|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 7 # Begin Function number 8 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 8 # Begin Function number 9 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 9 # Begin Function number 10 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 10 # Begin Function number 11 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 11 # Begin Function number 12 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 12 # Begin Function number 13 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 16 # Begin Function number 17 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 17 # Begin Function number 18 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 6 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 7 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 8 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 9 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 10 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 11 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 12 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 12 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 20 # Begin Function number 21 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 21 # Begin Function number 22 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 22 # Begin Function number 23 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 23 # Begin Function number 24 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 24 # Begin Function number 25 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 25 # Begin Function number 26 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 26 # Begin Function number 27 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := sqrt(rcs)*float_abs(glob_h) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 30 # Begin Function number 31 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 31 # Begin Function number 32 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 32 # Begin Function number 33 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 33 # Begin Function number 34 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 34 # Begin Function number 35 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 35 # Begin Function number 36 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 36 # Begin Function number 37 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 37 # Begin Function number 38 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 38 # Begin Function number 39 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 39 # Begin Function number 40 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 40 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(-0.05) * c(x) * c(x) - c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)); > end; exact_soln_y := proc(x) return c(-0.05)*c(x)*c(x) - c(0.2)*c(x) - cos(c(0.3)*c(x) + c(0.1))/c(0.3) 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_0D3, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > 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_0D3, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, 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_0D3, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > 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_0D3, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, 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_0D3, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > 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_0D3, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, 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_0D3, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > 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_0D3, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, 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_0D3, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > 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)*29*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_0D3, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, 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)*29*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_0D3, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > 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_0D3, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, 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_0D3, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > 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_0D3, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, 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_0D3, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > 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_0D3[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D1[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_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp6[1] := array_tmp5[1] + array_const_0D2[1]; > #emit pre sub FULL - LINEAR $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp4[1] - array_tmp6[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_tmp7[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_0D3[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_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp6[2] := array_tmp5[2]; > #emit pre sub FULL - LINEAR $eq_no = 1 i = 2 > array_tmp7[2] := array_tmp4[2] - array_tmp6[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_tmp7[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 sub FULL - LINEAR $eq_no = 1 i = 3 > array_tmp7[3] := array_tmp4[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_tmp7[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 sub FULL - LINEAR $eq_no = 1 i = 4 > array_tmp7[4] := array_tmp4[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_tmp7[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 sub FULL - LINEAR $eq_no = 1 i = 5 > array_tmp7[5] := array_tmp4[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_tmp7[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 FULL - NOT FULL sub $eq_no = 1 > array_tmp7[kkk] := array_tmp4[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_tmp7[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_0D3, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, 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_0D3[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D1[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_0D1[1]*array_x[1]; array_tmp6[1] := array_tmp5[1] + array_const_0D2[1]; array_tmp7[1] := array_tmp4[1] - array_tmp6[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp7[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_0D3[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_0D1[1]*array_x[2]; array_tmp6[2] := array_tmp5[2]; array_tmp7[2] := array_tmp4[2] - array_tmp6[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp7[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] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp7[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] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp7[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] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp7[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] := array_tmp4[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_tmp7[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_0D3, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > 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 := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=40; > #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..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > 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..(40),[]); > array_x:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3_g:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_tmp4:= Array(0..(40),[]); > array_tmp5:= Array(0..(40),[]); > array_tmp6:= Array(0..(40),[]); > array_tmp7:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..40+ 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..(40) ,(0..40+ 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 <= 40) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) 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 <= 40) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp6[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp7[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <=40) do # do number 1 > term := 1; > while (term <= 40) 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); > 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_0D3); > array_const_0D3[1] := c(0.3); > zero_ats_ar(array_const_0D1); > array_const_0D1[1] := c(0.1); > zero_ats_ar(array_const_0D2); > array_const_0D2[1] := c(0.2); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > array_y_set_initial[1,31] := false; > array_y_set_initial[1,32] := false; > array_y_set_initial[1,33] := false; > array_y_set_initial[1,34] := false; > array_y_set_initial[1,35] := false; > array_y_set_initial[1,36] := false; > array_y_set_initial[1,37] := false; > array_y_set_initial[1,38] := false; > array_y_set_initial[1,39] := false; > array_y_set_initial[1,40] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 40; > 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/sub_full_linpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=40;"); > 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,""); > 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:=false;"); > 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,""); > omniout_str(ALWAYS,"return(c(-0.05) * c(x) * c(x) - c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3));"); > 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:=false; > 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 ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2016-08-26T17:01:48-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sub_full_lin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 308.maple.seems.ok ") > ; > logitem_str(html_log_file,"sub_full_lin diffeq.mxt") > ; > logitem_str(html_log_file,"sub_full_lin 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_0D3, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, 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 := 40; Digits := 32; max_terms := 40; glob_html_log := true; array_y_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); 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 .. 40, []); array_x := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3_g := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_tmp4 := Array(0 .. 40, []); array_tmp5 := Array(0 .. 40, []); array_tmp6 := Array(0 .. 40, []); array_tmp7 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y_higher := Array(0 .. 2, 0 .. 41, []); array_y_higher_work := Array(0 .. 2, 0 .. 41, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y_set_initial := Array(0 .. 2, 0 .. 41, []); 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 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 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 <= 40 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp6[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp7[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 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 <= 40 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 <= 40 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 <= 40 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 <= 40 do term := 1; while term <= 40 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); 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_0D3); array_const_0D3[1] := c(0.3); zero_ats_ar(array_const_0D1); array_const_0D1[1] := c(0.1); zero_ats_ar(array_const_0D2); array_const_0D2[1] := c(0.2); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; array_y_set_initial[1, 31] := false; array_y_set_initial[1, 32] := false; array_y_set_initial[1, 33] := false; array_y_set_initial[1, 34] := false; array_y_set_initial[1, 35] := false; array_y_set_initial[1, 36] := false; array_y_set_initial[1, 37] := false; array_y_set_initial[1, 38] := false; array_y_set_initial[1, 39] := false; array_y_set_initial[1, 40] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 40; 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/sub_full_linpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( 0.3 * x \ + 0.1 ) - ( 0.1 * x + 0.2 ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=40;"); 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, ""); 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:=false;"); 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, ""); omniout_str(ALWAYS, "return(c(-0.05) * c(x) * c(x) - c(0.2) * c(x) - \ cos(c(0.3) * c(x) + c(0.1)) / c(0.3));"); 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 := false; 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 ( 0.3 * \ x + 0.1 ) - ( 0.1 * x + 0.2 ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2016-08-26T17:01:48-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sub_full_lin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = s\ in ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ;\ "); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 308.maple.seems.ok "); logitem_str(html_log_file, "sub_full_lin diffeq.mxt"); logitem_str(html_log_file, "sub_full_lin 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/sub_full_linpostode.ode################# diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #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:=false; 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(-0.05) * c(x) * c(x) - c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)); 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) = -3.3257063123826267986483739038394 y[1] (numeric) = -3.3257063123826267986483739038394 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 memory used=4.0MB, alloc=40.3MB, time=0.09 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = -3.3265000994836904604552861567236 y[1] (numeric) = -3.3265000994836904604552861567236 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = -3.3272741515511600542791827214267 y[1] (numeric) = -3.3272741515511600542791827214267 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = -3.328028480653557921497890021765 y[1] (numeric) = -3.3280284806535579214978900217649 absolute error = 1e-31 relative error = 3.0047819777179914446189806112699e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = -3.328763099126912888504819883098 y[1] (numeric) = -3.328763099126912888504819883098 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = -3.3294780195746492425328001612199 y[1] (numeric) = -3.3294780195746492425328001612199 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (closed_form) = -3.330173254867473300920562735326 y[1] (numeric) = -3.3301732548674733009205627353261 absolute error = 1e-31 relative error = 3.0028467694236999600770245876212e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (closed_form) = -3.330848818143257574842764701004 y[1] (numeric) = -3.3308488181432575748427647010043 absolute error = 3e-31 relative error = 9.0067131947234838775620419486395e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (closed_form) = -3.3315047228069225285460684111671 y[1] (numeric) = -3.3315047228069225285460684111674 absolute error = 3e-31 relative error = 9.0049399583992878637027243414734e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=31.0MB, alloc=40.3MB, time=0.42 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (closed_form) = -3.3321409825303159351554464420811 