|\^/| Maple 18 (X86 64 WINDOWS) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" 0.0 Seconds\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 7; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 6 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 7 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 8 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 9 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 10 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 11 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 12 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 12 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 21 # Begin Function number 22 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 12 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 12; > if (errflag) then # if number 12 > quit; > fi;# end if 12 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 22 # Begin Function number 23 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 12 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 13 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 13 > fi;# end if 12; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 23 # Begin Function number 24 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 12 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 12; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 24 # Begin Function number 25 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 25 # Begin Function number 26 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 12 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalf(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalf(in_val); ret end proc # End Function number 27 # Begin Function number 28 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 12 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 12; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 28 # Begin Function number 29 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 29 # Begin Function number 30 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 15 > if (rcs > glob__0) then # if number 16 > rad_c := sqrt(rcs) * float_abs(glob_h); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 16 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > fi;# end if 13 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 12; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := sqrt(rcs)*float_abs(glob_h) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 30 # Begin Function number 31 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 31 # Begin Function number 32 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 32 # Begin Function number 33 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 12 > if (array_fact_1[nnn] = 0) then # if number 13 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 13; > else > ret := factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 33 # Begin Function number 34 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12 > if (array_fact_2[mmm,nnn] = 0) then # if number 13 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 13; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 12; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 35 # Begin Function number 36 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 36 # Begin Function number 37 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 37 # Begin Function number 38 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 38 # Begin Function number 39 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 39 # Begin Function number 40 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 40 # Begin Function number 41 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 41 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(2.0) + cos(c(x)) + c(x)); > end; exact_soln_y := proc(x) return c(2.0) + cos(c(x)) + c(x) end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if (rad_given < glob_least_given_sing) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])* (array_x[1] - array_given_rad_poles[1, 1]) + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if rad_given < glob_least_given_sing then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if array_rad_test_poles[1, 1] < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if array_rad_test_poles[1, 2] < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if array_rad_test_poles[1, 3] < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #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_g, > array_tmp2, > array_tmp3, > 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_1D0, 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_g, array_tmp2, array_tmp3, 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_1D0, #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_g, > array_tmp2, > array_tmp3, > 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_1D0, 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_g, array_tmp2, array_tmp3, 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_1D0, #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_g, > array_tmp2, > array_tmp3, > 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_1D0, 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_g, array_tmp2, array_tmp3, 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_1D0, #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_g, > array_tmp2, > array_tmp3, > 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_1D0, 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_g, array_tmp2, array_tmp3, 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_1D0, #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_g, > array_tmp2, > array_tmp3, > 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)*19*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_1D0, 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_g, array_tmp2, array_tmp3, 