form) = 0.65850806036353198099509563302281 y[1] (numeric) = 0.65850806036353198099509563302254 absolute error = 2.7e-31 relative error = 4.1001776022444650317937617291121e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (closed_form) = 0.6678412784887953472376506891811 y[1] (numeric) = 0.66784127848879534723765068918081 absolute error = 2.9e-31 relative error = 4.3423491380499543564298213260370e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=860.0MB, alloc=52.3MB, time=9.00 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = 0.67702370856741161797366984010136 y[1] (numeric) = 0.67702370856741161797366984010109 absolute error = 2.7e-31 relative error = 3.9880434995596015160011354275893e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = 0.68605153493615487325441707871082 y[1] (numeric) = 0.68605153493615487325441707871055 absolute error = 2.7e-31 relative error = 3.9355644037022183882582124162318e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = 0.69492097762744398277890039915461 y[1] (numeric) = 0.69492097762744398277890039915434 absolute error = 2.7e-31 relative error = 3.8853338536680418159672714087260e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = 0.70362829391929394235195552332776 y[1] (numeric) = 0.70362829391929394235195552332751 absolute error = 2.5e-31 relative error = 3.5530123242695377134261599297692e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = 0.71216977987624315505815441416162 y[1] (numeric) = 0.71216977987624315505815441416136 absolute error = 2.6e-31 relative error = 3.6508148386355474475432086697112e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = 0.72054177188063043208201490926586 y[1] (numeric) = 0.72054177188063043208201490926559 absolute error = 2.7e-31 relative error = 3.7471803930991238970597639977321e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 0.72874064815359802875552931556092 y[1] (numeric) = 0.72874064815359802875552931556068 absolute error = 2.4e-31 relative error = 3.2933527258028668565775274323062e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = 0.73676283026519982404863396649208 y[1] (numeric) = 0.73676283026519982404863396649181 absolute error = 2.7e-31 relative error = 3.6646799880337713453580357866487e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = 0.74460478463299679551616961811662 y[1] (numeric) = 0.74460478463299679551616961811634 absolute error = 2.8e-31 relative error = 3.7603841095112933209000525059575e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = 0.75226302400852523575429988991662 y[1] (numeric) = 0.75226302400852523575429988991634 absolute error = 2.8e-31 relative error = 3.7221023905705994126048423622253e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = 0.75973410895102669967763436571203 y[1] (numeric) = 0.75973410895102669967763436571173 absolute error = 3.0e-31 relative error = 3.9487499174443190829607956216259e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=900.7MB, alloc=52.3MB, time=9.42 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = 0.76701464928783246328236664466946 y[1] (numeric) = 0.76701464928783246328236664466916 absolute error = 3.0e-31 relative error = 3.9112681912731109284822716602516e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = 0.77410130556079931278744034458064 y[1] (numeric) = 0.77410130556079931278744034458033 absolute error = 3.1e-31 relative error = 4.0046438078982420841832679421287e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = 0.78099079045819776682230840930488 y[1] (numeric) = 0.78099079045819776682230840930458 absolute error = 3.0e-31 relative error = 3.8412744896004940174948171840038e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = 0.78767987023145836223428278572898 y[1] (numeric) = 0.78767987023145836223428278572867 absolute error = 3.1e-31 relative error = 3.9356090172636637044814630501313e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = 0.79416536609618640460013465185207 y[1] (numeric) = 0.79416536609618640460013465185175 absolute error = 3.2e-31 relative error = 4.0293875011573190457199522064368e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 0.80044415561686059602671713668313 y[1] (numeric) = 0.8004441556168605960267171366828 absolute error = 3.3e-31 relative error = 4.1227110933889722483964167159664e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = 0.80651317407463620359760770267301 y[1] (numeric) = 0.80651317407463620359760770267267 absolute error = 3.4e-31 relative error = 4.2156781926110952579607626277652e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = 0.81236941581767892005384014645365 y[1] (numeric) = 0.81236941581767892005384014645331 absolute error = 3.4e-31 relative error = 4.1852880398971915940762134001609e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.81800993559346129207718056820609 y[1] (numeric) = 0.81800993559346129207718056820576 absolute error = 3.3e-31 relative error = 4.0341808288744926219302609498577e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = 0.82343184986245954886899120030621 y[1] (numeric) = 0.82343184986245954886899120030589 absolute error = 3.2e-31 relative error = 3.8861746731493398241990042880929e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = 0.82863233809269485248658173301948 y[1] (numeric) = 0.82863233809269485248658173301914 absolute error = 3.4e-31 relative error = 4.1031466474334717875629685433112e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=941.4MB, alloc=52.3MB, time=9.83 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = 0.83360864403456940941807460838349 y[1] (numeric) = 0.83360864403456940941807460838317 absolute error = 3.2e-31 relative error = 3.8387317872717467996884467312268e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = 0.8383580769754545278589716191584 y[1] (numeric) = 0.83835807697545452785897161915807 absolute error = 3.3e-31 relative error = 3.9362655297667246019752720286311e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = 0.84287801297349457471917695203123 y[1] (numeric) = 0.8428780129734945747191769520309 absolute error = 3.3e-31 relative error = 3.9151572934715677642249520078974e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = 0.84716589607009787806707862330125 y[1] (numeric) = 0.84716589607009787806707862330092 absolute error = 3.3e-31 relative error = 3.8953409424391475569823947497750e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 0.85121923948059293194571349007963 y[1] (numeric) = 0.8512192394805929319457134900793 absolute error = 3.3e-31 relative error = 3.8767920729959454441971066236570e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = 0.85503562676253578862372624989072 y[1] (numeric) = 0.85503562676253578862372624989039 absolute error = 3.3e-31 relative error = 3.8594883028382750022525601394885e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = 0.85861271296116226563085283468699 y[1] (numeric) = 0.85861271296116226563085283468666 absolute error = 3.3e-31 relative error = 3.8434091997299244573042413001531e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = 0.86194822573148654854650823907883 y[1] (numeric) = 0.86194822573148654854650823907849 absolute error = 3.4e-31 relative error = 3.9445524667268883006903728998357e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = 0.86503996643655593254672545513061 y[1] (numeric) = 0.86503996643655593254672545513026 absolute error = 3.5e-31 relative error = 4.0460558307125318689462432425259e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = 0.86788581122137981316976107452012 y[1] (numeric) = 0.86788581122137981316976107451978 absolute error = 3.4e-31 relative error = 3.9175660623085471287258287301346e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = 0.87048371206205960655047745590935 y[1] (numeric) = 0.87048371206205960655047745590901 absolute error = 3.4e-31 relative error = 3.9058743465123020875315852951021e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=982.1MB, alloc=52.3MB, time=10.25 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = 0.8728316977896550483313664814498 y[1] (numeric) = 0.87283169778965504833136648144949 absolute error = 3.1e-31 relative error = 3.5516583642074298348439561497163e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = 0.87492787508833128533515126100198 y[1] (numeric) = 0.87492787508833128533515126100166 absolute error = 3.2e-31 relative error = 3.6574443346852256145976454003519e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = 0.87677042946734033155100636532059 y[1] (numeric) = 0.87677042946734033155100636532026 absolute error = 3.3e-31 relative error = 3.7638130679256956930736026603491e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 0.87835762620639980663492616619099 y[1] (numeric) = 0.87835762620639980663492616619067 absolute error = 3.2e-31 relative error = 3.6431629948050930479798786126604e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = 0.8796878112740414074679379410753 y[1] (numeric) = 0.87968781127404140746793794107498 absolute error = 3.2e-31 relative error = 3.6376541302368143671691112741542e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = 0.88075941221851127779027426968625 y[1] (numeric) = 0.88075941221851127779027426968592 absolute error = 3.3e-31 relative error = 3.7467666586585273185074164201352e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = 0.88157093903081433389650922947579 y[1] (numeric) = 0.88157093903081433389650922947545 absolute error = 3.4e-31 relative error = 3.8567514529663469010659479956139e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = 0.88212098497950467212329483334904 y[1] (numeric) = 0.88212098497950467212329483334868 absolute error = 3.6e-31 relative error = 4.0810728474888769663471993166113e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = 0.88240822741683442260245649119233 y[1] (numeric) = 0.88240822741683442260245649119198 absolute error = 3.5e-31 relative error = 3.9664181398737801941026138287424e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = 0.88243142855588381963150572617075 y[1] (numeric) = 0.88243142855588381963150572617039 absolute error = 3.6e-31 relative error = 4.0796371066378154229245637422460e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = 0.88218943621830582810521859968423 y[1] (numeric) = 0.88218943621830582810521859968387 absolute error = 3.6e-31 relative error = 4.0807561870522638419919383517137e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1022.7MB, alloc=52.3MB, time=10.67 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = 0.88168118455232939376186704089202 y[1] (numeric) = 0.88168118455232939376186704089167 absolute error = 3.5e-31 relative error = 3.9696888867795370165706490447048e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = 0.88090569472067626846552434148804 y[1] (numeric) = 0.88090569472067626846552434148768 absolute error = 3.6e-31 relative error = 4.0867030620587748033206038355661e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 0.87986207555805739624620354011847 y[1] (numeric) = 0.87986207555805739624620354011812 absolute error = 3.5e-31 relative error = 3.9778961921731944276131454034857e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = 0.87854952419792602716369646863502 y[1] (numeric) = 0.87854952419792602716369646863467 absolute error = 3.5e-31 relative error = 3.9838391617084235559427618456686e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = 0.87696732666817604999841498895817 y[1] (numeric) = 0.8769673266681760499984149889578 absolute error = 3.7e-31 relative error = 4.2190853495731130768674218712692e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = 0.87511485845548549699278266503564 y[1] (numeric) = 0.87511485845548549699278266503526 absolute error = 3.8e-31 relative error = 4.3422871446917556298817914893126e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = 0.87299158503801677000088305813486 y[1] (numeric) = 0.87299158503801677000088305813448 absolute error = 3.8e-31 relative error = 4.3528483723408614122895575126559e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = 0.87059706238619686302654723378247 y[1] (numeric) = 0.87059706238619686302654723378208 absolute error = 3.9e-31 relative error = 4.4796843091918910845587558064582e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = 0.8679309374313127067602964327917 y[1] (numeric) = 0.8679309374313127067602964327913 absolute error = 4.0e-31 relative error = 4.6086616198268154165476002635311e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = 0.86499294850166873182976099541438 y[1] (numeric) = 0.86499294850166873182976099541399 absolute error = 3.9e-31 relative error = 4.5087072753084716928864279428648e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = 0.86178292572606583447113168081146 y[1] (numeric) = 0.86178292572606583447113168081108 absolute error = 3.8e-31 relative error = 4.4094630870046995931884824386553e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1063.4MB, alloc=52.3MB, time=11.09 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = 0.85830079140437312657595432594326 y[1] (numeric) = 0.85830079140437312657595432594289 absolute error = 3.7e-31 relative error = 4.3108430483280434473808743065365e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = 0.85454656034497615688538382371469 y[1] (numeric) = 0.85454656034497615688538382371431 absolute error = 3.8e-31 relative error = 4.4468027563834076807652473943105e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = 0.85052034016889769676406867146526 y[1] (numeric) = 0.85052034016889769676406867146488 absolute error = 3.8e-31 relative error = 4.4678531723831435820858200546078e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = 0.84622233158039968771516040705119 y[1] (numeric) = 0.84622233158039968771516040705081 absolute error = 3.8e-31 relative error = 4.4905456381695140043943585937253e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = 0.84165282860388754378123471690073 y[1] (numeric) = 0.84165282860388754378123471690034 absolute error = 3.9e-31 relative error = 4.6337395508659092916463465019028e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = 0.83681221878695068535744272124827 y[1] (numeric) = 0.83681221878695068535744272124787 absolute error = 4.0e-31 relative error = 4.7800449254892934293256630124517e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = 0.8317009833693859468287211822806 y[1] (numeric) = 0.83170098336938594682872118228021 absolute error = 3.9e-31 relative error = 4.6891852696870996235209913428004e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = 0.82631969741806334390150520264632 y[1] (numeric) = 0.82631969741806334390150520264592 absolute error = 4.0e-31 relative error = 4.8407414376039779282094270186191e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (closed_form) = 0.82066902992750660256655208144753 