y[1] (numeric) = -3.3321409825303159351554464420814 absolute error = 3e-31 relative error = 9.0032204991575739701335859785753e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = -3.3327576112520898301365084133945 y[1] (numeric) = -3.3327576112520898301365084133948 absolute error = 3e-31 relative error = 9.0015547181450273192814964049539e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = -3.3333546231775750635212676706652 y[1] (numeric) = -3.3333546231775750635212676706655 absolute error = 3e-31 relative error = 8.9999425177876835325588742208404e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = -3.333932032778653452026376951713 y[1] (numeric) = -3.3339320327786534520263769517132 absolute error = 2e-31 relative error = 5.9989225345218190279098536687192e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = -3.3344898547936275322144631097015 y[1] (numeric) = -3.3344898547936275322144631097018 absolute error = 3e-31 relative error = 8.9968784750903697121222693254074e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = -3.3350281042270879158707815617738 y[1] (numeric) = -3.3350281042270879158707815617741 absolute error = 3e-31 relative error = 8.9954264439257772912848530923519e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = -3.3355467963497782487889911779985 y[1] (numeric) = -3.3355467963497782487889911779989 absolute error = 4e-31 relative error = 1.1992036821001460283915923318513e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (closed_form) = -3.3360459466984577741814196271259 y[1] (numeric) = -3.3360459466984577741814196271266 absolute error = 7e-31 relative error = 2.0982924431624213998661402716664e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (closed_form) = -3.336525571075761501950747559069 y[1] (numeric) = -3.3365255710757615019507475590696 absolute error = 6e-31 relative error = 1.7982778408814897615091800849879e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (closed_form) = -3.3369856855500579850815872350936 y[1] (numeric) = -3.3369856855500579850815872350944 absolute error = 8e-31 relative error = 2.3973731846204505778630713292160e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (closed_form) = -3.3374263064553047044319671215027 y[1] (numeric) = -3.3374263064553047044319671215035 absolute error = 8e-31 relative error = 2.3970566734391314586207740875616e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = -3.3378474503909010632262583472997 y[1] (numeric) = -3.3378474503909010632262583473004 absolute error = 7e-31 relative error = 2.0971599523460000980189850417057e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=71.5MB, alloc=44.3MB, time=0.90 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (closed_form) = -3.3382491342215389925725915972059 y[1] (numeric) = -3.3382491342215389925725915972065 absolute error = 6e-31 relative error = 1.7973493765015733034348375910385e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (closed_form) = -3.3386313750770511693493137748686 y[1] (numeric) = -3.3386313750770511693493137748692 absolute error = 6e-31 relative error = 1.7971435974603599309693322528451e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (closed_form) = -3.3389941903522568478265224336202 y[1] (numeric) = -3.3389941903522568478265224336207 absolute error = 5e-31 relative error = 1.4974569331228787016793710372934e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (closed_form) = -3.3393375977068053064101923403414 y[1] (numeric) = -3.3393375977068053064101923403419 absolute error = 5e-31 relative error = 1.4973029391917747863681109665927e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (closed_form) = -3.3396616150650169109178724185576 y[1] (numeric) = -3.3396616150650169109178724185581 absolute error = 5e-31 relative error = 1.4971576693414968729346594019007e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (closed_form) = -3.3399662606157217958163825166702 y[1] (numeric) = -3.3399662606157217958163825166708 absolute error = 6e-31 relative error = 1.7964253324205442028243664337701e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (closed_form) = -3.3402515528120961648733777731541 y[1] (numeric) = -3.3402515528120961648733777731548 absolute error = 7e-31 relative error = 2.0956505488656472979168661930487e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (closed_form) = -3.3405175103714962126960736096685 y[1] (numeric) = -3.3405175103714962126960736096691 absolute error = 6e-31 relative error = 1.7961288876263800577212924769385e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (closed_form) = -3.3407641522752896686518363825296 y[1] (numeric) = -3.3407641522752896686518363825303 absolute error = 7e-31 relative error = 2.0953289968801058826532484123183e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = -3.340991497768684964686743270149 y[1] (numeric) = -3.3409914977686849646867432701498 absolute error = 8e-31 relative error = 2.3944987604257242456848137331339e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (closed_form) = -3.3411995663605580285795998762834 y[1] (numeric) = -3.3411995663605580285795998762841 absolute error = 7e-31 relative error = 2.0950559405300158477030396116140e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (closed_form) = -3.341388377823276704190275093791 y[1] (numeric) = -3.3413883778232767041902750937918 absolute error = 8e-31 relative error = 2.3942143490699342615127076249658e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=111.9MB, alloc=44.3MB, time=1.38 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (closed_form) = -3.3415579521925228002825698087188 y[1] (numeric) = -3.3415579521925228002825698087195 absolute error = 7e-31 relative error = 2.0948312434345287161713024964251e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (closed_form) = -3.3417083097671117695231788377313 y[1] (numeric) = -3.3417083097671117695231788377321 absolute error = 8e-31 relative error = 2.3939851292878195465682832821997e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (closed_form) = -3.3418394711088100192796338910574 y[1] (numeric) = -3.3418394711088100192796338910583 absolute error = 9e-31 relative error = 2.6931275657636041900849128902517e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (closed_form) = -3.3419514570421498558614291463175 y[1] (numeric) = -3.3419514570421498558614291463184 absolute error = 9e-31 relative error = 2.6930373213636085633529519743813e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (closed_form) = -3.3420442886542420638698300139739 y[1] (numeric) = -3.3420442886542420638698300139747 absolute error = 8e-31 relative error = 2.3937444596885939544785479446141e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (closed_form) = -3.3421179872945861223431496810361 y[1] (numeric) = -3.342117987294586122343149681037 absolute error = 9e-31 relative error = 2.6929031333467127257652002713092e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (closed_form) = -3.3421725745748780594055468444938 y[1] (numeric) = -3.3421725745748780594055468444947 absolute error = 9e-31 relative error = 2.6928591505017641130661364943187e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = -3.342208072368815947148651498314 y[1] (numeric) = -3.3422080723688159471486514983148 absolute error = 8e-31 relative error = 2.3936271550950859332592964138675e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (closed_form) = -3.3422245028119030384965635264639 y[1] (numeric) = -3.3422245028119030384965635264648 absolute error = 9e-31 relative error = 2.6928173114726610434918053223394e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = -3.3422218883012485478259909881449 y[1] (numeric) = -3.3422218883012485478259909881458 absolute error = 9e-31 relative error = 2.6928194179753968689158681733645e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = -3.3422002514953660771345011692623 y[1] (numeric) = -3.3422002514953660771345011692631 absolute error = 8e-31 relative error = 2.3936327562720524526179475256419e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = -3.3421596153139696895710475252506 y[1] (numeric) = -3.3421596153139696895710475252513 absolute error = 7e-31 relative error = 2.0944541271833915352565922461580e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = -3.3421000029377676321641093640055 y[1] (numeric) = -3.3421000029377676321641093640061 absolute error = 6e-31 relative error = 1.7952784161832049245127714884805e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=152.4MB, alloc=44.3MB, time=1.86 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (closed_form) = -3.3420214378082537096039383232972 y[1] (numeric) = -3.3420214378082537096039383232978 absolute error = 6e-31 relative error = 1.7953206200660661557878448998954e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (closed_form) = -3.341923943627496310956546194218 y[1] (numeric) = -3.3419239436274963109565461942185 absolute error = 5e-31 relative error = 1.4961441625666509243266328312195e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (closed_form) = -3.3418075443579250912081922407056 y[1] (numeric) = -3.3418075443579250912081922407061 absolute error = 5e-31 relative error = 1.4961962751091550626310388699704e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (closed_form) = -3.3416722642221153095602346748574 y[1] (numeric) = -3.3416722642221153095602346748579 absolute error = 5e-31 relative error = 1.4962568452726213990058276826591e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = -3.3415181277025698264153001786549 y[1] (numeric) = -3.3415181277025698264153001786556 absolute error = 7e-31 relative error = 2.0948562098068837548792875450240e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (closed_form) = -3.3413451595414987610167971250549 y[1] (numeric) = -3.3413451595414987610167971250555 absolute error = 6e-31 relative error = 1.7956839875899930473307672613218e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (closed_form) = -3.3411533847405968117248522555154 y[1] (numeric) = -3.3411533847405968117248522555159 absolute error = 5e-31 relative error = 1.4964892132266457060995897063174e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (closed_form) = -3.340942828560818240932786827441 y[1] (numeric) = -3.3409428285608182409327868274415 absolute error = 5e-31 relative error = 1.4965835264394080374527331834264e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (closed_form) = -3.3407135165221495266492664644088 y[1] (numeric) = -3.3407135165221495266492664644093 absolute error = 5e-31 relative error = 1.4966862543799478496596254120956e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (closed_form) = -3.3404654744033796827922589352268 y[1] (numeric) = -3.3404654744033796827922589352274 absolute error = 6e-31 relative error = 1.7961568667527161554025244979507e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (closed_form) = -3.3401987282418682502619156658658 y[1] (numeric) = -3.3401987282418682502619156658665 absolute error = 7e-31 relative error = 2.0956836911570492198922278137600e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (closed_form) = -3.3399133043333109608804557622718 y[1] (numeric) = -3.3399133043333109608804557622725 absolute error = 7e-31 relative error = 2.0958627850962403188253487614697e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=193.0MB, alloc=44.3MB, time=2.35 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (closed_form) = -3.3396092292315030763080755033352 y[1] (numeric) = -3.3396092292315030763080755033359 absolute error = 7e-31 relative error = 2.0960536157132404247094982905480e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (closed_form) = -3.3392865297481004040648314633692 y[1] (numeric) = -3.3392865297481004040648314633699 absolute error = 7e-31 relative error = 2.0962561725806877922661156534563e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = -3.3389452329523779928093514540074 y[1] (numeric) = -3.3389452329523779928093514540082 absolute error = 8e-31 relative error = 2.3959662234190652029542329913893e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (closed_form) = -3.3385853661709865090461141483171 y[1] (numeric) = -3.3385853661709865090461141483179 absolute error = 8e-31 relative error = 2.3962244850953671676768263845014e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (closed_form) = -3.3382069569877062974539053771537 y[1] (numeric) = -3.3382069569877062974539053771545 absolute error = 8e-31 relative error = 2.3964961139554241874338768468833e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (closed_form) = -3.3378100332431991270489064815571 y[1] (numeric) = -3.337810033243199127048906481558 absolute error = 9e-31 relative error = 2.6963787364660495180128854550467e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (closed_form) = -3.3373946230347576254166975776839 y[1] (numeric) = -3.3373946230347576254166975776847 absolute error = 8e-31 relative error = 2.3970794297994778099350220991751e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (closed_form) = -3.3369607547160524032682659549249 y[1] (numeric) = -3.3369607547160524032682659549257 absolute error = 8e-31 relative error = 2.3973910956830337191200368452047e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (closed_form) = -3.3365084568968768715958968962261 y[1] (numeric) = -3.336508456896876871595896896227 absolute error = 9e-31 relative error = 2.6974305973647851244913554480150e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (closed_form) = -3.3360377584428897537255907951102 y[1] (numeric) = -3.3360377584428897537255907951111 absolute error = 9e-31 relative error = 2.6978111915018580151806541504728e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (closed_form) = -3.3355486884753552945833963596028 y[1] (numeric) = -3.3355486884753552945833963596036 absolute error = 8e-31 relative error = 2.3984060036781285944733890117958e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (closed_form) = -3.3350412763708811695137747524766 y[1] (numeric) = -3.3350412763708811695137747524773 absolute error = 7e-31 relative error = 2.0989245469301197366390218527536e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=233.5MB, alloc=44.3MB, time=2.84 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (closed_form) = -3.3345155517611540950088135334219 y[1] (numeric) = -3.3345155517611540950088135334225 absolute error = 6e-31 relative error = 1.7993618283864492842250079970282e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (closed_form) = -3.3339715445326731437277920555908 y[1] (numeric) = -3.3339715445326731437277920555912 absolute error = 4e-31 relative error = 1.1997702879496786097843930442925e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (closed_form) = -3.333409284826480766207261340303 y[1] (numeric) = -3.3334092848264807662072613403034 absolute error = 4e-31 relative error = 1.1999726580854646945051710920889e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (closed_form) = -3.3328288030378915216824412235928 y[1] (numeric) = -3.3328288030378915216824412235933 absolute error = 5e-31 relative error = 1.5002270730025115284431067736426e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (closed_form) = -3.3322301298162185204613555509543 y[1] (numeric) = -3.3322301298162185204613555509548 absolute error = 5e-31 relative error = 1.5004966059399275302400420448337e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (closed_form) = -3.3316132960644975803137222065566 y[1] (numeric) = -3.3316132960644975803137222065571 absolute error = 5e-31 relative error = 1.5007744163784858666102673147963e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (closed_form) = -3.3309783329392090993571886149744 