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)*19*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_1D0, #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_g, > array_tmp2, > array_tmp3, > 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_1D0, 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_g, array_tmp2, array_tmp3, 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_1D0, #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_g, > array_tmp2, > array_tmp3, > 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_1D0, 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_g, array_tmp2, array_tmp3, 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_1D0, #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_g, > array_tmp2, > array_tmp3, > 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 add CONST CONST $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D0[1] + array_const_1D0[1]; > #emit pre sin 1 $eq_no = 1 > array_tmp2[1] := sin(array_x[1]); > array_tmp2_g[1] := cos(array_x[1]); > #emit pre sub CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp1[1] - array_tmp2[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_tmp3[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 sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp2[2] := array_tmp2_g[1] * array_x[2] / c(1); > array_tmp2_g[2] := neg(array_tmp2[1]) * array_x[2] / c(1); > #emit pre sub CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp1[2] - array_tmp2[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_tmp3[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_tmp2[3] := array_tmp2_g[2] * array_x[2] / c(2); > array_tmp2_g[3] := neg(array_tmp2[2]) * array_x[2] / c(2); > #emit pre sub CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp1[3] - array_tmp2[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_tmp3[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_tmp2[4] := array_tmp2_g[3] * array_x[2] / c(3); > array_tmp2_g[4] := neg(array_tmp2[3]) * array_x[2] / c(3); > #emit pre sub CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp1[4] - array_tmp2[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_tmp3[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_tmp2[5] := array_tmp2_g[4] * array_x[2] / c(4); > array_tmp2_g[5] := neg(array_tmp2[4]) * array_x[2] / c(4); > #emit pre sub CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp1[5] - array_tmp2[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_tmp3[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_tmp2[kkk] := array_tmp2_g[kkk - 1] * array_x[2] / c(kkk - 1); > array_tmp2_g[kkk] := neg(array_tmp2[kkk - 1]) * array_x[2] / c(kkk - 1); > #emit NOT FULL - FULL sub $eq_no = 1 > array_tmp3[kkk] := neg( array_tmp2[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_tmp3[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_1D0, 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_g, array_tmp2, array_tmp3, 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_0D0[1] + array_const_1D0[1]; array_tmp2[1] := sin(array_x[1]); array_tmp2_g[1] := cos(array_x[1]); array_tmp3[1] := array_tmp1[1] - array_tmp2[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp3[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_tmp2[2] := array_tmp2_g[1]*array_x[2]/c(1); array_tmp2_g[2] := neg(array_tmp2[1])*array_x[2]/c(1); array_tmp3[2] := array_tmp1[2] - array_tmp2[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp3[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_tmp2[3] := array_tmp2_g[2]*array_x[2]/c(2); array_tmp2_g[3] := neg(array_tmp2[2])*array_x[2]/c(2); array_tmp3[3] := array_tmp1[3] - array_tmp2[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp3[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_tmp2[4] := array_tmp2_g[3]*array_x[2]/c(3); array_tmp2_g[4] := neg(array_tmp2[3])*array_x[2]/c(3); array_tmp3[4] := array_tmp1[4] - array_tmp2[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp3[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_tmp2[5] := array_tmp2_g[4]*array_x[2]/c(4); array_tmp2_g[5] := neg(array_tmp2[4])*array_x[2]/c(4); array_tmp3[5] := array_tmp1[5] - array_tmp2[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp3[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_tmp2[kkk] := array_tmp2_g[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp2_g[kkk] := neg(array_tmp2[kkk - 1])*array_x[2]/c(kkk - 1) ; array_tmp3[kkk] := neg(array_tmp2[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_tmp3[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_1D0, > #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_g, > array_tmp2, > array_tmp3, > 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_g:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= 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_g[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[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_g); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > 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_1D0); > array_const_1D0[1] := c(1.0); > 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_c_sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = 1.0 - sin ( x ) ; "); > 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,"return(c(2.0) + cos(c(x)) + c(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(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 ) = 1.0 - sin ( x ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2015-04-24T20:37:13-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sub_c_sin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = 1.0 - sin ( x ) ; ") > ; > 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_c_sin diffeq.mxt") > ; > logitem_str(html_log_file,"sub_c_sin 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_1D0, 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_g, array_tmp2, array_tmp3, 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_g := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := 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_g[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[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_g); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); 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_1D0); array_const_1D0[1] := c(1.0); 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_c_sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; "); 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, "return(c(2.0) + cos(c(x)) + c(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(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 ) = 1.0 - sin ( x ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2015-04-24T20:37:13-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sub_c_sin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0 - sin ( x ) ; "); 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_c_sin diffeq.mxt"); logitem_str(html_log_file, "sub_c_sin 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_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 - sin ( x ) ; ! #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(2.0) + cos(c(x)) + c(x)); 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) = 3.0950041652780257660955619878039 y[1] (numeric) = 3.0950041652780257660955619878039 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = 0.001 memory used=4.1MB, alloc=40.3MB, time=0.08 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 3.1039560979566968503578396114198 y[1] (numeric) = 3.1039560979566968503578396114199 absolute error = 1e-31 relative error = 3.2216950512228248477322727786089e-30 % 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) = 3.1128086358538662522480981678576 y[1] (numeric) = 3.1128086358538662522480981678577 absolute error = 1e-31 relative error = 3.2125328504997952162002531895393e-30 % 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) = 3.1215618937147880395945121711518 y[1] (numeric) = 3.121561893714788039594512171152 absolute error = 2e-31 relative error = 6.4070489969363288892167084945809e-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) = 3.1302159962126371718989482270114 y[1] (numeric) = 3.1302159962126371718989482270116 absolute error = 2e-31 relative error = 6.3893354401736913818032079183781e-30 % 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) = 3.1387710779360422867349809986543 y[1] (numeric) = 3.1387710779360422867349809986545 absolute error = 2e-31 relative error = 6.3719205712674575207885231191766e-30 % 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) = 3.1472272833756269490409525240183 y[1] (numeric) = 3.1472272833756269490409525240185 absolute error = 2e-31 relative error = 6.3548000189387548141437004093540e-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) = 3.1555847669095607091719299902125 y[1] (numeric) = 3.1555847669095607091719299902126 absolute error = 1e-31 relative error = 3.1689847488373937676984049941661e-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) = 3.1638436927881214145927160246115 y[1] (numeric) = 3.1638436927881214145927160246116 absolute error = 1e-31 relative error = 3.1607124027001315177688082954641e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (closed_form) = 3.1720042351172703189678775041899 y[1] (numeric) = 3.1720042351172703189678775041901 absolute error = 2e-31 relative error = 6.3051618212169857528837128575665e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 3.1800665778412416311241965167482 y[1] (numeric) = 3.1800665778412416311241965167485 absolute error = 3e-31 relative error = 9.4337647548137871422993462318180e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = 3.1880309147241482449161385680994 y[1] (numeric) = 3.1880309147241482449161385680997 absolute error = 3e-31 relative error = 9.4101973294684375571744837799890e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 3.1958974493306054894060229810447 y[1] (numeric) = 3.1958974493306054894060229810452 absolute error = 5e-31 relative error = 1.5645057700606981535878863022397e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 memory used=44.7MB, alloc=44.3MB, time=0.55 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = 3.2036663950053748369677306480716 y[1] (numeric) = 3.2036663950053748369677306480722 absolute error = 6e-31 relative error = 1.8728541802461718908522134049683e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = 3.2113379748520296049261752469634 y[1] (numeric) = 3.2113379748520296049261752469641 absolute error = 7e-31 relative error = 2.1797767954718445459166360502552e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = 3.2189124217106447841445954494942 y[1] (numeric) = 3.218912421710644784144595449495 absolute error = 8e-31 relative error = 2.4853114816179170469619777949262e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (closed_form) = 3.2263899781345132255582176464501 y[1] (numeric) = 3.226389978134513225558217646451 absolute error = 9e-31 relative error = 2.7894953991903256451830886985686e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (closed_form) = 3.2337708963658905130162327094922 y[1] (numeric) = 3.2337708963658905130162327094933 absolute error = 1.1e-30 relative error = 3.4016015211101665732735952032914e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (closed_form) = 3.2410554383107709479245900535965 y[1] (numeric) = 3.2410554383107709479245900535975 absolute error = 1.0e-30 relative error = 3.0854146713429783541537511765125e-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) = 3.2482438755126971680701247779319 y[1] (numeric) = 3.2482438755126971680701247779329 absolute error = 1.0e-30 relative error = 3.0785865788545871973244494334454e-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) = 3.255336489125606019642310227568 y[1] (numeric) = 3.255336489125606019642310227569 absolute error = 1.0e-30 relative error = 3.0718790617820379484054632327009e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (closed_form) = 3.2623335698857133978428054362022 y[1] (numeric) = 3.2623335698857133978428054362032 absolute error = 1.0e-30 relative error = 3.0652904694691664017608299846823e-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) = 3.2692354180824408675753072737661 y[1] (numeric) = 3.2692354180824408675753072737671 absolute error = 1.0e-30 relative error = 3.0588191797657284199482888292012e-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) = 3.2760423435283869715294105783662 y[1] (numeric) = 3.2760423435283869715294105783671 absolute error = 9e-31 relative error = 2.7472172384398287379667693935807e-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) = 3.2827546655283462285026440600266 y[1] (numeric) = 3.2827546655283462285026440600275 absolute error = 9e-31 relative error = 2.7415999418133447418861107306778e-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) = 3.2893727128473789200350323573037 y[1] (numeric) = 3.2893727128473789200350323573045 absolute error = 8e-31 relative error = 2.4320746532474764467756603702147e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=85.1MB, alloc=44.3MB, time=1.00 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (closed_form) = 3.2958968236779348583509123681247 y[1] (numeric) = 3.2958968236779348583509123681255 absolute error = 8e-31 relative error = 2.4272604477565818304043947817664e-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) = 3.3023273456060344232038129044909 y[1] (numeric) = 3.3023273456060344232038129044916 absolute error = 7e-31 relative error = 2.1197171774366839526676132426475e-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) = 3.3086646355765102494925308077246 y[1] (numeric) = 3.3086646355765102494925308077251 absolute error = 5e-31 relative error = 1.5111836800373656242717441491613e-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) = 3.3149090598573130414506767528811 y[1] (numeric) = 3.3149090598573130414506767528816 absolute error = 5e-31 relative error = 1.5083370040369131633352938616644e-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) = 3.3210609940028850827985267320518 y[1] (numeric) = 3.3210609940028850827985267320523 absolute error = 5e-31 relative error = 1.5055429602253358626219229467023e-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) = 3.327120822816605105475642058277 y[1] (numeric) = 3.3271208228166051054756420582777 absolute error = 7e-31 relative error = 2.1039211897553166811107232138159e-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) = 3.3330889403123082724360887896657 y[1] (numeric) = 3.3330889403123082724360887896664 absolute error = 7e-31 relative error = 2.1001539788926558134396067398811e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (closed_form) = 3.3389657496748851224759104776634 y[1] (numeric) = 3.3389657496748851224759104776642 absolute error = 8e-31 relative error = 2.3959515010835194936720830049415e-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) = 3.3447516632199634171655373889984 y[1] (numeric) = 3.3447516632199634171655373889991 absolute error = 7e-31 relative error = 2.0928310095408281256279916717820e-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) = 3.3504471023526769216688406114864 y[1] (numeric) = 3.3504471023526769216688406114873 absolute error = 9e-31 relative error = 2.6862086536690040244855102532545e-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) = 3.3560524975255252425363899035004 y[1] (numeric) = 3.3560524975255252425363899035012 absolute error = 8e-31 relative error = 2.3837529376845375548595006002408e-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) = 3.3615682881953289364540192765334 y[1] (numeric) = 3.3615682881953289364540192765343 absolute error = 9e-31 relative error = 2.6773217820994156117400110373070e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=125.7MB, alloc=44.3MB, time=1.45 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (closed_form) = 3.3669949227792841943999548311587 y[1] (numeric) = 3.3669949227792841943999548311596 absolute error = 9e-31 relative error = 2.6730067037258715902100506393341e-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) = 3.3723328586101214957054681591367 y[1] (numeric) = 3.3723328586101214957054681591375 absolute error = 8e-31 relative error = 2.3722450705228227175766798548358e-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) = 3.3775825618903727161162815826038 y[1] (numeric) = 3.3775825618903727161162815826046 absolute error = 8e-31 relative error = 2.3685579414889395600351408061544e-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) = 3.3827445076457512631058084735755 y[1] (numeric) = 3.3827445076457512631058084735763 absolute error = 8e-31 relative error = 2.3649436077475639747223164746453e-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) = 3.3878191796776499003878475719885 y[1] (numeric) = 3.3878191796776499003878475719893 absolute error = 8e-31 relative error = 2.3614011184508371210522739589581e-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) = 3.3928070705147610118066950185642 y[1] (numeric) = 3.3928070705147610118066950185649 absolute error = 7e-31 relative error = 2.0631883436089253022854878876514e-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) = 3.3977086813638241425379687789178 y[1] (numeric) = 3.3977086813638241425379687789184 absolute error = 6e-31 relative error = 1.7658959500882307749997115559134e-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) = 3.4025245220595057428049817976178 y[1] (numeric) = 3.4025245220595057428049817976184 absolute error = 6e-31 relative error = 1.7633965489742524120134895672683e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (closed_form) = 3.4072551110134161260945255038663 y[1] (numeric) = 3.4072551110134161260945255038669 absolute error = 6e-31 relative error = 1.7609482719993416119456868101603e-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) = 3.411900975162268740133756363916 y[1] (numeric) = 3.4119009751622687401337563639167 absolute error = 7e-31 relative error = 2.0516421932987321257435257465307e-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) = 