y[1] (numeric) = 0.82066902992750660256655208144714 absolute error = 3.9e-31 relative error = 4.7522202712395575507634995227046e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = 0.81474974388607383530491323770799 y[1] (numeric) = 0.81474974388607383530491323770759 absolute error = 4.0e-31 relative error = 4.9094829793028060975589293609425e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = 0.80856269630763679640472398745125 y[1] (numeric) = 0.80856269630763679640472398745084 absolute error = 4.1e-31 relative error = 5.0707261400049280221099787373958e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1104.2MB, alloc=52.3MB, time=11.52 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = 0.80210883822867025203446318816949 y[1] (numeric) = 0.80210883822867025203446318816908 absolute error = 4.1e-31 relative error = 5.1115257738017170595296531159640e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = 0.79538921467067615693400125895588 y[1] (numeric) = 0.79538921467067615693400125895546 absolute error = 4.2e-31 relative error = 5.2804336826958015937398974614470e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = 0.78840496456788053312862950618856 y[1] (numeric) = 0.78840496456788053312862950618812 absolute error = 4.4e-31 relative error = 5.5808882461966870713646638377551e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = 0.78115732066015419181106777389743 y[1] (numeric) = 0.781157320660154191811067773897 absolute error = 4.3e-31 relative error = 5.5046530145375585010041257272936e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = 0.77364760935112172231912034231835 y[1] (numeric) = 0.77364760935112172231912034231794 absolute error = 4.1e-31 relative error = 5.2995704380690533488531713421272e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = 0.76587725053143648679037679023943 y[1] (numeric) = 0.76587725053143648679037679023902 absolute error = 4.1e-31 relative error = 5.3533382760162163244743065469590e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = 0.7578477573672127004116031196333 y[1] (numeric) = 0.7578477573672127004116031196329 absolute error = 4.0e-31 relative error = 5.2781049506514707914025299256482e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = 0.74956073605361903999603403334791 y[1] (numeric) = 0.74956073605361903999603403334752 absolute error = 3.9e-31 relative error = 5.2030473481484729159270800132386e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = 0.7410178855336516027008336463633 y[1] (numeric) = 0.74101788553365160270083364636292 absolute error = 3.8e-31 relative error = 5.1280813515903076589623408585330e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = 0.73222099718211742681314866492881 y[1] (numeric) = 0.73222099718211742681314866492841 absolute error = 4.0e-31 relative error = 5.4628315978285489760271150086479e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = 0.72317195445487318245154287881141 y[1] (numeric) = 0.72317195445487318245154287881101 absolute error = 4.0e-31 relative error = 5.5311879496422104535992880047851e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1144.8MB, alloc=52.3MB, time=11.94 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (closed_form) = 0.71387273250337703650884716750164 y[1] (numeric) = 0.71387273250337703650884716750124 absolute error = 4.0e-31 relative error = 5.6032396502566760457309709204886e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = 0.70432539775462508795689257151349 y[1] (numeric) = 0.70432539775462508795689257151307 absolute error = 4.2e-31 relative error = 5.9631528458146104012017550165985e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = 0.69453210745655715149523058267775 y[1] (numeric) = 0.69453210745655715149523058267732 absolute error = 4.3e-31 relative error = 6.1912184531641169163957500429476e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = 0.68449510918903003420658242780922 y[1] (numeric) = 0.68449510918903003420658242780878 absolute error = 4.4e-31 relative error = 6.4280956005850684153511205033245e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = 0.67421674034046979613505376047948 y[1] (numeric) = 0.67421674034046979613505376047904 absolute error = 4.4e-31 relative error = 6.5260912948825077040843031981314e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = 0.66369942755032780628669300922142 y[1] (numeric) = 0.66369942755032780628669300922099 absolute error = 4.3e-31 relative error = 6.4788363851254555699405476538694e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = 0.65294568611747869522936031581233 y[1] (numeric) = 0.6529456861174786952293603158119 absolute error = 4.3e-31 relative error = 6.5855401014569829648896776464537e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = 0.64195811937471155901179254614607 y[1] (numeric) = 0.64195811937471155901179254614564 absolute error = 4.3e-31 relative error = 6.6982562728365243237073338149129e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = 0.63073941802947898131203623144595 y[1] (numeric) = 0.63073941802947898131203623144552 absolute error = 4.3e-31 relative error = 6.8173953887864197647739262639556e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = 0.61929235947108160635713591598011 y[1] (numeric) = 0.61929235947108160635713591597969 absolute error = 4.2e-31 relative error = 6.7819341475278166116922539924256e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = 0.60761980704447910903745970482424 y[1] (numeric) = 0.60761980704447910903745970482382 absolute error = 4.2e-31 relative error = 6.9122170661769601322804231199257e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1185.4MB, alloc=52.3MB, time=12.36 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = 0.59572470929093146559501416170214 y[1] (numeric) = 0.59572470929093146559501416170172 absolute error = 4.2e-31 relative error = 7.0502363499393885404892456108449e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = 0.58361009915568742313864661245208 y[1] (numeric) = 0.58361009915568742313864661245165 absolute error = 4.3e-31 relative error = 7.3679328137412946419385726276014e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = 0.57127909316294999389370395139127 y[1] (numeric) = 0.57127909316294999389370395139084 absolute error = 4.3e-31 relative error = 7.5269689569638783445285942289300e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = 0.55873489055836165541555360386258 y[1] (numeric) = 0.55873489055836165541555360386214 absolute error = 4.4e-31 relative error = 7.8749333080003992624441538111999e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = 0.54598077241926471589593824420016 y[1] (numeric) = 0.54598077241926471589593824419972 absolute error = 4.4e-31 relative error = 8.0588918552999719848221442260592e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = 0.53302010073300499910554246702381 y[1] (numeric) = 0.53302010073300499910554246702338 absolute error = 4.3e-31 relative error = 8.0672379786178311712804797466022e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = 0.51985631744355961141106977659341 y[1] (numeric) = 0.51985631744355961141106977659297 absolute error = 4.4e-31 relative error = 8.4638771375086819342345539836894e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = 0.50649294346678206867680040028551 y[1] (numeric) = 0.50649294346678206867680040028505 absolute error = 4.6e-31 relative error = 