y[1] (numeric) = -3.330978332939209099357188614975 absolute error = 6e-31 relative error = 1.8012725993043861037972508299605e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (closed_form) = -3.3303252718499976479440548619566 y[1] (numeric) = -3.3303252718499976479440548619572 absolute error = 6e-31 relative error = 1.8016258203712925824322951016144e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (closed_form) = -3.3296541444593892820721555609705 y[1] (numeric) = -3.3296541444593892820721555609712 absolute error = 7e-31 relative error = 2.1023204502029555288537659585517e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (closed_form) = -3.3289649826825065808640778594523 y[1] (numeric) = -3.3289649826825065808640778594528 absolute error = 5e-31 relative error = 1.5019683373091416692880771584793e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (closed_form) = -3.3282578186867814106793763483029 y[1] (numeric) = -3.3282578186867814106793763483035 absolute error = 6e-31 relative error = 1.8027449575307835346822510128863e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (closed_form) = -3.3275326848916654184449059258564 y[1] (numeric) = -3.3275326848916654184449059258569 absolute error = 5e-31 relative error = 1.5026148421327332957995943479585e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=273.9MB, alloc=44.3MB, time=3.32 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (closed_form) = -3.3267896139683382568088306891525 y[1] (numeric) = -3.326789613968338256808830689153 absolute error = 5e-31 relative error = 1.5029504658203450889088449748795e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (closed_form) = -3.3260286388394135437442804969567 y[1] (numeric) = -3.3260286388394135437442804969572 absolute error = 5e-31 relative error = 1.5032943317483589200822810239893e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (closed_form) = -3.325249792678642559249016786844 y[1] (numeric) = -3.3252497926786425592490167868445 absolute error = 5e-31 relative error = 1.5036464361290189457080460211186e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (closed_form) = -3.3244531089106156818078353493093 y[1] (numeric) = -3.3244531089106156818078353493098 absolute error = 5e-31 relative error = 1.5040067753094106343033481616609e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (closed_form) = -3.3236386212104615673047758819753 y[1] (numeric) = -3.3236386212104615673047758819758 absolute error = 5e-31 relative error = 1.5043753457705974848564788981557e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (closed_form) = -3.3228063635035440730925260834705 y[1] (numeric) = -3.322806363503544073092526083471 absolute error = 5e-31 relative error = 1.5047521441267599307145360289852e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (closed_form) = -3.3219563699651569299467016165777 y[1] (numeric) = -3.321956369965156929946701616578 absolute error = 3e-31 relative error = 9.0308230027460178829873126721220e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (closed_form) = -3.3210886750202161646529522911714 y[1] (numeric) = -3.3210886750202161646529522911718 absolute error = 4e-31 relative error = 1.2044243293129326513531253786326e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = -3.3202033133429502759950891068393 y[1] (numeric) = -3.3202033133429502759950891068398 absolute error = 5e-31 relative error = 1.5059318746856332192168859945893e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = -3.3193003198565881669326461707355 y[1] (numeric) = -3.319300319856588166932646170736 absolute error = 5e-31 relative error = 1.5063415533958154179306135021300e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = -3.318379729733044835776485786148 y[1] (numeric) = -3.3183797297330448357764857861485 absolute error = 5e-31 relative error = 1.5067594450386295046153800121488e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = -3.3174415783926048291912240097545 y[1] (numeric) = -3.317441578392604829191224009755 absolute error = 5e-31 relative error = 1.5071855470089823766467115005241e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = -3.316485901503603459873397519041 y[1] (numeric) = -3.3164859015036034598733975190417 absolute error = 7e-31 relative error = 2.1106677995604903955531594275296e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=314.4MB, alloc=44.3MB, time=3.80 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = -3.3155127349821057917744105346046 y[1] (numeric) = -3.3155127349821057917744105346052 absolute error = 6e-31 relative error = 1.8096748465761458456666869725594e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (closed_form) = -3.3145221149915833957573926239669 y[1] (numeric) = -3.3145221149915833957573926239673 absolute error = 4e-31 relative error = 1.2068104725890951691971487693277e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = -3.3135140779425888785971642932799 y[1] (numeric) = -3.3135140779425888785971642932803 absolute error = 4e-31 relative error = 1.2071776083968415299518325843398e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = -3.3124886604924281882525471703067 y[1] (numeric) = -3.312488660492428188252547170307 absolute error = 3e-31 relative error = 9.0566347766878869089473567352603e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (closed_form) = -3.3114458995448306983602691159434 y[1] (numeric) = -3.3114458995448306983602691159438 absolute error = 4e-31 relative error = 1.2079315565897704573828486479016e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = -3.3103858322496170749197015922115 y[1] (numeric) = -3.3103858322496170749197015922119 absolute error = 4e-31 relative error = 1.2083183661046985485893633577647e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (closed_form) = -3.3093084960023649281576268821809 y[1] (numeric) = -3.3093084960023649281576268821813 absolute error = 4e-31 relative error = 1.2087117308138508110829642036024e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = -3.3082139284440722525821661220729 y[1] (numeric) = -3.3082139284440722525821661220732 absolute error = 3e-31 relative error = 9.0683373714316225429703589931062e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = -3.3071021674608186582549053884098 y[1] (numeric) = -3.3071021674608186582549053884102 absolute error = 4e-31 relative error = 1.2095181211384182441806007821519e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = -3.3059732511834243963301361043887 y[1] (numeric) = -3.3059732511834243963301361043892 absolute error = 5e-31 relative error = 1.5124139308175504617047195149913e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = -3.3048272179871071819299776107393 y[1] (numeric) = -3.3048272179871071819299776107396 absolute error = 3e-31 relative error = 9.0776303937221556244073409419697e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = -3.3036641064911368174439737085169 y[1] (numeric) = -3.3036641064911368174439737085171 absolute error = 2e-31 relative error = 6.0538842192532253069742542942394e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=354.9MB, alloc=44.3MB, time=4.27 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = -3.3024839555584876193615511461702 y[1] (numeric) = -3.3024839555584876193615511461704 absolute error = 2e-31 relative error = 6.0560475899776998004319131439784e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = -3.3012868042954886517654962126398 y[1] (numeric) = -3.30128680429548865176549621264 absolute error = 2e-31 relative error = 6.0582437048416644431567938965995e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (closed_form) = -3.3000726920514717696343456342736 y[1] (numeric) = -3.3000726920514717696343456342737 absolute error = 1e-31 relative error = 3.0302362805782789636284892124929e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = -3.2988416584184174751212996783347 y[1] (numeric) = -3.298841658418417475121299678335 absolute error = 3e-31 relative error = 9.0941012350326240250056149734363e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = -3.2975937432305985899969485624153 y[1] (numeric) = -3.2975937432305985899969485624157 absolute error = 4e-31 relative error = 1.2130056979308996088178440129798e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = -3.2963289865642217474627577800071 y[1] (numeric) = -3.2963289865642217474627577800075 absolute error = 4e-31 relative error = 1.2134711117439821004675153515651e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (closed_form) = -3.2950474287370667065618836009314 y[1] (numeric) = -3.295047428737066706561883600932 absolute error = 6e-31 relative error = 1.8209146088982681757893450051821e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = -3.2937491103081234924334866146632 y[1] (numeric) = -3.2937491103081234924334866146639 absolute error = 7e-31 relative error = 2.1252377657098370547652140461672e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (closed_form) = -3.2924340720772273656762785784231 y[1] (numeric) = -3.2924340720772273656762785784239 absolute error = 8e-31 relative error = 2.4298132703239598603107935578836e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (closed_form) = -3.2911023550846916241065758341615 y[1] (numeric) = -3.2911023550846916241065758341624 absolute error = 9e-31 relative error = 2.7346460331430191529538474963519e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (closed_form) = -3.2897540006109382402156409933645 y[1] (numeric) = -3.2897540006109382402156409933656 absolute error = 1.1e-30 relative error = 3.3437150613563192277089521832899e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (closed_form) = -3.2883890501761263376505732804125 y[1] (numeric) = -3.2883890501761263376505732804137 absolute error = 1.2e-30 relative error = 3.6492032472122722816893952660950e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=395.4MB, alloc=44.3MB, time=4.75 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (closed_form) = -3.287007545539778510062456698693 y[1] (numeric) = -3.2870075455397785100624566986941 absolute error = 1.1e-30 relative error = 3.3465088983218705733007580618726e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = -3.2856095287004049856848938637889 y[1] (numeric) = -3.2856095287004049856848938637899 absolute error = 1.0e-30 relative error = 3.0435752978703514056355085984826e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = -3.2841950418951256410254417600485 y[1] (numeric) = -3.2841950418951256410254417600496 absolute error = 1.1e-30 relative error = 3.3493747660164890814519231853643e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (closed_form) = -3.2827641275992898670718236462092 y[1] (numeric) = -3.2827641275992898670718236462104 absolute error = 1.2e-30 relative error = 3.6554560527550574845359666117275e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = -3.2813168285260942914341186882642 y[1] (numeric) = -3.2813168285260942914341186882655 absolute error = 1.3e-30 relative error = 3.9618240722702035196195241191542e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (closed_form) = -3.2798531876261983598634274594928 y[1] (numeric) = -3.2798531876261983598634274594941 absolute error = 1.3e-30 relative error = 3.9635920440112081037706677993404e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = -3.2783732480873377806067770448384 y[1] (numeric) = -3.2783732480873377806067770448397 absolute error = 1.3e-30 relative error = 3.9653813084231440133026381226972e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (closed_form) = -3.2768770533339358350772639462408 y[1] (numeric) = -3.2768770533339358350772639462421 absolute error = 1.3e-30 relative error = 3.9671918684814973039780080258301e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (closed_form) = -3.2753646470267125583376361339824 y[1] (numeric) = -3.2753646470267125583376361339836 absolute error = 1.2e-30 relative error = 3.6637142099256873429991972430618e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (closed_form) = -3.2738360730622917929146872537802 y[1] (numeric) = -3.2738360730622917929146872537817 absolute error = 1.5e-30 relative error = 4.5817810254528870068999466831805e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (closed_form) = -3.2722913755728061194809760076898 y[1] (numeric) = -3.2722913755728061194809760076912 absolute error = 1.4e-30 relative error = 4.2783476143072180744472948977689e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = -3.2707305989254996679594919066284 y[1] (numeric) = -3.2707305989254996679594919066297 absolute error = 1.3e-30 relative error = 3.9746471336620508166780007364504e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (closed_form) = -3.2691537877223288126259647715032 y[1] (numeric) = -3.2691537877223288126259647715045 absolute error = 1.3e-30 relative error = 3.9765642255261737812656745783350e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=435.9MB, alloc=44.3MB, time=5.23 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = -3.26756098679956075480255936685 y[1] (numeric) = -3.2675609867995607548025593668514 absolute error = 1.4e-30 relative error = 4.2845413005473584521955773864917e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = -3.2659522412273699967557082141659 y[1] (numeric) = -3.2659522412273699967557082141674 absolute error = 1.5e-30 relative error = 4.5928411967110959697601760115530e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (closed_form) = -3.2643275963094327104298147806401 y[1] (numeric) = -3.2643275963094327104298147806415 absolute error = 1.4e-30 relative error = 4.2887852358409280071602131051782e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = -3.2626870975825190046675057019428 y[1] (numeric) = -3.2626870975825190046675057019442 absolute error = 1.4e-30 relative error = 4.2909416628929172895936107093774e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (closed_form) = -3.2610307908160830945860243046089 y[1] (numeric) = -3.2610307908160830945860243046103 absolute error = 1.4e-30 relative error = 4.2931210706221073341212595088552e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = -3.2593587220118513767982382741164 y[1] (numeric) = -3.2593587220118513767982382741178 absolute error = 1.4e-30 relative error = 4.2953234651503617168114177820666e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (closed_form) = -3.2576709374034084141855816991013 y[1] (numeric) = -3.2576709374034084141855816991026 absolute error = 1.3e-30 relative error = 3.9905810776461999715435828255239e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (closed_form) = -3.255967483455780833949065740627 y[1] (numeric) = -3.2559674834557808339490657406283 absolute error = 1.3e-30 relative error = 3.9926688660300168159137504194239e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = -3.2542484068650191426832726587259 y[1] (numeric) = -3.2542484068650191426832726587271 absolute error = 1.2e-30 relative error = 3.6874874009879910838441380740307e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (closed_form) = -3.2525137545577774622369947075191 y[1] (numeric) = -3.2525137545577774622369947075203 absolute error = 1.2e-30 relative error = 3.6894540363385979675617445437458e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = -3.2507635736908911901428923163821 y[1] (numeric) = -3.2507635736908911901428923163833 absolute error = 1.2e-30 relative error = 3.6914404040695260817390874007211e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (closed_form) = -3.2489979116509525884172248394417 y[1] (numeric) = -3.2489979116509525884172248394429 absolute error = 1.2e-30 relative error = 3.6934465106819028156928378184958e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=476.4MB, alloc=44.3MB, time=5.71 