3.41646264991518693465788732805 y[1] (numeric) = 3.4164626499151869346578873280507 absolute error = 7e-31 relative error = 2.0489028323414493437529648005735e-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) = 3.4209406791001634952479965224907 y[1] (numeric) = 3.4209406791001634952479965224913 absolute error = 6e-31 relative error = 1.7539035495869008870777639754127e-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) = 3.4253356149096782972409524989554 y[1] (numeric) = 3.425335614909678297240952498956 absolute error = 6e-31 relative error = 1.7516531734535485210460504566841e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=166.3MB, alloc=44.3MB, time=1.91 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (closed_form) = 3.4296480178454795179007465786548 y[1] (numeric) = 3.4296480178454795179007465786555 absolute error = 7e-31 relative error = 2.0410257739502468928191318509279e-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) = 3.4338784566625339286839996543607 y[1] (numeric) = 3.4338784566625339286839996543613 absolute error = 6e-31 relative error = 1.7472953908309087571681230740420e-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) = 3.4380275083121518725237089657771 y[1] (numeric) = 3.4380275083121518725237089657775 absolute error = 4e-31 relative error = 1.1634578229316553979036766759670e-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) = 3.4420957578842926135861107792603 y[1] (numeric) = 3.4420957578842926135861107792608 absolute error = 5e-31 relative error = 1.4526033997012575101274572316985e-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) = 3.4460837985490558289176045706799 y[1] (numeric) = 3.4460837985490558289176045706802 absolute error = 3e-31 relative error = 8.7055340942757236345350690234214e-30 % 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) = 3.4499922314973650927838170912302 y[1] (numeric) = 3.4499922314973650927838170912306 absolute error = 4e-31 relative error = 1.1594229005738719072148524674861e-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) = 3.4538216658808492853029421448381 y[1] (numeric) = 3.4538216658808492853029421448386 absolute error = 5e-31 relative error = 1.4476717340079628540247213243432e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (closed_form) = 3.4575727187509279371823940840443 y[1] (numeric) = 3.4575727187509279371823940840448 absolute error = 5e-31 relative error = 1.4461011833198072513981000322964e-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) = 3.4612460149971066019735393154978 y[1] (numeric) = 3.4612460149971066019735393154981 absolute error = 3e-31 relative error = 8.6673989280201679726463711093535e-30 % 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) = 3.4648421872844884262558599901919 y[1] (numeric) = 3.4648421872844884262558599901922 absolute error = 3e-31 relative error = 8.6584030032005566075527761925502e-30 % 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) = 3.4683618759905081665414579441396 y[1] (numeric) = 3.4683618759905081665414579441398 absolute error = 2e-31 relative error = 5.7664109787529949809262151864750e-30 % 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) = 3.471805729140894979445486962252 y[1] (numeric) = 3.4718057291408949794454869622521 absolute error = 1e-31 relative error = 2.8803454974637994153557481678468e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=206.8MB, alloc=44.3MB, time=2.36 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (closed_form) = 3.4751744023448703887901321585503 y[1] (numeric) = 3.4751744023448703887901321585504 absolute error = 1e-31 relative error = 2.8775534238662986767554043513814e-30 % 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) = 3.4784685587295879097914245606988 y[1] (numeric) = 3.4784685587295879097914245606988 absolute error = 0 relative error = 0 % 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) = 3.4816888688738208863118387530001 y[1] (numeric) = 3.4816888688738208863118387529999 absolute error = 2e-31 relative error = 5.7443386681674270998377364051669e-30 % 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) = 3.484836010740905172339688366667 y[1] (numeric) = 3.4848360107409051723396883666669 absolute error = 1e-31 relative error = 2.8695754891128769866267188675785e-30 % 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) = 3.4879106696109433633712905653243 y[1] (numeric) = 3.4879106696109433633712905653243 absolute error = 0 relative error = 0 % 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) = 3.4909135380122773572162650237646 y[1] (numeric) = 3.4909135380122773572162650237646 absolute error = 0 relative error = 0 % 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) = 3.493845315652236096912780861085 y[1] (numeric) = 3.4938453156522360969127808610848 absolute error = 2e-31 relative error = 5.7243518796900059877538253196633e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (closed_form) = 3.4967067093471654209207499816423 y[1] (numeric) = 3.496706709347165420920749981642 absolute error = 3e-31 relative error = 8.5795013690470468897208934427449e-30 % 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) = 3.4994984329517470175496392406801 y[1] (numeric) = 3.4994984329517470175496392406799 absolute error = 2e-31 relative error = 5.7151047166294790129981739161012e-30 % 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) = 3.5022212072876135516665579784369 y[1] (numeric) = 3.5022212072876135516665579784369 absolute error = 0 relative error = 0 % 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) = 3.5048757600712671021124629178644 y[1] (numeric) = 3.5048757600712671021124629178645 absolute error = 1e-31 relative error = 2.8531681818577965718931818123351e-30 % 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) = 3.5074628258413081179226710368709 y[1] (numeric) = 3.507462825841308117922671036871 absolute error = 1e-31 relative error = 2.8510637165773458911937855044444e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=247.3MB, alloc=44.3MB, time=2.81 