9.0820613778238892505353087612583e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = 0.49293357767457047873782105710906 y[1] (numeric) = 0.49293357767457047873782105710858 absolute error = 4.8e-31 relative error = 9.7376202746101201979777869132117e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = 0.4791818958482767905782221223706 y[1] (numeric) = 0.47918189584827679057822212237011 absolute error = 4.9e-31 relative error = 1.0225761954812010307182371869055e-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] = 3.42 y[1] (closed_form) = 0.46524164960168732946238729785076 y[1] (numeric) = 0.46524164960168732946238729785028 absolute error = 4.8e-31 relative error = 1.0317219028239365636459021083348e-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=1226.0MB, alloc=52.3MB, time=12.78 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (closed_form) = 0.45111666527391693318935824731658 y[1] (numeric) = 0.4511166652739169331893582473161 absolute error = 4.8e-31 relative error = 1.0640263083797739477787147680249e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = 0.4368108427925709835478444680575 y[1] (numeric) = 0.43681084279257098354784446805701 absolute error = 4.9e-31 relative error = 1.1217670258993251018513674745299e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = 0.42232815450754148416379482249563 y[1] (numeric) = 0.42232815450754148416379482249514 absolute error = 4.9e-31 relative error = 1.1602352217587002110436608087810e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.40767264399581506651881336395228 y[1] (numeric) = 0.4076726439958150665188133639518 absolute error = 4.8e-31 relative error = 1.1774152793164296906408859789474e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = 0.39284842483768240528747594720406 y[1] (numeric) = 0.39284842483768240528747594720358 absolute error = 4.8e-31 relative error = 1.2218452961809048606645069992337e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = 0.37785967936474998765417368574245 y[1] (numeric) = 0.37785967936474998765417368574197 absolute error = 4.8e-31 relative error = 1.2703128336078785734229872641139e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = 0.3627106573801665043347195623269 y[1] (numeric) = 0.36271065738016650433471956232642 absolute error = 4.8e-31 relative error = 1.3233688898666671246829967763101e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = 0.34740567485148730810554474553814 y[1] (numeric) = 0.34740567485148730810554474553766 absolute error = 4.8e-31 relative error = 1.3816700035346156378555050219674e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = 0.33194911257661141424833292053876 y[1] (numeric) = 0.33194911257661141424833292053827 absolute error = 4.9e-31 relative error = 1.4761298688120806562966796882834e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (closed_form) = 0.3163454148232363920201553094569 y[1] (numeric) = 0.31634541482323639202015530945642 absolute error = 4.8e-31 relative error = 1.5173287726272514755468239644972e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = 0.30059908794228721268542303123272 y[1] (numeric) = 0.30059908794228721268542303123221 absolute error = 5.1e-31 relative error = 1.6966119341583504861180881071023e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1266.7MB, alloc=52.3MB, time=13.19 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = 0.28471469895578567348195439273655 y[1] (numeric) = 0.28471469895578567348195439273606 absolute error = 4.9e-31 relative error = 1.7210210846054484464084037047674e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = 0.26869687411963740388542227918667 y[1] (numeric) = 0.26869687411963740388542227918617 absolute error = 5.0e-31 relative error = 1.8608329614485011665147962989859e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = 0.25255029746182367649294171271089 y[1] (numeric) = 0.25255029746182367649294171271039 absolute error = 5.0e-31 relative error = 1.9798036471352072927710075050135e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = 0.23627970929649528564008639522587 y[1] (numeric) = 0.23627970929649528564008639522538 absolute error = 4.9e-31 relative error = 2.0738132845132467039056627693518e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = 0.21988990471447561843431822189925 y[1] (numeric) = 0.21988990471447561843431822189874 absolute error = 5.1e-31 relative error = 2.3193424939731945913146963353914e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = 0.20338573205068972123706894640304 y[1] (numeric) = 0.20338573205068972123706894640254 absolute error = 5.0e-31 relative error = 2.4583828715938896713999616749316e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = 0.18677209132904565583079209081159 y[1] (numeric) = 0.18677209132904565583079209081109 absolute error = 5.0e-31 relative error = 2.6770594923581232682080642431664e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = 0.17005393268530373971092211317767 y[1] (numeric) = 0.17005393268530373971092211317717 absolute error = 5.0e-31 relative error = 2.9402436750773867069894127976292e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (closed_form) = 0.15323625476847837036256098713129 y[1] (numeric) = 0.1532362547684783703625609871308 absolute error = 4.9e-31 relative error = 3.1976766904172339530162138685083e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = 0.13632410312132604030811934986551 y[1] (numeric) = 0.13632410312132604030811934986501 absolute error = 5.0e-31 relative error = 3.6677299798921753743012279931444e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = 0.11932256854048185451036438167658 y[1] (numeric) = 0.11932256854048185451036438167609 absolute error = 4.9e-31 relative error = 4.1065156909839786867566307625149e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1307.4MB, alloc=52.3MB, time=13.61 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = 0.10223678541681536082716828611405 y[1] (numeric) = 0.10223678541681536082716828611356 absolute error = 4.9e-31 relative error = 4.7927954503096829092225367648120e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = 0.08507193005658479415945331162775 y[1] (numeric) = 0.085071930056584794159453311627258 absolute error = 4.92e-31 relative error = 5.7833412228069920049255417784901e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = 0.06783321898397691231149055168277 y[1] (numeric) = 0.067833218983976912311490551682274 absolute error = 4.96e-31 relative error = 7.3120516382564956055335218121620e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = 0.05052590722562746307266377772135 y[1] (numeric) = 0.05052590722562746307266377772085 absolute error = 5.00e-31 relative error = 9.8959133532666751596471662157827e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = 0.03315528657772496439397255357911 y[1] (numeric) = 0.033155286577724964393972553578617 absolute error = 4.93e-31 relative error = 1.4869423578779045742237900075127e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = 0.01572668385630789961623611319209 y[1] (numeric) = 0.0157266838563078996162361131916 absolute error = 4.90e-31 relative error = 3.1157235974032967106184907912231e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = -0.00175454086862737555983092983673 y[1] (numeric) = -0.0017545408686273755598309298372242 absolute error = 4.942e-31 relative error = 2.8166912999104200511833222960930e-26 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = -0.01928299605458375127283614063789 