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = -3.2472168160538843045493518110525 y[1] (numeric) = -3.2472168160538843045493518110537 absolute error = 1.2e-30 relative error = 3.6954723628780542881202442542934e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (closed_form) = -3.2454203347445108285193129230097 y[1] (numeric) = -3.245420334744510828519312923011 absolute error = 1.3e-30 relative error = 4.0056444648558593522130697038550e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (closed_form) = -3.2436085157961278897003706726133 y[1] (numeric) = -3.2436085157961278897003706726144 absolute error = 1.1e-30 relative error = 3.3912847208381753960915325659580e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (closed_form) = -3.2417814075100697975219406521301 y[1] (numeric) = -3.2417814075100697975219406521313 absolute error = 1.2e-30 relative error = 3.7016684629630521897194293765536e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (closed_form) = -3.2399390584152747297868405928328 y[1] (numeric) = -3.2399390584152747297868405928338 absolute error = 1.0e-30 relative error = 3.0864778070520929417689565033967e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = -3.2380815172678479725552603740685 y[1] (numeric) = -3.2380815172678479725552603740694 absolute error = 9e-31 relative error = 2.7794235419971167573925260421605e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = -3.2362088330506231155262910935001 y[1] (numeric) = -3.236208833050623115526291093501 absolute error = 9e-31 relative error = 2.7810319000693536209875638405449e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (closed_form) = -3.2343210549727212068662518028266 y[1] (numeric) = -3.2343210549727212068662518028274 absolute error = 8e-31 relative error = 2.4734712058656382550578583319761e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = -3.2324182324691078714514174783385 y[1] (numeric) = -3.2324182324691078714514174783392 absolute error = 7e-31 relative error = 2.1655613527006359625486583130494e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (closed_form) = -3.2305004152001483965110810523045 y[1] (numeric) = -3.2305004152001483965110810523053 absolute error = 8e-31 relative error = 2.4763965243150582311665565146864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (closed_form) = -3.2285676530511607886751757144625 y[1] (numeric) = -3.2285676530511607886751757144632 absolute error = 7e-31 relative error = 2.1681441283674646406522951973879e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (closed_form) = -3.2266199961319668064489410381473 y[1] (numeric) = -3.2266199961319668064489410381479 absolute error = 6e-31 relative error = 1.8595310285043568014495021078474e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=516.9MB, alloc=44.3MB, time=6.19 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = -3.2246574947764409721553376285322 y[1] (numeric) = -3.2246574947764409721553376285328 absolute error = 6e-31 relative error = 1.8606627245588970526772759842258e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (closed_form) = -3.2226801995420575674040997670831 y[1] (numeric) = -3.2226801995420575674040997670838 absolute error = 7e-31 relative error = 2.1721050698715619004178171018559e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (closed_form) = -3.2206881612094356161644637729721 y[1] (numeric) = -3.2206881612094356161644637729728 absolute error = 7e-31 relative error = 2.1734485456584390085688482625072e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (closed_form) = -3.2186814307818818595367213555316 y[1] (numeric) = -3.2186814307818818595367213555323 absolute error = 7e-31 relative error = 2.1748036115209949523015662680150e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = -3.2166600594849317263358219288494 y[1] (numeric) = -3.2166600594849317263358219288502 absolute error = 8e-31 relative error = 2.4870517406433682788869734765388e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = -3.2146240987658883036182855376373 y[1] (numeric) = -3.2146240987658883036182855376379 absolute error = 6e-31 relative error = 1.8664701736988261465187583169550e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (closed_form) = -3.2125736002933593113016885402071 y[1] (numeric) = -3.2125736002933593113016885402078 absolute error = 7e-31 relative error = 2.1789384060682028047005780845852e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (closed_form) = -3.2105086159567920850439473477642 y[1] (numeric) = -3.2105086159567920850439473477649 absolute error = 7e-31 relative error = 2.1803398892028414791545806700414e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (closed_form) = -3.2084291978660065715675511675993 y[1] (numeric) = -3.2084291978660065715675511676002 absolute error = 9e-31 relative error = 2.8051109888870505281240470673996e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = -3.2063353983507263406317826798036 y[1] (numeric) = -3.2063353983507263406317826798044 absolute error = 8e-31 relative error = 2.4950602498151120274431515448794e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (closed_form) = -3.2042272699601076178738157318529 y[1] (numeric) = -3.2042272699601076178738157318537 absolute error = 8e-31 relative error = 2.4967018023348884932103696731249e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (closed_form) = -3.202104865462266342757391302154 y[1] (numeric) = -3.2021048654622663427573913021549 absolute error = 9e-31 relative error = 2.8106512366517173796762809886461e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=557.4MB, alloc=44.3MB, time=6.67 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = -3.1999682378438032558855470021118 y[1] (numeric) = -3.1999682378438032558855470021129 absolute error = 1.1e-30 relative error = 3.4375341198423893972730497778125e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (closed_form) = -3.1978174403093270199516110964921 y[1] (numeric) = -3.1978174403093270199516110964931 absolute error = 1.0e-30 relative error = 3.1271328606653334504353806128225e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = -3.1956525262809753786203692642011 y[1] (numeric) = -3.1956525262809753786203692642022 absolute error = 1.1e-30 relative error = 3.4421764911974141074396873902946e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = -3.1934735493979343576489709368039 y[1] (numeric) = -3.1934735493979343576489709368051 absolute error = 1.2e-30 relative error = 3.7576638147707095549230854095175e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (closed_form) = -3.1912805635159555125747618812348 y[1] (numeric) = -3.1912805635159555125747618812359 absolute error = 1.1e-30 relative error = 3.4468921741812886733269517899445e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = -3.1890736227068712273148105776266 y[1] (numeric) = -3.1890736227068712273148105776277 absolute error = 1.1e-30 relative error = 3.4492775336629732270352243557488e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (closed_form) = -3.186852781258108068039437724791 y[1] (numeric) = -3.1868527812581080680394377247921 absolute error = 1.1e-30 relative error = 3.4516812526424304946242560411831e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (closed_form) = -3.1846180936721981966995607267213 y[1] (numeric) = -3.1846180936721981966995607267225 absolute error = 1.2e-30 relative error = 3.7681127366084713798965214557444e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (closed_form) = -3.182369614666288848605128116062 y[1] (numeric) = -3.1823696146662888486051281160632 absolute error = 1.2e-30 relative error = 3.7707750679546221376231350249069e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (closed_form) = -3.1801073991716498784693423976073 y[1] (numeric) = -3.1801073991716498784693423976086 absolute error = 1.3e-30 relative error = 4.0879122520787262124593896024066e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = -3.1778315023331793793507535897631 y[1] (numeric) = -3.1778315023331793793507535897644 absolute error = 1.3e-30 relative error = 4.0908399298248936834781435662366e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (closed_form) = -3.1755419795089073789426496480555 y[1] (numeric) = -3.1755419795089073789426496480569 absolute error = 1.4e-30 relative error = 4.4086962447163360108574105936838e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = -3.1732388862694976176764738161271 y[1] (numeric) = -3.1732388862694976176764738161285 absolute error = 1.4e-30 relative error = 4.4118960159531476680209510660684e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=597.9MB, alloc=44.3MB, time=7.15 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = -3.1709222783977474131232626104643 y[1] (numeric) = -3.1709222783977474131232626104658 absolute error = 1.5e-30 relative error = 4.7304849135499567305436441053502e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (closed_form) = -3.1685922118880856151943214500028 y[1] (numeric) = -3.1685922118880856151943214500041 absolute error = 1.3e-30 relative error = 4.1027684001828755367485087092291e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (closed_form) = -3.1662487429460686566595377357267 y[1] (numeric) = -3.1662487429460686566595377357278 absolute error = 1.1e-30 relative error = 3.4741427136785649514287589163208e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (closed_form) = -3.1638919279878747035188733137868 y[1] (numeric) = -3.1638919279878747035188733137879 absolute error = 1.1e-30 relative error = 3.4767306375713084690943238585884e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = -3.1615218236397959097796795642219 y[1] (numeric) = -3.1615218236397959097796795642231 absolute error = 1.2e-30 relative error = 3.7956404128770629678006182563083e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (closed_form) = -3.1591384867377287812095386921676 y[1] (numeric) = -3.1591384867377287812095386921688 absolute error = 1.2e-30 relative error = 3.7985039435202950185980376039300e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (closed_form) = -3.1567419743266626526513540059379 y[1] (numeric) = -3.1567419743266626526513540059391 absolute error = 1.2e-30 relative error = 3.8013876641151883457307867565231e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (closed_form) = -3.1543323436601662835043898933892 y[1] (numeric) = -3.1543323436601662835043898933905 absolute error = 1.3e-30 relative error = 4.1213158867449263598093864249476e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = -3.1519096521998725759918987017286 y[1] (numeric) = -3.1519096521998725759918987017299 absolute error = 1.3e-30 relative error = 4.1244837049585673901966657117750e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = -3.1494739576149614208528666339729 y[1] (numeric) = -3.1494739576149614208528666339741 absolute error = 1.2e-30 relative error = 3.8101600970491525588575479418515e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (closed_form) = -3.147025317781640675112263945555 y[1] (numeric) = -3.1470253177816406751122639455563 absolute error = 1.3e-30 relative error = 4.1308851017327650498435467135675e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = -3.1445637907826252766009960054276 y[1] (numeric) = -3.1445637907826252766009960054288 absolute error = 1.2e-30 relative error = 3.8161095777972486880721596558633e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=638.5MB, alloc=44.3MB, time=7.69 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = -3.1420894349066144999135210261274 y[1] (numeric) = -3.1420894349066144999135210261286 absolute error = 1.2e-30 relative error = 3.8191147160509293197906848191732e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (closed_form) = -3.1396023086477673585078273157203 y[1] (numeric) = -3.1396023086477673585078273157216 absolute error = 1.3e-30 relative error = 4.1406518157387661440138871689838e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = -3.1371024707051761576691476107969 y[1] (numeric) = -3.1371024707051761576691476107982 absolute error = 1.3e-30 relative error = 4.1439513440814651851690176204676e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (closed_form) = -3.1345899799823382030754302635724 y[1] (numeric) = -3.1345899799823382030754302635738 absolute error = 1.4e-30 relative error = 4.4662938659935621868052515675899e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = -3.1320648955866256697191866278861 y[1] (numeric) = -3.1320648955866256697191866278872 absolute error = 1.1e-30 relative error = 3.5120600519804157569707658327276e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = -3.1295272768287536359568907690869 y[1] (numeric) = -3.1295272768287536359568907690879 absolute error = 1.0e-30 relative error = 3.1953707750179151504457169749627e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = -3.1269771832222462874736214624423 y[1] (numeric) = -3.1269771832222462874736214624435 absolute error = 1.2e-30 relative error = 3.8375719734655684169680295510759e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = -3.1244146744829012959671071951678 y[1] (numeric) = -3.124414674482901295967107195169 absolute error = 1.2e-30 relative error = 3.8407193827387944320701420993094e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = -3.1218398105282523773717624002295 y[1] (numeric) = -3.1218398105282523773717624002306 absolute error = 1.1e-30 relative error = 3.5235632407861021354695934480438e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = -3.1192526514770300344596872778642 y[1] (numeric) = -3.1192526514770300344596872778655 absolute error = 1.3e-30 relative error = 4.1676649673902605066630726653915e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = -3.1166532576486204886719441558311 y[1] (numeric) = -3.1166532576486204886719441558324 absolute error = 1.3e-30 relative error = 4.1711409403970512093832554157503e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = -3.1140416895625228060497202546981 y[1] (numeric) = -3.1140416895625228060497202546993 absolute error = 1.2e-30 relative error = 3.8535129572031593563438396347974e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=679.0MB, alloc=44.3MB, time=8.17 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = -3.1114180079378042221512398133014 y[1] (numeric) = -3.1114180079378042221512398133027 absolute error = 1.3e-30 relative error = 4.1781592723428962894655125005640e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = -3.1087822736925536708564976456109 y[1] (numeric) = -3.1087822736925536708564976456124 absolute error = 1.5e-30 relative error = 4.8250403789723361477466460218191e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = -3.1061345479433335219780511977215 y[1] (numeric) = -3.106134547943333521978051197723 absolute error = 1.5e-30 relative error = 4.8291533314073460771148845987340e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = -3.1034748920046295326122289070712 y[1] (numeric) = -3.1034748920046295326122289070727 absolute error = 1.5e-30 relative error = 4.8332918815112566786669277885919e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (closed_form) = -3.100803367388299017181188990184 y[1] (numeric) = -3.1008033673882990171811889901857 absolute error = 1.7e-30 relative error = 5.4824501865523064561406976732563e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = -3.0981200358030172411322945555567 y[1] (numeric) = -3.0981200358030172411322945555584 absolute error = 1.7e-30 relative error = 5.4871986248246462467192275714508e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = -3.0954249591537220432772580104725 y[1] (numeric) = -3.0954249591537220432772580104741 absolute error = 1.6e-30 relative error = 