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (closed_form) = 3.5099831458849821703954160294615 y[1] (numeric) = 3.5099831458849821703954160294617 absolute error = 2e-31 relative error = 5.6980330584913228513271161503349e-30 % 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) = 3.5124374681640518462720306642239 y[1] (numeric) = 3.5124374681640518462720306642241 absolute error = 2e-31 relative error = 5.6940515471878232255879479949261e-30 % 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) = 3.5148265472400011947776638054828 y[1] (numeric) = 3.5148265472400011947776638054831 absolute error = 3e-31 relative error = 8.5352718254496342189314744105305e-30 % 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) = 3.5171511441985802080154986057221 y[1] (numeric) = 3.5171511441985802080154986057223 absolute error = 2e-31 relative error = 5.6864203953786040236837041048553e-30 % 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) = 3.5194120265736968802035530573802 y[1] (numeric) = 3.5194120265736968802035530573805 absolute error = 3e-31 relative error = 8.5241511290754795786635193640504e-30 % 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) = 3.5216099682706644564847161514071 y[1] (numeric) = 3.5216099682706644564847161514076 absolute error = 5e-31 relative error = 1.4198051587340660345373738094225e-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) = 3.5237457494888115465211782261747 y[1] (numeric) = 3.5237457494888115465211782261753 absolute error = 6e-31 relative error = 1.7027335189749197183852839667981e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (closed_form) = 3.5258201566434628417974047066744 y[1] (numeric) = 3.5258201566434628417974047066748 absolute error = 4e-31 relative error = 1.1344878134135889963402796414009e-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) = 3.527833982287298238494907084433 y[1] (numeric) = 3.5278339822872982384949070844334 absolute error = 4e-31 relative error = 1.1338402033892108777899890804239e-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) = 3.529788025031098229960989815224 y[1] (numeric) = 3.5297880250310982299609898152243 absolute error = 3e-31 relative error = 8.4990939363095870954768141733338e-30 % 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) = 3.5316830894638834941661809737605 y[1] (numeric) = 3.5316830894638834941661809737605 absolute error = 0 relative error = 0 % 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) = 3.5335199860724566621250508003519 y[1] (numeric) = 3.5335199860724566621250508003518 absolute error = 1e-31 relative error = 2.8300391788968205392836334383088e-30 % 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) = 3.5352995311603543130365277548499 y[1] (numeric) = 3.5352995311603543130365277548498 absolute error = 1e-31 relative error = 2.8286146369945080172726327160233e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=287.8MB, alloc=44.3MB, time=3.28 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (closed_form) = 3.5370225467662173008766582673599 y[1] (numeric) = 3.5370225467662173008766582673599 absolute error = 0 relative error = 0 % 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) = 3.5386898605815875753431264086536 y[1] (numeric) = 3.5386898605815875753431264086538 absolute error = 2e-31 relative error = 5.6518092254383033093144319418547e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 3.540302305868139717400936607443 y[1] (numeric) = 3.5403023058681397174009366074431 absolute error = 1e-31 relative error = 2.8246175428083499001141460877422e-30 % 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) = 3.5418607213743554662067313557792 y[1] (numeric) = 3.5418607213743554662067313557791 absolute error = 1e-31 relative error = 2.8233747136504225748167411954768e-30 % 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) = 3.5433659512516495698896138080338 y[1] (numeric) = 3.5433659512516495698896138080338 absolute error = 0 relative error = 0 % 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) = 3.5448188449699553475335022998374 y[1] (numeric) = 3.5448188449699553475335022998373 absolute error = 1e-31 relative error = 2.8210186295386715380447050770795e-30 % 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) = 3.5462202572327784037344734209922 y[1] (numeric) = 3.5462202572327784037344734209922 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = 3.5475710478917269902908495728121 y[1] (numeric) = 3.5475710478917269902908495728121 absolute error = 0 relative error = 0 % 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) = 3.5488720818605275619186375399564 y[1] (numeric) = 3.5488720818605275619186375399566 absolute error = 2e-31 relative error = 5.6355933769004216107193802276430e-30 % 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) = 3.5501242290285341243650930681759 y[1] (numeric) = 3.5501242290285341243650930681762 absolute error = 3e-31 relative error = 8.4504085109746380631831148086955e-30 % 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) = 3.551328364173740023913524788526 y[1] (numeric) = 3.5513283641737400239135247885263 absolute error = 3e-31 relative error = 8.4475432637105262146219261679583e-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) = 3.5524853668753008770278970738751 y[1] (numeric) = 3.5524853668753008770278970738754 absolute error = 3e-31 relative error = 8.4447919982250156741772983142584e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=328.5MB, alloc=44.3MB, time=3.73 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 3.5535961214255773877713700517847 y[1] (numeric) = 3.553596121425577387771370051785 absolute error = 3e-31 relative error = 8.4421523929300830181340110898159e-30 % 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) = 3.5546615167417068486437375119336 y[1] (numeric) = 3.5546615167417068486437375119338 absolute error = 2e-31 relative error = 5.6264147530796430532292249408566e-30 % 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) = 3.5556824462767121676139887939611 