y[1] (numeric) = -0.01928299605458375127283614063838 absolute error = 4.90e-31 relative error = 2.5410988967325041119686311184285e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = -0.03685326048295450861318394663043 y[1] (numeric) = -0.036853260482954508613183946630924 absolute error = 4.94e-31 relative error = 1.3404512749380384039942118846900e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = -0.05445988506971099226561462984089 y[1] (numeric) = -0.054459885069710992265614629841379 absolute error = 4.89e-31 relative error = 8.9790861544062936331557706112919e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = -0.07209739468974304693060065246633 y[1] (numeric) = -0.072097394689743046930600652466826 absolute error = 4.96e-31 relative error = 6.8795828494835134233248102724563e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1348.1MB, alloc=52.3MB, time=14.03 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = -0.08976029001420242879302128864399 y[1] (numeric) = -0.089760290014202428793021288644483 absolute error = 4.93e-31 relative error = 5.4924064964807320456674646677093e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = -0.10744304936019362025062883006537 y[1] (numeric) = -0.10744304936019362025062883006588 absolute error = 5.1e-31 relative error = 4.7467007222614157440970055505208e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = -0.12514013055215093742747790856477 y[1] (numeric) = -0.12514013055215093742747790856527 absolute error = 5.0e-31 relative error = 3.9955208436643738556104150461552e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = -0.14284597279423552802908769308178 y[1] (numeric) = -0.14284597279423552802908769308228 absolute error = 5.0e-31 relative error = 3.5002736879410101897157425788714e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (closed_form) = -0.1605549985530808141023206661785 y[1] (numeric) = -0.16055499855308081410232066617901 absolute error = 5.1e-31 relative error = 3.1764816081474397090071608949663e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = -0.17826161545021014240383549265456 y[1] (numeric) = -0.17826161545021014240383549265509 absolute error = 5.3e-31 relative error = 2.9731582913206187561769818978598e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = -0.19596021816344586642002147329514 y[1] (numeric) = -0.19596021816344586642002147329566 absolute error = 5.2e-31 relative error = 2.6535998218081186151393108800597e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (closed_form) = -0.2136451903366248005846783148136 y[1] (numeric) = -0.21364519033662480058467831481411 absolute error = 5.1e-31 relative error = 2.3871354145461033646944944216704e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = -0.23131090649693096077629095929374 y[1] (numeric) = -0.23131090649693096077629095929424 absolute error = 5.0e-31 relative error = 2.1615928430362794554219045498261e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = -0.24895173397915273751350002706011 y[1] (numeric) = -0.24895173397915273751350002706062 absolute error = 5.1e-31 relative error = 2.0485898685996197588962395492001e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = -0.26656203485616814107448737713952 y[1] (numeric) = -0.26656203485616814107448737714004 absolute error = 5.2e-31 relative error = 1.9507654204417452648489325310879e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1388.8MB, alloc=52.3MB, time=14.45 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = -0.2841361678749585126122508868566 y[1] (numeric) = -0.28413616787495851261225088685712 absolute error = 5.2e-31 relative error = 1.8301084437403952103914408569472e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = -0.30166849039744811369079964923578 y[1] (numeric) = -0.30166849039744811369079964923632 absolute error = 5.4e-31 relative error = 1.7900444268758404933689582508907e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = -0.31915336034546428989310136403671 y[1] (numeric) = -0.31915336034546428989310136403724 absolute error = 5.3e-31 relative error = 1.6606436461339680773620494356202e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = -0.33658513814911045351378750848643 y[1] (numeric) = -0.33658513814911045351378750848697 absolute error = 5.4e-31 relative error = 1.6043489114506737555929719011870e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = -0.353958188697841947008942193459 y[1] (numeric) = -0.35395818869784194700894219345955 absolute error = 5.5e-31 relative error = 1.5538558438875673432091280695501e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = -0.37126688329353293388917932265824 y[1] (numeric) = -0.3712668832935329338891793226588 absolute error = 5.6e-31 relative error = 1.5083489134075282392449006729699e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = -0.38850560160482081806423589181609 y[1] (numeric) = -0.38850560160482081806423589181664 absolute error = 5.5e-31 relative error = 1.4156810036408372327686218219440e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = -0.40566873362201331712681370561011 y[1] (numeric) = -0.40566873362201331712681370561067 absolute error = 5.6e-31 relative error = 1.3804366804413048055029093980339e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = -0.42275068161184221044509204633104 y[1] (numeric) = -0.4227506816118422104450920463316 absolute error = 5.6e-31 relative error = 1.3246578287345642998116140509216e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = -0.43974586207134694985694073860979 y[1] (numeric) = -0.43974586207134694985694073861035 absolute error = 5.6e-31 relative error = 1.2734628072728568687357528636518e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = -0.45664870768017075975884329089646 y[1] (numeric) = -0.45664870768017075975884329089703 absolute error = 5.7e-31 relative error = 1.2482242704587234265675084800115e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1429.4MB, alloc=52.3MB, time=14.87 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = -0.47345366925055156488781680979613 y[1] (numeric) = -0.47345366925055156488781680979669 absolute error = 5.6e-31 relative error = 1.1827978878829812981022954947760e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = -0.49015521767429006842836182924094 y[1] (numeric) = -0.4901552176742900684283618292415 absolute error = 5.6e-31 relative error = 1.1424952337692384709284099018230e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = -0.50674784586597756045593690870319 y[1] (numeric) = -0.50674784586597756045593690870376 absolute error = 5.7e-31 relative error = 1.1248197790084954615280841067326e-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] = 4.01 y[1] (closed_form) = -0.52322607070176656726481448861717 y[1] (numeric) = -0.52322607070176656726481448861774 absolute error = 5.7e-31 relative error = 1.0893952574563014984714398823734e-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] = 4.02 y[1] (closed_form) = -0.53958443495296825582646687037358 y[1] (numeric) = -0.53958443495296825582646687037414 absolute error = 5.6e-31 relative error = 1.0378357189803134777770914108731e-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] = 4.03 y[1] (closed_form) = -0.55581750921376158438368041430869 y[1] (numeric) = -0.55581750921376158438368041430924 absolute error = 5.5e-31 relative error = 