5.1689187142738365616789511915533e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = -3.0927181995410566917694499606439 y[1] (numeric) = -3.0927181995410566917694499606457 absolute error = 1.8e-30 relative error = 5.8201228946986202802445272954003e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = -3.0899998192608109787336650461838 y[1] (numeric) = -3.0899998192608109787336650461855 absolute error = 1.7e-30 relative error = 5.5016184447760699072062855244241e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = -3.0872698808033605585784892734012 y[1] (numeric) = -3.0872698808033605585784892734029 absolute error = 1.7e-30 relative error = 5.5064832866429897314449789232784e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = -3.0845284468531045350372202466516 y[1] (numeric) = -3.0845284468531045350372202466533 absolute error = 1.7e-30 relative error = 5.5113772795137383695069130772531e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = -3.0817755802879013019990531356729 y[1] (numeric) = -3.0817755802879013019990531356745 absolute error = 1.6e-30 relative error = 5.1918121820230889470092457672867e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=719.5MB, alloc=44.3MB, time=8.66 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = -3.07901134417850264320796108966 y[1] (numeric) = -3.0790113441785026432079610896616 absolute error = 1.6e-30 relative error = 5.1964732219162670920411381783327e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = -3.0762358017879860959223689883283 y[1] (numeric) = -3.0762358017879860959223689883301 absolute error = 1.8e-30 relative error = 5.8513069737820307818744373585864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = -3.0734490165711855836443437613588 y[1] (numeric) = -3.0734490165711855836443437613605 absolute error = 1.7e-30 relative error = 5.5312451608407069487972429471351e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = -3.0706510521741203230426028702832 y[1] (numeric) = -3.0706510521741203230426028702849 absolute error = 1.7e-30 relative error = 5.5362852082992138798957729821547e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = -3.0678419724334220102091747908561 y[1] (numeric) = -3.0678419724334220102091747908577 absolute error = 1.6e-30 relative error = 5.2153924953666205661483645001979e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = -3.0650218413757602914050313194782 y[1] (numeric) = -3.0650218413757602914050313194798 absolute error = 1.6e-30 relative error = 5.2201911855930750083394169860509e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = -3.0621907232172665234654511149086 y[1] (numeric) = -3.0621907232172665234654511149103 absolute error = 1.7e-30 relative error = 5.5515810531027551822596571915609e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = -3.0593486823629558290512669373775 y[1] (numeric) = -3.0593486823629558290512669373792 absolute error = 1.7e-30 relative error = 5.5567383011960810039724814123497e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = -3.0564957834061474519474954227494 y[1] (numeric) = -3.056495783406147451947495422751 absolute error = 1.6e-30 relative error = 5.2347528456818808148675935502338e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = -3.0536320911278834176261477914676 y[1] (numeric) = -3.053632091127883417626147791469 absolute error = 1.4e-30 relative error = 4.5847042414428478551115649677542e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = -3.0507576704963455043052725029433 y[1] (numeric) = -3.0507576704963455043052725029447 absolute error = 1.4e-30 relative error = 4.5890239449016147506068015459482e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = -3.0478725866662705297514863885618 y[1] (numeric) = -3.0478725866662705297514863885632 absolute error = 1.4e-30 relative error = 4.5933678662443845211362451792082e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = -3.0449769049783639590884090937133 y[1] (numeric) = -3.0449769049783639590884090937146 absolute error = 1.3e-30 relative error = 4.2693263054789478998069030582560e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=760.1MB, alloc=44.3MB, time=9.14 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = -3.0420706909587118388885265947898 y[1] (numeric) = -3.0420706909587118388885265947911 absolute error = 1.3e-30 relative error = 4.2734049667672371104549247763780e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = -3.0391540103181910628410729949361 y[1] (numeric) = -3.0391540103181910628410729949375 absolute error = 1.4e-30 relative error = 4.6065450952695347348030101596926e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (closed_form) = -3.0362269289518779743035356069107 y[1] (numeric) = -3.0362269289518779743035356069121 absolute error = 1.4e-30 relative error = 4.6109860453786555520540113075916e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (closed_form) = -3.0332895129384553110593563675796 y[1] (numeric) = -3.0332895129384553110593563675811 absolute error = 1.5e-30 relative error = 4.9451263837552278726585190986961e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = -3.0303418285396174976193227616103 y[1] (numeric) = -3.0303418285396174976193227616118 absolute error = 1.5e-30 relative error = 4.9499366238919656246916242913996e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = -3.0273839421994742904190135275694 y[1] (numeric) = -3.0273839421994742904190135275708 absolute error = 1.4e-30 relative error = 4.6244547329628202716969398324046e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = -3.0244159205439527812794883440211 y[1] (numeric) = -3.0244159205439527812794883440226 absolute error = 1.5e-30 relative error = 4.9596353127588987752361890649621e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = -3.0214378303801977645131863129418 y[1] (numeric) = -3.0214378303801977645131863129432 absolute error = 1.4e-30 relative error = 4.6335555407533679227342835502052e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = -3.018449738695970473071725239846 y[1] (numeric) = -3.0184497386959704730717252398474 absolute error = 1.4e-30 relative error = 4.6381424943150700805399559653604e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = -3.0154517126590456891469723218978 y[1] (numeric) = -3.0154517126590456891469723218991 absolute error = 1.3e-30 relative error = 4.3111285600844565297147576653710e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = -3.0124438196166072346513867648716 y[1] (numeric) = -3.0124438196166072346513867648728 absolute error = 1.2e-30 relative error = 3.9834767778431918367059488536065e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = -3.0094261270946418470182159254384 y[1] (numeric) = -3.0094261270946418470182159254399 absolute error = 1.5e-30 relative error = 4.9843389957145384187995576113993e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=800.5MB, alloc=44.3MB, time=9.62 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = -3.0063987027973314457766586856783 y[1] (numeric) = -3.0063987027973314457766586856798 absolute error = 1.5e-30 relative error = 4.9893581932573053041028538630336e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = -3.0033616146064437953715927811452 y[1] (numeric) = -3.0033616146064437953715927811468 absolute error = 1.6e-30 relative error = 5.3273638186577865966185549551674e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = -3.0003149305807215697118965919177 y[1] (numeric) = -3.0003149305807215697118965919192 absolute error = 1.5e-30 relative error = 4.9994751707937196216535238287476e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = -2.9972587189552698239457803379228 y[1] (numeric) = -2.9972587189552698239457803379243 absolute error = 1.5e-30 relative error = 5.0045729803493334772370100773255e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = -2.9941930481409418789758765659908 y[1] (numeric) = -2.9941930481409418789758765659924 absolute error = 1.6e-30 relative error = 5.3436768246904473300641644516961e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = -2.9911179867237236242411251475458 y[1] (numeric) = -2.9911179867237236242411251475475 absolute error = 1.7e-30 relative error = 5.6834936219352202436262316246458e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = -2.9880336034641162443067235940147 y[1] (numeric) = -2.9880336034641162443067235940165 absolute error = 1.8e-30 relative error = 6.0240286384771792851600758775054e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = -2.9849399672965173748175992138048 y[1] (numeric) = -2.9849399672965173748175992138066 absolute error = 1.8e-30 relative error = 6.0302720313342635369097769154443e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = -2.981837147328600693384995352407 y[1] (numeric) = -2.9818371473286006933849953524089 absolute error = 1.9e-30 relative error = 6.3719106917096119094383782487424e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = -2.978725212840693950989849548586 y[1] (numeric) = -2.9787252128406939509898495485879 absolute error = 1.9e-30 relative error = 6.3785675557096593440102722765973e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = -2.9756042332851554495006767779696 y[1] (numeric) = -2.9756042332851554495006767779714 absolute error = 1.8e-30 relative error = 6.0491915553324325651083593247427e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (closed_form) = -2.9724742782857489709176559143099 y[1] (numeric) = -2.9724742782857489709176559143118 absolute error = 1.9e-30 relative error = 6.3919812994840986548471380361493e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=841.0MB, alloc=44.3MB, time=10.11 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = -2.9693354176370171639685519924143 y[1] (numeric) = -2.9693354176370171639685519924161 absolute error = 1.8e-30 relative error = 6.0619625162873358977588937438962e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = -2.9661877213036533936959906798049 y[1] (numeric) = -2.9661877213036533936959906798068 absolute error = 1.9e-30 relative error = 6.4055285050028495924177818103398e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = -2.963031259419872059689434431623 y[1] (numeric) = -2.9630312594198720596894344316249 absolute error = 1.9e-30 relative error = 6.4123521949343135419344774494380e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = -2.9598661022887773886289919906428 y[1] (numeric) = -2.9598661022887773886289919906447 absolute error = 1.9e-30 relative error = 6.4192092964299496215231192203473e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = -2.9566923203817307068219240774588 y[1] (numeric) = -2.9566923203817307068219240774608 absolute error = 2.0e-30 relative error = 6.7643156043432524028024261013409e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = -2.9535099843377161984263881713874 y[1] (numeric) = -2.9535099843377161984263881713894 absolute error = 2.0e-30 relative error = 6.7716039918804349782801292149251e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = -2.9503191649627051550705940872489 y[1] (numeric) = -2.950319164962705155070594087251 absolute error = 2.1e-30 relative error = 7.1178739742435493436170209566651e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = -2.9471199332290187225891194843154 y[1] (numeric) = -2.9471199332290187225891194843174 absolute error = 2.0e-30 relative error = 6.7862864264526059080778996045676e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = -2.9439123602746891506116603791272 y[1] (numeric) = -2.9439123602746891506116603791293 absolute error = 2.1e-30 relative error = 7.1333645265311302124509626851297e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = -2.9406965174028195507529660518597 y[1] (numeric) = -2.9406965174028195507529660518618 absolute error = 2.1e-30 relative error = 7.1411653245153277379578290745517e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = -2.937472476080942169166130315194 y[1] (numeric) = -2.9374724760809421691661303151961 absolute error = 2.1e-30 relative error = 7.1490031552627028520411324251831e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = -2.9342403079403751792347818344126 y[1] (numeric) = -2.9342403079403751792347818344146 absolute error = 2.0e-30 relative error = 6.8160743160257913031898288565215e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = -2.9310000847755780001930349273582 y[1] (numeric) = -2.9310000847755780001930349273602 absolute error = 2.0e-30 relative error = 6.8236094921612286777305270189624e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=881.7MB, alloc=44.3MB, time=10.59 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = -2.9277518785435051474753289131013 y[1] (numeric) = -2.9277518785435051474753289131032 absolute error = 1.9e-30 relative error = 6.4896209747979393474522632328325e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = -2.9244957613629586206114984992521 y[1] (numeric) = -2.924495761362958620611498499254 absolute error = 1.9e-30 relative error = 6.4968464823984108221191593800887e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = -2.9212318055139388344955797809049 y[1] (numeric) = -2.9212318055139388344955797809069 absolute error = 2.0e-30 relative error = 6.8464268950684505302684562013550e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = -2.9179600834369940998699660507467 y[1] (numeric) = -2.9179600834369940998699660507487 absolute error = 2.0e-30 relative error = 6.8541033558082423136467777052562e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = -2.9146806677325686588795846719229 y[1] (numeric) = -2.914680667732568658879584671925 absolute error = 2.1e-30 relative error = 7.2049059207356082319988628428863e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = -2.9113936311603492815637706253097 y[1] (numeric) = -2.9113936311603492815637706253117 absolute error = 2.0e-30 relative error = 6.8695623243597288121674026058229e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = -2.9080990466386104291664638938584 y[1] (numeric) = -2.9080990466386104291664638938606 absolute error = 2.2e-30 relative error = 7.5650793343607669680469073000140e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = -2.9047969872435579901582564720901 y[1] (numeric) = -2.9047969872435579901582564720922 absolute error = 2.1e-30 relative error = 7.2294208828436852064823709150808e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = -2.9014875262086715948766603725351 y[1] (numeric) = -2.9014875262086715948766603725371 absolute error = 2.0e-30 relative error = 6.8930160200046379084778675447793e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = -2.8981707369240455147037604273318 y[1] (numeric) = -2.8981707369240455147037604273338 absolute error = 2.0e-30 relative error = 6.9009046793519379403624789388133e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = -2.8948466929357281517131548371806 y[1] (numeric) = -2.8948466929357281517131548371826 absolute error = 2.0e-30 relative error = 6.9088287296200673767251335993377e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = -2.8915154679450601247307721867428 y[1] (numeric) = -2.8915154679450601247307721867447 absolute error = 1.9e-30 relative error = 6.5709487673959789122183666370105e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=922.2MB, alloc=44.3MB, time=11.07 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = -2.8881771358080109577667859112155 y[1] (numeric) = -2.8881771358080109577667859112173 absolute error = 1.8e-30 relative error = 6.2323047214914778739473709741442e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = -2.8848317705345143767884258494995 y[1] (numeric) = -2.8848317705345143767884258495014 absolute error = 1.9e-30 relative error = 6.5861726129283428025959408291104e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = -2.8814794462878022208160114419108 