y[1] (numeric) = 3.5556824462767121676139887939615 absolute error = 4e-31 relative error = 1.1249598524155466499607038189823e-29 % 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) = 3.5566598079301573103712158356535 y[1] (numeric) = 3.5566598079301573103712158356538 absolute error = 3e-31 relative error = 8.4348803709340071727779559702811e-30 % 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) = 3.5575945039583580921751867408226 y[1] (numeric) = 3.5575945039583580921751867408229 absolute error = 3e-31 relative error = 8.4326642529440877018902364096697e-30 % 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) = 3.5584874408841572981525767188099 y[1] (numeric) = 3.5584874408841572981525767188102 absolute error = 3e-31 relative error = 8.4305482310613605127913005729037e-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) = 3.559339529406273154451639623394 y[1] (numeric) = 3.5593395294062731544516396233941 absolute error = 1e-31 relative error = 2.8095099996453784530148562784690e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = 3.5601516843082302153326619350505 y[1] (numeric) = 3.5601516843082302153326619350506 absolute error = 1e-31 relative error = 2.8088690838865453456989259190617e-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) = 3.5609248243668817730295994667128 y[1] (numeric) = 3.5609248243668817730295994667129 absolute error = 1e-31 relative error = 2.8082592284935304983915488680830e-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) = 3.5616598722605329380656795583505 y[1] (numeric) = 3.5616598722605329380656795583507 absolute error = 2e-31 relative error = 5.6153593316888777680061881698663e-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) = 3.5623577544766735776383733556231 y[1] (numeric) = 3.5623577544766735776383733556233 absolute error = 2e-31 relative error = 5.6142592570515395108606732783355e-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) = 3.5630194012193303387030107136648 y[1] (numeric) = 3.5630194012193303387030107136649 absolute error = 1e-31 relative error = 2.8066083492494644544744698055316e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=369.1MB, alloc=44.3MB, time=4.19 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = 3.5636457463160470204755229744352 y[1] (numeric) = 3.5636457463160470204755229744353 absolute error = 1e-31 relative error = 2.8061150607738145518606059662321e-30 % 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) = 3.5642377271245025982395472454977 y[1] (numeric) = 3.5642377271245025982395472454979 absolute error = 2e-31 relative error = 5.6112979916564860547368349499170e-30 % 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) = 3.5647962844387762365776934156974 y[1] (numeric) = 3.5647962844387762365776934156976 absolute error = 2e-31 relative error = 5.6104187740839446983340185764566e-30 % 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) = 3.565322362395268665447538552438 y[1] (numeric) = 3.5653223623952686654475385524382 absolute error = 2e-31 relative error = 5.6095909337531887608621139971802e-30 % 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) = 3.5658169083782893268863424891765 y[1] (numeric) = 3.5658169083782893268863424891766 absolute error = 1e-31 relative error = 2.8044064675625580283075079444078e-30 % 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) = 3.566280872925318733551137016088 y[1] (numeric) = 3.5662808729253187335511370160881 absolute error = 1e-31 relative error = 2.8040416210395914543645534716043e-30 % 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) = 3.5667152096319555127793868935926 y[1] (numeric) = 3.5667152096319555127793868935927 absolute error = 1e-31 relative error = 2.8037001589010764858075389149045e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (closed_form) = 3.5671208750565576413866060900612 y[1] (numeric) = 3.5671208750565576413866060900613 absolute error = 1e-31 relative error = 2.8033813123423936019736437289817e-30 % 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) = 3.5674988286245874069979841092929 y[1] (numeric) = 3.5674988286245874069979841092932 absolute error = 3e-31 relative error = 8.4092529363397695596107311165831e-30 % 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) = 3.5678500325326696613381769786162 y[1] (numeric) = 3.5678500325326696613381769786166 absolute error = 4e-31 relative error = 1.1211233553896223858902063885313e-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) = 3.5681754516523729595739827294274 y[1] (numeric) = 3.5681754516523729595739827294276 absolute error = 2e-31 relative error = 5.6051055423124653711533770331213e-30 % 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) = 3.5684760534337232075157849860106 y[1] (numeric) = 3.5684760534337232075157849860109 absolute error = 3e-31 relative error = 8.4069500679801004821512877288444e-30 % 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) = 3.5687528078084594652326394923001 y[1] (numeric) = 3.5687528078084594652326394923006 absolute error = 5e-31 relative error = 1.4010496857781688661159836958788e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=409.9MB, alloc=44.3MB, time=4.64 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = 3.5690066870930415814200221730106 y[1] (numeric) = 3.5690066870930415814200221730112 absolute error = 6e-31 relative error = 1.6811400274755450670454784050255e-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) = 3.5692386658914193576759752523919 y[1] (numeric) = 3.5692386658914193576759752523924 absolute error = 5e-31 relative error = 1.4008589696680446548574759246964e-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) = 3.5694497209975729656881983896453 y[1] (numeric) = 3.5694497209975729656881983896459 absolute error = 6e-31 relative error = 1.6809313672929810342898520015739e-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) = 3.5696408312978343632091500735982 y[1] (numeric) = 3.5696408312978343632091500735989 absolute error = 7e-31 relative error = 