9.8953341858195361140255473707693e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (closed_form) = -0.57191989382230053979801440463609 y[1] (numeric) = -0.57191989382230053979801440463663 absolute error = 5.4e-31 relative error = 9.4418817361121858226497048971840e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = -0.58788622077450742442043968925099 y[1] (numeric) = -0.58788622077450742442043968925154 absolute error = 5.5e-31 relative error = 9.3555518153734844464344030133260e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = -0.60371115562984204952733574637586 y[1] (numeric) = -0.60371115562984204952733574637642 absolute error = 5.6e-31 relative error = 9.2759591201484605604710278881989e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = -0.61938939940833885823082755199218 y[1] (numeric) = -0.61938939940833885823082755199274 absolute error = 5.6e-31 relative error = 9.0411621596193030204917839760883e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = -0.63491569047820643760220758229074 y[1] (numeric) = -0.63491569047820643760220758229131 absolute error = 5.7e-31 relative error = 8.9775699127971908737623005924102e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1470.1MB, alloc=52.3MB, time=15.30 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = -0.65028480643328658680278306910537 y[1] (numeric) = -0.65028480643328658680278306910594 absolute error = 5.7e-31 relative error = 8.7653900930941850186305777471683e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = -0.66549156595967308445539273367973 y[1] (numeric) = -0.6654915659596730844553927336803 absolute error = 5.7e-31 relative error = 8.5650972777999172337417464183490e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = -0.68053083069079354336442100927318 y[1] (numeric) = -0.68053083069079354336442100927375 absolute error = 5.7e-31 relative error = 8.3758145008860824459191712062414e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = -0.69539750705026125294998782041297 y[1] (numeric) = -0.69539750705026125294998782041355 absolute error = 5.8e-31 relative error = 8.3405533399198587274190820938163e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = -0.71008654808180768824627686708177 y[1] (numeric) = -0.71008654808180768824627686708237 absolute error = 6.0e-31 relative error = 8.4496742209919341910227110825043e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = -0.72459295526561040776384248609372 y[1] (numeric) = -0.7245929552656104077638424860943 absolute error = 5.8e-31 relative error = 8.0044940512482943904756692436543e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = -0.73891178032033536956679877753888 y[1] (numeric) = -0.73891178032033536956679877753946 absolute error = 5.8e-31 relative error = 7.8493808793866646369220271504927e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = -0.75303812699021726410056470563108 y[1] (numeric) = -0.75303812699021726410056470563166 absolute error = 5.8e-31 relative error = 7.7021332547685834976236987134040e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = -0.76696715281650629205429042562014 y[1] (numeric) = -0.76696715281650629205429042562072 absolute error = 5.8e-31 relative error = 7.5622534533595937798684306385303e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = -0.78069407089261490418222350033283 y[1] (numeric) = -0.78069407089261490418222350033341 absolute error = 5.8e-31 relative error = 7.4292866005354799901589435291407e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for 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=1510.7MB, alloc=52.3MB, time=15.72 x[1] = 4.19 y[1] (closed_form) = -0.79421415160230336576672484946596 y[1] (numeric) = -0.79421415160230336576672484946655 absolute error = 5.9e-31 relative error = 7.4287268592443561350186184982015e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = -0.80752272434024860940833503710436 y[1] (numeric) = -0.80752272434024860940833503710495 absolute error = 5.9e-31 relative error = 7.3062959371457179791517562355279e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = -0.82061517921434669410111975303078 y[1] (numeric) = -0.82061517921434669410111975303139 absolute error = 6.1e-31 relative error = 7.4334476798736683666016375921929e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = -0.8334869687291052940210927911854 y[1] (numeric) = -0.83348696872910529402109279118598 absolute error = 5.8e-31 relative error = 6.9587170736979807727141755326762e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = -0.84613360944948899494990396823931 y[1] (numeric) = -0.84613360944948899494990396823989 absolute error = 5.8e-31 relative error = 6.8547093924960538525225771427790e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = -0.85855068364458677750554948413913 y[1] (numeric) = -0.85855068364458677750554948413971 absolute error = 5.8e-31 relative error = 6.7555708829893835566648238902304e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = -0.8707338409104779119901037751612 y[1] (numeric) = -0.87073384091047791199010377516177 absolute error = 5.7e-31 relative error = 6.5462024469381220610965005378302e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = -0.882678799771679577228889807363 y[1] (numeric) = -0.88267879977167957722888980736358 absolute error = 5.8e-31 relative error = 6.5709066553997583102147400537220e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = -0.89438134926056684270854109247392 y[1] (numeric) = -0.89438134926056684270854109247449 absolute error = 5.7e-31 relative error = 6.3731203750083748064413118482382e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = -0.90583735047416321697140337785873 y[1] (numeric) = -0.90583735047416321697140337785928 absolute error = 5.5e-31 relative error = 6.0717302031330557017769225388730e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -0.9170427381077077628459125277285 y[1] (numeric) = -0.91704273810770776284591252772905 absolute error = 5.5e-31 relative error = 5.9975394509410731990977659917416e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1551.5MB, alloc=52.3MB, time=16.13 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = -0.92799352196441280885013353321729 y[1] (numeric) = -0.92799352196441280885013353321785 absolute error = 5.6e-31 relative error = 6.0345248834773135307801564845254e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = -0.93868578844083454307072144371348 y[1] (numeric) = -0.93868578844083454307072144371403 absolute error = 5.5e-31 relative error = 5.8592556398830209169605760374774e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = -0.9491157019872872579744447941618 y[1] (numeric) = -0.94911570198728725797444479416236 absolute error = 5.6e-31 relative error = 5.9002290113571507315691634126851e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = -0.95927950654274071884762415603906 y[1] (numeric) = -0.9592795065427407188476241560396 absolute error = 5.4e-31 relative error = 5.6292248121318568843778405012252e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = -0.96917352694364905168634109241212 y[1] (numeric) = -0.96917352694364905168634109241265 absolute error = 5.3e-31 relative error = 5.4685769396878702573946989186261e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = -0.97879417030616868509666724427228 y[1] (numeric) = -0.97879417030616868509666724427282 absolute error = 5.4e-31 relative error = 5.5169924012837854263176073597771e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = -0.98813792738123223174394072788978 