y[1] (numeric) = -2.8814794462878022208160114419127 absolute error = 1.9e-30 relative error = 6.5938349914234577003378711987846e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = -2.8781202373837369733370022120385 y[1] (numeric) = -2.8781202373837369733370022120407 absolute error = 2.2e-30 relative error = 7.6438780125455757277691873395153e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = -2.8747542182901429200452783008831 y[1] (numeric) = -2.8747542182901429200452783008853 absolute error = 2.2e-30 relative error = 7.6528281478912803858232742354156e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = -2.8713814636261359389252268850663 y[1] (numeric) = -2.8713814636261359389252268850686 absolute error = 2.3e-30 relative error = 8.0100816597716539619142674940185e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = -2.8680020481614519287125191984192 y[1] (numeric) = -2.8680020481614519287125191984213 absolute error = 2.1e-30 relative error = 7.3221705031424794330919981195352e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = -2.8646160468157738817757174768489 y[1] (numeric) = -2.8646160468157738817757174768509 absolute error = 2.0e-30 relative error = 6.9817384505094265336964960066672e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = -2.8612235346580576074750513497645 y[1] (numeric) = -2.8612235346580576074750513497664 absolute error = 1.9e-30 relative error = 6.6405157688145025864216791465746e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = -2.857824586905856112066848897709 y[1] (numeric) = -2.8578245869058561120668488977109 absolute error = 1.9e-30 relative error = 6.6484136524877296500889250055885e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = -2.8544192789246426412341986758835 y[1] (numeric) = -2.8544192789246426412341986758854 absolute error = 1.9e-30 relative error = 6.6563451768578124824112377502437e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = -2.8510076862271323913364553581433 y[1] (numeric) = -2.8510076862271323913364553581452 absolute error = 1.9e-30 relative error = 6.6643103390379001791600424927051e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=962.8MB, alloc=44.3MB, time=11.65 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = -2.8475898844726028954821831774678 y[1] (numeric) = -2.8475898844726028954821831774697 absolute error = 1.9e-30 relative error = 6.6723091353862413788039149254333e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = -2.8441659494662130905420579190215 y[1] (numeric) = -2.8441659494662130905420579190234 absolute error = 1.9e-30 relative error = 6.6803415614921762480956329933811e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = -2.8407359571583210712301197533899 y[1] (numeric) = -2.840735957158321071230119753392 absolute error = 2.1e-30 relative error = 7.3924505187053607301746534218442e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = -2.8372999836438005373935855735579 y[1] (numeric) = -2.8372999836438005373935855735599 absolute error = 2.0e-30 relative error = 7.0489550330575245915596743252063e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = -2.8338581051613559406631906133399 y[1] (numeric) = -2.8338581051613559406631906133418 absolute error = 1.9e-30 relative error = 6.7046405624173502558776015676129e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = -2.8304103980928363366277348714274 y[1] (numeric) = -2.8304103980928363366277348714292 absolute error = 1.8e-30 relative error = 6.3595017924356873249491069856835e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (closed_form) = -2.8269569389625479487081601386415 y[1] (numeric) = -2.8269569389625479487081601386432 absolute error = 1.7e-30 relative error = 6.0135334096170395051433678772965e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = -2.8234978044365654499180781215028 y[1] (numeric) = -2.8234978044365654499180781215045 absolute error = 1.7e-30 relative error = 6.0209007328739125743767761265766e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = -2.8200330713220419687092091685204 y[1] (numeric) = -2.8200330713220419687092091685221 absolute error = 1.7e-30 relative error = 6.0282980979476020522778376993598e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = -2.8165628165665178251116743327912 y[1] (numeric) = -2.8165628165665178251116743327927 absolute error = 1.5e-30 relative error = 5.3256401425782828800574224370314e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = -2.8130871172572280033905108422517 y[1] (numeric) = -2.8130871172572280033905108422531 absolute error = 1.4e-30 relative error = 4.9767388695910917988037323702881e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = -2.8096060506204083674511523943855 y[1] (numeric) = -2.8096060506204083674511523943868 absolute error = 1.3e-30 relative error = 4.6269832018369197722664537448188e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1003.5MB, alloc=44.3MB, time=12.14 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = -2.8061196940206006252379309430181 y[1] (numeric) = -2.8061196940206006252379309430194 absolute error = 1.3e-30 relative error = 4.6327318209914401562686577125788e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = -2.8026281249599560483809156991947 y[1] (numeric) = -2.802628124959956048380915699196 absolute error = 1.3e-30 relative error = 4.6385033691138541630448223324587e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = -2.7991314210775379533576078246989 y[1] (numeric) = -2.7991314210775379533576078247003 absolute error = 1.4e-30 relative error = 5.0015515150805739649149577058275e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = -2.7956296601486229504471556547098 y[1] (numeric) = -2.7956296601486229504471556547111 absolute error = 1.3e-30 relative error = 4.6501152085032915832610855937375e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = -2.7921229200840009667658451450909 y[1] (numeric) = -2.7921229200840009667658451450921 absolute error = 1.2e-30 relative error = 4.2978050549576020171821179010367e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = -2.7886112789292740496836535000557 y[1] (numeric) = -2.7886112789292740496836535000569 absolute error = 1.2e-30 relative error = 4.3032171929705334615016745754788e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = -2.78509481486415395693263049815 y[1] (numeric) = -2.7850948148641539569326304981511 absolute error = 1.1e-30 relative error = 3.9495962368292072025874713339992e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = -2.7815736062017585397287917998547 y[1] (numeric) = -2.7815736062017585397287917998558 absolute error = 1.1e-30 relative error = 3.9545960514848681935023965850111e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (closed_form) = -2.7780477313879069252400713903567 y[1] (numeric) = -2.7780477313879069252400713903578 absolute error = 1.1e-30 relative error = 3.9596151915303566992310914201279e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = -2.7745172690004135047436861883984 y[1] (numeric) = -2.7745172690004135047436861883995 absolute error = 1.1e-30 relative error = 3.9646536436815959125721574050056e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = -2.7709822977483807338270146393469 y[1] (numeric) = -2.770982297748380733827014639348 absolute error = 1.1e-30 relative error = 3.9697113940201922819652381367722e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = -2.7674428964714907509967827109768 y[1] (numeric) = -2.7674428964714907509967827109777 absolute error = 9e-31 relative error = 3.2520996228955848007078831057294e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1044.3MB, alloc=44.3MB, time=12.62 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = -2.7638991441392958210719850277215 y[1] (numeric) = -2.7638991441392958210719850277225 absolute error = 1.0e-30 relative error = 3.6180770275950477987989350403743e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = -2.7603511198505076097465458175956 y[1] (numeric) = -2.7603511198505076097465458175965 absolute error = 9e-31 relative error = 3.2604547788425601371330150379046e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = -2.7567989028322852957182438104454 y[1] (numeric) = -2.7567989028322852957182438104463 absolute error = 9e-31 relative error = 3.2646559713708398885053277724814e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = -2.7532425724395225267908871219617 y[1] (numeric) = -2.7532425724395225267908871219625 absolute error = 8e-31 relative error = 2.9056647896126222145536942031323e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = -2.7496822081541332263671283908357 y[1] (numeric) = -2.7496822081541332263671283908363 absolute error = 6e-31 relative error = 2.1820703433317158292578423947396e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = -2.7461178895843362567596569129171 y[1] (numeric) = -2.7461178895843362567596569129178 absolute error = 7e-31 relative error = 2.5490529836865630356885814517806e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = -2.7425496964639389457587931431252 y[1] (numeric) = -2.7425496964639389457587931431261 absolute error = 9e-31 relative error = 3.2816178359881686099402579103956e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = -2.7389777086516194829047416205657 y[1] (numeric) = -2.7389777086516194829047416205665 absolute error = 8e-31 relative error = 2.9207977760207281188723182586398e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = -2.7354020061302081919229310227556 y[1] (numeric) = -2.7354020061302081919229310227564 absolute error = 8e-31 relative error = 2.9246158268771815257318833515869e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = -2.7318226690059676857909845794854 y[1] (numeric) = -2.7318226690059676857909845794861 absolute error = 7e-31 relative error = 2.5623917977615656321642314011309e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = -2.7282397775078719109159203846322 y[1] (numeric) = -2.7282397775078719109159203846329 absolute error = 7e-31 relative error = 2.5657568875394796894274737401193e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = -2.7246534119868840869101791446714 y[1] (numeric) = -2.724653411986884086910179144672 absolute error = 6e-31 relative error = 2.2021149455572967194844542261472e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1084.9MB, alloc=44.3MB, time=13.10 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = -2.7210636529152335484650165057321 y[1] (numeric) = -2.7210636529152335484650165057328 absolute error = 7e-31 relative error = 2.5725234293951533968766124279261e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = -2.7174705808856914958296782173495 y[1] (numeric) = -2.7174705808856914958296782173502 absolute error = 7e-31 relative error = 2.5759248505713446457818231167268e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = -2.713874276610845660414598931654 y[1] (numeric) = -2.7138742766108456604145989316547 absolute error = 7e-31 relative error = 2.5793383504639631883515219168241e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = -2.7102748209223738920466293132038 y[1] (numeric) = -2.7102748209223738920466293132044 absolute error = 6e-31 relative error = 2.2137976391479189019567744850377e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = -2.7066722947703166744140012591308 y[1] (numeric) = -2.7066722947703166744140012591314 absolute error = 6e-31 relative error = 2.2167441590889558244186666973609e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (closed_form) = -2.7030667792223485752483873143951 y[1] (numeric) = -2.7030667792223485752483873143956 absolute error = 5e-31 relative error = 1.8497508231884901353003190539165e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (closed_form) = -2.6994583554630486378009977259016 y[1] (numeric) = -2.699458355463048637800997725902 absolute error = 4e-31 relative error = 1.4817787397627270945731593309265e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = -2.6958471047931697201791869257517 y[1] (numeric) = -2.695847104793169720179186925752 absolute error = 3e-31 relative error = 1.1128227541784738721811531046484e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = -2.6922331086289067891195104822109 y[1] (numeric) = -2.6922331086289067891195104822113 absolute error = 4e-31 relative error = 1.4857554448682600161200724360088e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (closed_form) = -2.6886164485011641747825836218671 y[1] (numeric) = -2.6886164485011641747825836218676 absolute error = 5e-31 relative error = 1.8596925577790665639531719079773e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = -2.6849972060548217931644432232215 y[1] (numeric) = -2.6849972060548217931644432232221 absolute error = 6e-31 relative error = 2.2346391968191467355124030646634e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = -2.6813754630480003427284066264593 y[1] (numeric) = -2.6813754630480003427284066264599 absolute error = 6e-31 relative error = 2.2376575316235716861161074069334e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1125.6MB, alloc=44.3MB, time=13.59 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = -2.6777513013513254818706526127476 y[1] (numeric) = -2.6777513013513254818706526127483 absolute error = 7e-31 relative error = 2.6141337309657750801309841703250e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = -2.6741248029471909938419223960331 y[1] (numeric) = -2.6741248029471909938419223960338 absolute error = 7e-31 relative error = 2.6176788728354040922881468430457e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = -2.6704960499290209457568513583932 y[1] (numeric) = -2.670496049929020945756851358394 absolute error = 8e-31 relative error = 2.9956981214080551886438928955368e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (closed_form) = -2.666865124500530848331495464532 y[1] (numeric) = -2.6668651245005308483314954645329 absolute error = 9e-31 relative error = 3.3747488454953577537798546977514e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = -2.6632321089749878229986097305112 y[1] (numeric) = -2.6632321089749878229986097305121 absolute error = 9e-31 relative error = 3.3793524678792932659391731253833e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = -2.6595970857744697830591697153401 y[1] (numeric) = -2.6595970857744697830591697153409 absolute error = 8e-31 relative error = 3.0079744194299320733149955807411e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = -2.6559601374291236355375006712059 y[1] (numeric) = -2.6559601374291236355375006712068 absolute error = 9e-31 relative error = 3.3886050747401972286930684391073e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = -2.6523213465764225104161926490453 y[1] (numeric) = -2.6523213465764225104161926490462 absolute error = 9e-31 relative error = 3.3932539930039276676970597384378e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = -2.6486807959604220239357334315207 y[1] (numeric) = -2.6486807959604220239357334315216 absolute error = 9e-31 relative error = 3.3979179422926894339850840876936e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = -2.6450385684310155826524845764828 y[1] (numeric) = -2.6450385684310155826524845764836 absolute error = 8e-31 relative error = 3.0245305665790126186151315058664e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = -2.6413947469431887349572590224398 y[1] (numeric) = -2.6413947469431887349572590224404 absolute error = 6e-31 relative error = 2.2715271948441746232934741015037e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = -2.6377494145562725767653315557092 y[1] (numeric) = -2.63774941455627257676533155571 absolute error = 8e-31 relative error = 