y[1] (numeric) = -0.98813792738123223174394072789032 absolute error = 5.4e-31 relative error = 5.4648241408070483835521936758043e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = -0.99720137388195475466393965074554 y[1] (numeric) = -0.99720137388195475466393965074607 absolute error = 5.3e-31 relative error = 5.3148743461592900353571983047264e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0059811717828586287848177152338 y[1] (numeric) = -1.0059811717828586287848177152344 absolute error = 6e-31 relative error = 5.9643263395938607087113951137822e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0144740705904131746938541334906 y[1] (numeric) = -1.0144740705904131746938541334913 absolute error = 7e-31 relative error = 6.9001270736531236019205950010247e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0226769085843954063246204491226 y[1] (numeric) = -1.0226769085843954063246204491233 absolute error = 7e-31 relative error = 6.8447815152974404748801671517547e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1592.2MB, alloc=52.3MB, time=16.55 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = -1.0305866140295885930668938309 y[1] (numeric) = -1.0305866140295885930668938309008 absolute error = 8e-31 relative error = 7.7625692892711262171955489636524e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0382002063573458859654280564071 y[1] (numeric) = -1.0382002063573458859654280564078 absolute error = 7e-31 relative error = 6.7424374962902075356760748358399e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = -1.0455147973165569932509451979721 y[1] (numeric) = -1.0455147973165569932509451979729 absolute error = 8e-31 relative error = 7.6517329267199175102237103255748e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.052527592093566808439888583812 y[1] (numeric) = -1.0525275920935668084398885838128 absolute error = 8e-31 relative error = 7.6007508592599651300659719799542e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0592358904006059905786089697287 y[1] (numeric) = -1.0592358904006059905786089697295 absolute error = 8e-31 relative error = 7.5526141745200660800478974016445e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0656370875323047667519025597874 y[1] (numeric) = -1.0656370875323047667519025597882 absolute error = 8e-31 relative error = 7.5072462225630638646770996977985e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0717286753898726675150659333886 y[1] (numeric) = -1.0717286753898726675150659333895 absolute error = 9e-31 relative error = 8.3976478437753721895097693179062e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0775082434725385121651032346882 y[1] (numeric) = -1.0775082434725385121651032346891 absolute error = 9e-31 relative error = 8.3526043114020732238484023320874e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0829734798358567283966230505058 y[1] (numeric) = -1.0829734798358567283966230505068 absolute error = 1.0e-30 relative error = 9.2338364569330655497598409158714e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0881221720164980154831581503182 y[1] (numeric) = -1.0881221720164980154831581503192 absolute error = 1.0e-30 relative error = 9.1901445050679298663008297719176e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0929522079231544372143425832313 y[1] (numeric) = -1.0929522079231544372143425832322 absolute error = 9e-31 relative error = 8.2345778111395615261882581760558e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1633.0MB, alloc=52.3MB, time=17.00 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = -1.0974615766932012558718704159256 y[1] (numeric) = -1.0974615766932012558718704159265 absolute error = 9e-31 relative error = 8.2007426876102629672991009775842e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1016483695147701869515379059796 y[1] (numeric) = -1.1016483695147701869515379059807 absolute error = 1.1e-30 relative error = 9.9850372445474936394211806640421e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1055107804139012614866207847431 y[1] (numeric) = -1.1055107804139012614866207847441 absolute error = 1.0e-30 relative error = 9.0455924783076451433016123270970e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1090471070064531239954226309183 y[1] (numeric) = -1.1090471070064531239954226309192 absolute error = 9e-31 relative error = 8.1150745925417507242298088415960e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1122557512144643645053028118582 y[1] (numeric) = -1.112255751214464364505302811859 absolute error = 8e-31 relative error = 7.1925903653587363452943610283952e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.115135219946671377987134481789 y[1] (numeric) = -1.1151352199466713779871344817899 absolute error = 9e-31 relative error = 8.0707701084272121263150924869944e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = -1.117684125742901259008120259009 y[1] (numeric) = -1.1176841257429012590081202590099 absolute error = 9e-31 relative error = 8.0523645211636948491463736822160e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1199011873820713685691321709769 y[1] (numeric) = -1.1199011873820713685691321709776 absolute error = 7e-31 relative error = 6.2505514583509797190669967861206e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1217852304535404489808272975864 y[1] (numeric) = -1.121785230453540448980827297587 absolute error = 6e-31 relative error = 5.3486173976227032905893537809204e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1233351878915695062518774867097 y[1] (numeric) = -1.1233351878915695062518774867104 absolute error = 7e-31 relative error = 6.2314437181822515107807144834472e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1245501004726641227714017293584 y[1] (numeric) = -1.124550100472664122771401729359 absolute error = 6e-31 relative error = 5.3354670436453797391860375111951e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1673.7MB, alloc=52.3MB, time=17.42 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = -1.1254291172755834009842192558868 y[1] (numeric) = -1.1254291172755834009842192558873 absolute error = 5e-31 relative error = 4.4427498127149058796654743847722e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1259714961038143661613872187085 y[1] (numeric) = -1.1259714961038143661613872187091 absolute error = 6e-31 relative error = 5.3287316959281188558108298433886e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1261766038703243681025889583952 y[1] (numeric) = -1.1261766038703243681025889583957 absolute error = 5e-31 relative error = 4.4398009893088970606846152440510e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1260439169444178124796369039295 y[1] (numeric) = -1.1260439169444178124796369039301 absolute error = 6e-31 relative error = 5.3283889817382349178521526046832e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1255730214605374173173980320334 y[1] (numeric) = -1.1255730214605374173173980320339 absolute error = 5e-31 relative error = 4.4421818084374723678526032348528e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.124763613588864123555023655918 y[1] (numeric) = -1.1247636135888641235550236559185 absolute error = 5e-31 relative error = 4.4453785129536156839554825876019e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1236154997675837854531239367023 y[1] (numeric) = -1.1236154997675837854531239367029 absolute error = 6e-31 relative error = 5.3399049774954871136162882494136e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1221285968967028215016444255665 y[1] (numeric) = -1.122128596896702821501644425567 absolute error = 5e-31 relative error = 4.4558172867421124582788423617761e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1203029324933091141044282740815 y[1] (numeric) = -1.1203029324933091141044282740821 absolute error = 6e-31 relative error = 5.3556942733753259538796407030680e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1181386448081886013131811627087 y[1] (numeric) = -1.1181386448081886013131811627094 absolute error = 7e-31 relative error = 6.2604043179285847047768230128544e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = -1.1156359829037222008789188704167 y[1] (numeric) = -1.1156359829037222008789188704174 absolute error = 7e-31 relative error = 6.2744480343675774461359444776791e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1714.3MB, alloc=52.3MB, time=17.84 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = -1.1127953066930019404879033983701 y[1] (numeric) = -1.112795306693001940487903398371 absolute error = 9e-31 relative error = 8.0877407964148798574473021673716e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1096170869401194328404017624948 y[1] (numeric) = -1.1096170869401194328404017624958 absolute error = 1.0e-30 relative error = 9.0121178897632194902818608183697e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1061019052215941247891774397596 y[1] (numeric) = -1.1061019052215941247891774397604 absolute error = 8e-31 relative error = 7.2326066542641899332990896213677e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.1022504538489230606434066711344 y[1] (numeric) = -1.1022504538489230606434066711352 absolute error = 8e-31 relative error = 7.2578786173913411586012801805788e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0980635357522482255158842659755 y[1] (numeric) = -1.0980635357522482255158842659763 absolute error = 8e-31 relative error = 7.2855529206872858622984154640050e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0935420643251518697924715408527 y[1] (numeric) = -1.0935420643251518697924715408535 absolute error = 8e-31 relative error = 7.3156765166934576206665673475218e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0886870632306045549727290292241 y[1] (numeric) = -1.0886870632306045549727290292249 absolute error = 8e-31 relative error = 7.3483007837537317810092455824262e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.083499666168104998806138543072 y[1] (numeric) = -1.0834996661681049988061385430728 absolute error = 8e-31 relative error = 7.3834817395862490381069557914130e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0779811166020651283645305272012 y[1] (numeric) = -1.077981116602065128364530527202 absolute error = 8e-31 relative error = 7.4212802773549754253627556190697e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0721327674515080679844034743753 y[1] (numeric) = -1.0721327674515080679844034743762 absolute error = 9e-31 relative error = 8.3944827294041870479631311183112e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0659560807411610894218202353113 y[1] (numeric) = -1.0659560807411610894218202353122 absolute error = 9e-31 relative error = 8.4431245926589063395377066280266e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO 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=1755.0MB, alloc=52.3MB, time=18.26 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = -1.0594526272140398286316412572522 y[1] (numeric) = -1.0594526272140398286316412572532 absolute error = 1.0e-30 relative error = 9.4388363794011462476376279129940e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -1.0526240859056343218633619796739 y[1] (numeric) = -1.052624085905634321863361979675 absolute error = 1.1e-30 relative error = 1.0450074387701335912784489430267e-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] = 4.87 y[1] (closed_form) = -1.0454722436798216278184410709907 y[1] (numeric) = -1.0454722436798216278184410709919 absolute error = 1.2e-30 relative error = 1.1478066560392614944541839606761e-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] = 4.88 y[1] (closed_form) = -1.0379989947266439770108607762211 y[1] (numeric) = -1.0379989947266439770108607762222 absolute error = 1.1e-30 relative error = 1.0597312768011725553391033747700e-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] = 4.89 y[1] (closed_form) = -1.0302063400221055187994289675813 y[1] (numeric) = -1.0302063400221055187994289675824 absolute error = 1.1e-30 relative error = 1.0677472631127438924538383365686e-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] = 4.9 y[1] (closed_form) = -1.0220963867501548154183571143669 y[1] (numeric) = -1.0220963867501548154183571143681 absolute error = 1.2e-30 relative error = 1.1740575698692227450887672940398e-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) = -1.0136713476870342553410383360679 y[1] (numeric) = -1.013671347687034255341038336069 absolute error = 1.1e-30 relative error = 1.0851643409966632163873414569641e-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) = -1.004933540548191520109676379765 y[1] (numeric) = -1.0049335405481915201096763797662 absolute error = 1.2e-30 relative error = 1.1941088157386006572373841269945e-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) = -0.9958853872979621340114021050571 y[1] (numeric) = -0.99588538729796213401140210505813 absolute error = 1.03e-30 relative error = 1.0342555610687266826125265621784e-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) = -0.98652941342224594936471246539754 y[1] (numeric) = -0.98652941342224594936471246539859 absolute error = 1.05e-30 relative error = 1.0643372470341012616943245827112e-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] = 4.95 y[1] (closed_form) = -0.97686824716441416640953420837224 y[1] (numeric) = -0.97686824716441416640953420837327 absolute error = 1.03e-30 relative error = 1.0543898862408651571034886475320e-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=1795.7MB, alloc=52.3MB, time=18.69 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = -0.96690461872469715060917076736961 y[1] (numeric) = -0.96690461872469715060917076737064 absolute error = 1.03e-30 relative error = 1.0652550210780074292215820916990e-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) = -0.95664135942331688634227109398597 y[1] (numeric) = -0.95664135942331688634227109398702 absolute error = 1.05e-30 relative error = 1.0975900107778756554441735213595e-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] = 4.98 y[1] (closed_form) = -0.94608140082764138928945264957129 y[1] (numeric) = -0.94608140082764138928945264957236 absolute error = 1.07e-30 relative error = 1.1309809061503094676355690002219e-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) = -0.93522777384365178513828781660911 y[1] (numeric) = -0.93522777384365178513828781661016 absolute error = 1.05e-30 relative error = 1.1227211481163041756451045197737e-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 Finished! diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; Iterations = 4900 Total Elapsed Time = 18 Seconds Elapsed Time(since restart) = 18 Seconds Time to Timeout = 2 Minutes 41 Seconds Percent Done = 100 % > quit memory used=1811.7MB, alloc=52.3MB, time=18.84