3.0328885510702599555782039970676e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1166.3MB, alloc=44.3MB, time=14.07 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = -2.6341026544331962180972258896467 y[1] (numeric) = -2.6341026544331962180972258896474 absolute error = 7e-31 relative error = 2.6574514809508263259489620130787e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (closed_form) = -2.6304545498397383172780740830206 y[1] (numeric) = -2.6304545498397383172780740830214 absolute error = 8e-31 relative error = 3.0412994592464651286220177630489e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = -2.6268051841437776894917354511536 y[1] (numeric) = -2.6268051841437776894917354511544 absolute error = 8e-31 relative error = 3.0455246732001734542020784961189e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = -2.623154640814542996434192924372 y[1] (numeric) = -2.6231546408145429964341929243728 absolute error = 8e-31 relative error = 3.0497630126433708449865911493820e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = -2.6195030034218615238190149086001 y[1] (numeric) = -2.6195030034218615238190149086008 absolute error = 7e-31 relative error = 2.6722626356434359134356919469117e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = -2.6158503556354070534958800281944 y[1] (numeric) = -2.6158503556354070534958800281949 absolute error = 5e-31 relative error = 1.9114243248771268116938872511928e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = -2.6121967812239468369513106074327 y[1] (numeric) = -2.6121967812239468369513106074331 absolute error = 4e-31 relative error = 1.5312782056663422131935259396835e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = -2.6085423640545876769688483011286 y[1] (numeric) = -2.6085423640545876769688483011288 absolute error = 2e-31 relative error = 7.6671171898902960977772966607996e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = -2.6048871880920211242339318438447 y[1] (numeric) = -2.604887188092021124233931843845 absolute error = 3e-31 relative error = 1.1516813525415600405570693935299e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = -2.6012313373977677956767023788826 y[1] (numeric) = -2.6012313373977677956767023788829 absolute error = 3e-31 relative error = 1.1532999610104475751034854878449e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = -2.5975748961294208213538661809524 y[1] (numeric) = -2.5975748961294208213538661809527 absolute error = 3e-31 relative error = 1.1549233881456979042599254396848e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = -2.593917948539888426678587729025 y[1] (numeric) = -2.5939179485398884266785877290253 absolute error = 3e-31 relative error = 1.1565516178677488246659087749289e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1206.9MB, alloc=44.3MB, time=14.55 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = -2.5902605789766356568151679477611 y[1] (numeric) = -2.5902605789766356568151679477613 absolute error = 2e-31 relative error = 7.7212308917204123069671603587218e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = -2.5866028718809252500629829470542 y[1] (numeric) = -2.5866028718809252500629829470544 absolute error = 2e-31 relative error = 7.7321494603678394753862091256095e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = -2.5829449117870576670618176801359 y[1] (numeric) = -2.5829449117870576670618176801362 absolute error = 3e-31 relative error = 1.1614649566507383017292755219874e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = -2.5792867833216102826583265424381 y[1] (numeric) = -2.5792867833216102826583265424384 absolute error = 3e-31 relative error = 1.1631122290855127245617541701247e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = -2.5756285712026757472808889776155 y[1] (numeric) = -2.5756285712026757472808889776158 absolute error = 3e-31 relative error = 1.1647642185453651506338556741368e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = -2.5719703602390995246776025759664 y[1] (numeric) = -2.5719703602390995246776025759668 absolute error = 4e-31 relative error = 1.5552278758096363731534442775237e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = -2.5683122353297166128795688766971 y[1] (numeric) = -2.5683122353297166128795688766975 absolute error = 4e-31 relative error = 1.5574430339800507776201978658944e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (closed_form) = -2.5646542814625874552589780523246 y[1] (numeric) = -2.564654281462587455258978052325 absolute error = 4e-31 relative error = 1.5596644073675514671592659263088e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = -2.5609965837142330485587877948568 y[1] (numeric) = -2.5609965837142330485587877948572 absolute error = 4e-31 relative error = 1.5618919702730603512688796676742e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = -2.5573392272488692547780189736216 y[1] (numeric) = -2.5573392272488692547780189736221 absolute error = 5e-31 relative error = 1.9551571206213783637461172114997e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (closed_form) = -2.55368229731764032380385592869 y[1] (numeric) = -2.5536822973176403238038559286906 absolute error = 6e-31 relative error = 2.3495483390014230516501779713611e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = -2.5500258792578516336888425372703 y[1] (numeric) = -2.5500258792578516336888425372708 absolute error = 5e-31 relative error = 1.9607644144596595650677433906456e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1247.6MB, alloc=44.3MB, time=15.03 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = -2.5463700584922016554785063793067 y[1] (numeric) = -2.5463700584922016554785063793073 absolute error = 6e-31 relative error = 2.3562953781952723204915778508895e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = -2.5427149205280131495017223694303 y[1] (numeric) = -2.5427149205280131495017223694308 absolute error = 5e-31 relative error = 1.9664021159563234975500322917543e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = -2.5390605509564636000430440525642 y[1] (numeric) = -2.5390605509564636000430440525649 absolute error = 7e-31 relative error = 2.7569251932030929331951555739976e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = -2.5354070354518148953230853176387 y[1] (numeric) = -2.5354070354518148953230853176395 absolute error = 8e-31 relative error = 3.1553119038239093165812389429389e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = -2.5317544597706422597198275063216 y[1] (numeric) = -2.5317544597706422597198275063223 absolute error = 7e-31 relative error = 2.7648810780150247572574369596332e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = -2.5281029097510624451704567202932 y[1] (numeric) = -2.5281029097510624451704567202939 absolute error = 7e-31 relative error = 2.7688746265037434252039236800217e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = -2.5244524713119611887000035008251 y[1] (numeric) = -2.5244524713119611887000035008257 absolute error = 6e-31 relative error = 2.3767530061208846213069472113048e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = -2.5208032304522199430296619082445 y[1] (numeric) = -2.5208032304522199430296619082453 absolute error = 8e-31 relative error = 3.1735916168930165087932021786364e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = -2.5171552732499418872242073068458 y[1] (numeric) = -2.5171552732499418872242073068465 absolute error = 7e-31 relative error = 2.7809170432947432822055190101204e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = -2.5135086858616772243444118040629 y[1] (numeric) = -2.5135086858616772243444118040636 absolute error = 7e-31 relative error = 2.7849515855562960379523344016159e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = -2.5098635545216477730767732429238 y[1] (numeric) = -2.5098635545216477730767732429244 absolute error = 6e-31 relative error = 2.3905682000882847283401750192991e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = -2.506219965540970860319227846222 y[1] (numeric) = -2.5062199655409708603192278462226 absolute error = 6e-31 relative error = 2.3940436523914181434286148428378e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=1288.3MB, alloc=44.3MB, time=15.52 x[1] = 3.97 y[1] (closed_form) = -2.5025780053068825217078080022669 y[1] (numeric) = -2.5025780053068825217078080022676 absolute error = 7e-31 relative error = 2.7971156084469838967403215373490e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = -2.498937760281960017075435208899 y[1] (numeric) = -2.4989377602819600170754352088999 absolute error = 9e-31 relative error = 3.6015302754017020664212298007942e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = -2.4952993170033436678402037986135 y[1] (numeric) = -2.4952993170033436678402037986142 absolute error = 7e-31 relative error = 2.8052746828009571780202513185202e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = -2.4916627620819580233266136976429 y[1] (numeric) = -2.4916627620819580233266136976437 absolute error = 8e-31 relative error = 3.2107073724998972273719451479124e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (closed_form) = -2.488028182201732363029250070779 y[1] (numeric) = -2.4880281822017323630292500707797 absolute error = 7e-31 relative error = 2.8134729542353839192257231677596e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = -2.4843956641188205418343842172076 y[1] (numeric) = -2.4843956641188205418343842172084 absolute error = 8e-31 relative error = 3.2200990025626554513883361484104e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (closed_form) = -2.4807652946608201852208834569065 y[1] (numeric) = -2.4807652946608201852208834569073 absolute error = 8e-31 relative error = 3.2248113181919496764009447148839e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (closed_form) = -2.4771371607259912414676679289857 y[1] (numeric) = -2.4771371607259912414676679289865 absolute error = 8e-31 relative error = 3.2295345315700589692266977596512e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = -2.4735113492824738979007391600876 y[1] (numeric) = -2.4735113492824738979007391600885 absolute error = 9e-31 relative error = 3.6385521346448465378809204298431e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = -2.4698879473675058682185289005279 y[1] (numeric) = -2.4698879473675058682185289005287 absolute error = 8e-31 relative error = 3.2390133360206415840994994035666e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = -2.4662670420866390579399770167267 y[1] (numeric) = -2.4662670420866390579399770167276 absolute error = 9e-31 relative error = 3.6492398618704945967365883054824e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = -2.462648720612955615025344119723 y[1] (numeric) = -2.4626487206129556150253441197239 absolute error = 9e-31 relative error = 3.6546016184394709032219650520369e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=1328.9MB, alloc=44.3MB, time=16.00 x[1] = 4.09 y[1] (closed_form) = -2.4590330701862833727252980508027 y[1] (numeric) = -2.4590330701862833727252980508035 absolute error = 8e-31 relative error = 3.2533112697805085655639697606448e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = -2.4554201781124106917192832867019 y[1] (numeric) = -2.4554201781124106917192832867027 absolute error = 8e-31 relative error = 3.2580981745250425039523747906402e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = -2.451810131762300708609588719247 y[1] (numeric) = -2.4518101317623007086095887192478 absolute error = 8e-31 relative error = 3.2628953997550361393166821434672e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = -2.4482030185713049978428720590002 y[1] (numeric) = -2.4482030185713049978428720590011 absolute error = 9e-31 relative error = 3.6761657149055063186658768721372e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = -2.4445989260383766541361782614116 y[1] (numeric) = -2.4445989260383766541361782614124 absolute error = 8e-31 relative error = 3.2725204592004355704211323951538e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = -2.4409979417252828024897048296182 y[1] (numeric) = -2.440997941725282802489704829619 absolute error = 8e-31 relative error = 3.2773481137577886122925669138471e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = -2.4374001532558165428737185634477 y[1] (numeric) = -2.4374001532558165428737185634485 absolute error = 8e-31 relative error = 3.2821857294600582531513748411781e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = -2.4338056483150083366821162530041 y[1] (numeric) = -2.4338056483150083366821162530049 absolute error = 8e-31 relative error = 3.2870332130006451258567358017838e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = -2.4302145146483368420501459116485 y[1] (numeric) = -2.4302145146483368420501459116495 absolute error = 1.0e-30 relative error = 4.1148630870748649724578047949927e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = -2.4266268400609392051387653620253 y[1] (numeric) = -2.4266268400609392051387653620262 absolute error = 9e-31 relative error = 3.7088520787044395760274759925043e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (closed_form) = -2.4230427124168208144930112853723 y[1] (numeric) = -2.4230427124168208144930112853732 absolute error = 9e-31 relative error = 3.7143381558565718525284478042058e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = -2.4194622196380645255865841746395 y[1] (numeric) = -2.4194622196380645255865841746404 absolute error = 9e-31 relative error = 3.7198348984124001773817623489944e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = -2.4158854497040393626696229524164 y[1] (numeric) = -2.4158854497040393626696229524171 absolute error = 7e-31 relative error = 2.8974883725788995936896793308010e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1369.7MB, alloc=44.3MB, time=16.50 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = -2.4123124906506087050413472824371 y[1] (numeric) = -2.4123124906506087050413472824376 absolute error = 5e-31 relative error = 2.0726999588065323012366561860100e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = -2.4087434305693379648738857761415 y[1] (numeric) = -2.4087434305693379648738857761421 absolute error = 6e-31 relative error = 2.4909253197555464210638424103803e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = -2.4051783576067017637181843316641 y[1] (numeric) = -2.4051783576067017637181843316647 absolute error = 6e-31 relative error = 2.4946174910580700724195136918540e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = -2.4016173599632906148274007005201 y[1] (numeric) = -2.4016173599632906148274007005207 absolute error = 6e-31 relative error = 2.4983163846266133163054226454043e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = -2.3980605258930171184376390165437 y[1] (numeric) = -2.3980605258930171184376390165444 absolute error = 7e-31 relative error = 2.9190255727149589747774645595933e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = -2.3945079437023216771502614022885 y[1] (numeric) = -2.3945079437023216771502614022893 absolute error = 8e-31 relative error = 3.3409786845938051861842600434693e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = -2.3909597017493777385643328506655 y[1] (numeric) = -2.3909597017493777385643328506661 absolute error = 6e-31 relative error = 2.5094525832493201432382491046876e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = -2.3874158884432965723120103252038 y[1] (numeric) = -2.3874158884432965723120103252043 absolute error = 5e-31 relative error = 2.0943146203404999319750389135459e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = -2.3838765922433315886538773926802 y[1] (numeric) = -2.3838765922433315886538773926806 absolute error = 4e-31 relative error = 1.6779392075140206699806318262735e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = -2.3803419016580822057953516592556 y[1] (numeric) = -2.380341901658082205795351659256 absolute error = 4e-31 relative error = 1.6804308646643188044670373677795e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = -2.3768119052446972730893537885603 y[1] (numeric) = -2.3768119052446972730893537885606 absolute error = 3e-31 relative error = 1.2621949567738909217430455913846e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = -2.3732866916080780572944239008123 y[1] (numeric) = -2.3732866916080780572944239008125 absolute error = 2e-31 relative error = 8.4271319056057715878689794399368e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1410.3MB, alloc=44.3MB, time=16.98 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = -2.3697663494000807990614036500826 y[1] (numeric) = -2.3697663494000807990614036500828 absolute error = 2e-31 relative error = 8.4396506031335572158971817575157e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = -2.366250967318718846825670216824 y[1] (numeric) = -2.3662509673187188468256702168244 absolute error = 4e-31 relative error = 1.6904377664270070742896912020217e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = -2.3627406341073643752857117999657 y[1] (numeric) = -2.3627406341073643752857117999659 absolute error = 2e-31 relative error = 8.4647462828927619837028491722540e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = -2.3592354385539496956525729129928 y[1] (numeric) = -2.3592354385539496956525729129929 absolute error = 1e-31 relative error = 4.2386613207748852284671469905000e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = -2.3557354694901681648583718478512 y[1] (numeric) = -2.3557354694901681648583718478513 absolute error = 1e-31 relative error = 4.2449587950400114884613269526704e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = -2.3522408157906747009157020361581 y[1] (numeric) = -2.3522408157906747009157020361581 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = -2.3487515663722859116232736765864 y[1] (numeric) = -2.3487515663722859116232736765864 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = -2.3452678101931798438166318785189 y[1] (numeric) = -2.3452678101931798438166318785188 absolute error = 1e-31 relative error = 4.2639053657485280657119498528088e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = -2.3417896362520953603662026638186 y[1] (numeric) = -2.3417896362520953603662026638184 absolute error = 2e-31 relative error = 8.5404767748519429478526034225860e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = -2.3383171335875311521282684400961 y[1] (numeric) = -2.338317133587531152128268440096 absolute error = 1e-31 relative error = 4.2765798771946885006137599502245e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = -2.3348503912769443920577599800286 y[1] (numeric) = -2.3348503912769443920577599800285 absolute error = 1e-31 relative error = 4.2829296632282023795806961418806e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = -2.331389498435949038694972482518 y[1] (numeric) = -2.3313894984359490386949724825181 absolute error = 1e-31 relative error = 4.2892875715141825720414646358475e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1451.0MB, alloc=44.3MB, time=17.46 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (closed_form) = -2.3279345442175137962414689237959 y[1] (numeric) = -2.3279345442175137962414689237961 absolute error = 2e-31 relative error = 8.5913068516806511343282850364133e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = -2.3244856178111597384435246015749 y[1] (numeric) = -2.324485617811159738443524601575 absolute error = 1e-31 relative error = 4.3020270477803386060467640322838e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = -2.3210428084421576035044925052102 y[1] (numeric) = -2.3210428084421576035044925052104 absolute error = 2e-31 relative error = 8.6168165133600625347082258225897e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = -2.3176062053707247672504298823242 y[1] (numeric) = -2.3176062053707247672504298823246 absolute error = 4e-31 relative error = 1.7259187478574079732011284682352e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = -2.3141758978912219017762220908267 y[1] (numeric) = -2.3141758978912219017762220908271 absolute error = 4e-31 relative error = 1.7284770806078200930480464025645e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = -2.3107519753313493268022704986616 y[1] (numeric) = -2.3107519753313493268022704986622 absolute error = 6e-31 relative error = 2.5965573389327655875923824373779e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = -2.3073345270513430609745767964646 y[1] (numeric) = -2.3073345270513430609745767964651 absolute error = 5e-31 relative error = 2.1670026350230832616400843416762e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = -2.3039236424431705803437565957192 y[1] (numeric) = -2.3039236424431705803437565957195 absolute error = 3e-31 relative error = 1.3021264874988143590802967777504e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (closed_form) = -2.3005194109297262912611505726609 y[1] (numeric) = -2.3005194109297262912611505726613 absolute error = 4e-31 relative error = 1.7387377741722465092103566700278e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = -2.2971219219640267249327716623727 y[1] (numeric) = -2.297121921964026724932771662373 absolute error = 3e-31 relative error = 1.3059820514163289812391868089187e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = -2.2937312650284054608743318851117 y[1] (numeric) = -2.2937312650284054608743318851121 absolute error = 4e-31 relative error = 1.7438834535616203438681647949807e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = -2.2903475296337077865130322753616 y[1] (numeric) = -2.2903475296337077865130322753619 absolute error = 3e-31 relative error = 1.3098448865006028071211061196738e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1491.6MB, alloc=44.3MB, time=17.95 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = -2.2869708053184851001841740614532 y[1] (numeric) = -2.2869708053184851001841740614534 absolute error = 2e-31 relative error = 8.7451925286885271285178229209719e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = -2.2836011816481890647729586884774 y[1] (numeric) = -2.2836011816481890647729586884776 absolute error = 2e-31 relative error = 8.7580967117756528622162307619505e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = -2.2802387482143655192540884688261 y[1] (numeric) = -2.2802387482143655192540884688264 absolute error = 3e-31 relative error = 1.3156517063615698362864038800256e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = -2.276883594633848155383958562862 y[1] (numeric) = -2.2768835946338481553839585628624 absolute error = 4e-31 relative error = 1.7567872197890076506628052567812e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (closed_form) = -2.2735358105479519668023446173072 y[1] (numeric) = -2.2735358105479519668023446173076 absolute error = 4e-31 relative error = 1.7593740909829555341399273191336e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = -2.2701954856216664778025387019458 y[1] (numeric) = -2.2701954856216664778025387019461 absolute error = 3e-31 relative error = 1.3214721018522707056336081078499e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = -2.2668627095428487590308691677129 y[1] (numeric) = -2.2668627095428487590308691677132 absolute error = 3e-31 relative error = 1.3234149502618095415356172093745e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = -2.2635375720214162373784576833481 y[1] (numeric) = -2.2635375720214162373784576833484 absolute error = 3e-31 relative error = 1.3253590473079259300367234777472e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = -2.2602201627885393073299189762699 y[1] (numeric) = -2.2602201627885393073299189762702 absolute error = 3e-31 relative error = 1.3273043260966045510763736598226e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = -2.2569105715958337510354956894998 y[1] (numeric) = -2.2569105715958337510354956895001 absolute error = 3e-31 relative error = 1.3292507189944778534314776983313e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = -2.2536088882145529743748422542616 y[1] (numeric) = -2.2536088882145529743748422542619 absolute error = 3e-31 relative error = 1.3311981576256489612314250503677e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (closed_form) = -2.2503152024347800662823277517938 y[1] (numeric) = -2.2503152024347800662823277517942 absolute error = 4e-31 relative error = 1.7775287638247781460108177528112e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1532.2MB, alloc=44.3MB, time=18.43 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = -2.247029604064619688605318383054 y[1] (numeric) = -2.2470296040646196886053183830544 absolute error = 4e-31 relative error = 1.7801278598040974862126504327058e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = -2.2437521829293898037684253670284 y[1] (numeric) = -2.2437521829293898037684253670288 absolute error = 4e-31 relative error = 1.7827280706096938776296610840285e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = -2.2404830288708132475181638335818 y[1] (numeric) = -2.2404830288708132475181638335821 absolute error = 3e-31 relative error = 1.3389969758048011846320582063716e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = -2.2372222317462091540238625520325 y[1] (numeric) = -2.2372222317462091540238625520326 absolute error = 1e-31 relative error = 4.4698286375398407856022065640029e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = -2.2339698814276842406119931293884 y[1] (numeric) = -2.2339698814276842406119931293886 absolute error = 2e-31 relative error = 8.9526721762329271076057540837933e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = -2.2307260678013239594123506104535 y[1] (numeric) = -2.2307260678013239594123506104538 absolute error = 3e-31 relative error = 1.3448536076672549065048834333477e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = -2.227490880766383523195715204455 y[1] (numeric) = -2.2274908807663835231957152044553 absolute error = 3e-31 relative error = 1.3468068605371032599502335791171e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = -2.2242644102344788126837571386614 y[1] (numeric) = -2.2242644102344788126837571386618 absolute error = 4e-31 relative error = 1.7983473464732215219889139851711e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = -2.221046746128777172613013388475 y[1] (numeric) = -2.2210467461287771726130133884753 absolute error = 3e-31 relative error = 1.3507144796609601877788681031993e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = -2.2178379783831881038357662460808 y[1] (numeric) = -2.2178379783831881038357662460811 absolute error = 3e-31 relative error = 1.3526686932230328361370779338724e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = -2.2146381969415538587415893569213 y[1] (numeric) = -2.2146381969415538587415893569216 absolute error = 3e-31 relative error = 1.3546230730342507912042763972088e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = -2.2114474917568399472841969666007 y[1] (numeric) = -2.2114474917568399472841969666011 absolute error = 4e-31 relative error = 1.8087700544145773558263686556807e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1572.7MB, alloc=44.3MB, time=18.91 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = -2.2082659527903255608990366724942 y[1] (numeric) = -2.2082659527903255608990366724945 absolute error = 3e-31 relative error = 1.3585320174905805101492852519920e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = -2.2050936700107939215978049570901 y[1] (numeric) = -2.2050936700107939215978049570904 absolute error = 3e-31 relative error = 1.3604864232299551321158968143107e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = -2.2019307333937225635267381872835 y[1] (numeric) = -2.2019307333937225635267381872839 absolute error = 4e-31 relative error = 1.8165875698710130520348103602907e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = -2.1987772329204735542761395894042 y[1] (numeric) = -2.1987772329204735542761395894046 absolute error = 4e-31 relative error = 1.8191929314672296990831900042197e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = -2.1956332585774836632291449482316 y[1] (numeric) = -2.1956332585774836632291449482319 absolute error = 3e-31 relative error = 1.3663484046254850991374338561572e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = -2.1924989003554544842382064247431 y[1] (numeric) = -2.1924989003554544842382064247434 absolute error = 3e-31 relative error = 1.3683017124951036556975231862758e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = -2.1893742482485425199181849375727 y[1] (numeric) = -2.189374248248542519918184937573 absolute error = 3e-31 relative error = 1.3702545384371550734013658120955e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = -2.1862593922535492348452870034167 y[1] (numeric) = -2.186259392253549234845287003417 absolute error = 3e-31 relative error = 1.3722067978894601434126742412220e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = -2.1831544223691110849513617788178 y[1] (numeric) = -2.1831544223691110849513617788182 absolute error = 4e-31 relative error = 1.8322112073314942690764124470278e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = -2.1800594285948895304032882873528 y[1] (numeric) = -2.1800594285948895304032882873532 absolute error = 4e-31 relative error = 1.8348123668252998343131182992805e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (closed_form) = -2.1769745009307610392573314503282 y[1] (numeric) = -2.1769745009307610392573314503285 absolute error = 3e-31 relative error = 1.3780593198116726104664231544049e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = -2.1738997293760070891784285643056 y[1] (numeric) = -2.1738997293760070891784285643059 absolute error = 3e-31 relative error = 1.3800084518438739080318250329778e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1613.2MB, alloc=44.3MB, time=19.39 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = -2.1708352039285041745143852843921 y[1] (numeric) = -2.1708352039285041745143852843924 absolute error = 3e-31 relative error = 1.3819565826880722202736872945665e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = -2.1677810145839138260149119780801 y[1] (numeric) = -2.1677810145839138260149119780803 absolute error = 2e-31 relative error = 9.2260241534769696703494023529432e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = -2.1647372513348726504853175109455 y[1] (numeric) = -2.1647372513348726504853175109457 absolute error = 2e-31 relative error = 9.2389965515062468599670227656823e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = -2.161704004170182397664498113729 y[1] (numeric) = -2.1617040041701823976644981137291 absolute error = 1e-31 relative error = 4.6259802362898984535718163721004e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = -2.1586813630740000616166139618532 y[1] (numeric) = -2.1586813630740000616166139618533 absolute error = 1e-31 relative error = 4.6324576526476445279190189715421e-30 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = -2.1556694180250280239255354754732 y[1] (numeric) = -2.1556694180250280239255354754735 absolute error = 3e-31 relative error = 1.3916790649414728687615393810398e-29 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; Iterations = 4900 Total Elapsed Time = 19 Seconds Elapsed Time(since restart) = 19 Seconds Time to Timeout = 2 Minutes 40 Seconds Percent Done = 100 % > quit memory used=1636.8MB, alloc=44.3MB, time=19.65