1.9609816031421207970162049637676e-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) = 3.569812977672999476596163217804 y[1] (numeric) = 3.5698129776729994765961632178049 absolute error = 9e-31 relative error = 2.5211404788680821071754371765028e-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) = 3.5699671429002409386167480352036 y[1] (numeric) = 3.5699671429002409386167480352047 absolute error = 1.1e-30 relative error = 3.0812608519034158770303405299793e-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) = 3.5701043115548311901635625493609 y[1] (numeric) = 3.570104311554831190163562549362 absolute error = 1.1e-30 relative error = 3.0811424653329929157063787197962e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = 3.5702254699116857734869821029759 y[1] (numeric) = 3.570225469911685773486982102977 absolute error = 1.1e-30 relative error = 3.0810379043853775093322283107273e-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) = 3.5703316058467366625338976245749 y[1] (numeric) = 3.570331605846736662533897624576 absolute error = 1.1e-30 relative error = 3.0809463137783947664505990583943e-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) = 3.5704237087381454929775201561292 y[1] (numeric) = 3.5704237087381454929775201561303 absolute error = 1.1e-30 relative error = 3.0808668374789628832060728269566e-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) = 3.570502769367366570532866627248 y[1] (numeric) = 3.570502769367366570532866627249 absolute error = 1.0e-30 relative error = 2.8007260170174389488412488601674e-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) = 3.5705697798200695511746481091234 y[1] (numeric) = 3.5705697798200695511746481091242 absolute error = 8e-31 relative error = 2.2405387636488485446583083830627e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=450.5MB, alloc=44.3MB, time=5.09 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = 3.5706257333869317009069746014624 y[1] (numeric) = 3.5706257333869317009069746014632 absolute error = 8e-31 relative error = 2.2405036532382706912408356601084e-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) = 3.5706716244643096557762265406478 y[1] (numeric) = 3.5706716244643096557762265406487 absolute error = 9e-31 relative error = 2.5205342150022618899497262768631e-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) = 3.5707084484548006148683184845637 y[1] (numeric) = 3.5707084484548006148683184845646 absolute error = 9e-31 relative error = 2.5205082212451951247062536800349e-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) = 3.5707372016677029100881898514343 y[1] (numeric) = 3.5707372016677029100881898514352 absolute error = 9e-31 relative error = 2.5204879249575059605916179514793e-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) = 3.5707588812193859065815955149162 y[1] (numeric) = 3.5707588812193859065815955149171 absolute error = 9e-31 relative error = 2.5204726220344990661386722422815e-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) = 3.5707744849335791967261292701527 y[1] (numeric) = 3.5707744849335791967261292701536 absolute error = 9e-31 relative error = 2.5204616079716977939093882678710e-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) = 3.5707850112415910586889890070761 y[1] (numeric) = 3.570785011241591058688989007077 absolute error = 9e-31 relative error = 2.5204541779093630251551964793514e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = 3.5707914590824661576224768070764 y[1] (numeric) = 3.5707914590824661576224768070773 absolute error = 9e-31 relative error = 2.5204496266809705628924028006741e-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) = 3.5707948278030924736439127746956 y[1] (numeric) = 3.5707948278030924736439127746964 absolute error = 8e-31 relative error = 2.2403975545472452276443492867824e-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) = 3.5707961170582674458239206637609 y[1] (numeric) = 3.5707961170582674458239206637616 absolute error = 7e-31 relative error = 1.9603471524346836793928985124364e-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) = 3.5707963267107333254854085336454 y[1] (numeric) = 3.5707963267107333254854085336459 absolute error = 5e-31 relative error = 1.4002478838118971350802449555912e-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) = 3.5707964567311917351946109430173 y[1] (numeric) = 3.5707964567311917351946109430178 absolute error = 5e-31 relative error = 1.4002478328258289156915161481605e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=491.1MB, alloc=44.3MB, time=5.55 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = 3.5707975070983074319049726537566 y[1] (numeric) = 3.5707975070983074319049726537572 absolute error = 6e-31 relative error = 1.6802969051235014000527684053598e-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) = 3.5708004776987112737942295370535 y[1] (numeric) = 3.5708004776987112737942295370541 absolute error = 6e-31 relative error = 1.6802955072602782633075832619437e-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) = 3.570806368227012390414672390399 y[1] (numeric) = 3.5708063682270123904146723903995 absolute error = 5e-31 relative error = 1.4002439461545530868224835343648e-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) = 3.5708161780858295548562557252877 y[1] (numeric) = 3.5708161780858295548562557252883 absolute error = 6e-31 relative error = 1.6802881192322697095991590822774e-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) = 3.5708309062858517547020283025802 y[1] (numeric) = 3.5708309062858517547020283025809 absolute error = 7e-31 relative error = 1.9603280535288491160234084785487e-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) = 3.5708515513459379556355072925434 y[1] (numeric) = 3.570851551345937955635507292544 absolute error = 6e-31 relative error = 1.6802714741077541706338223796187e-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) = 3.5708791111932660476403854026587 y[1] (numeric) = 3.5708791111932660476403854026594 absolute error = 7e-31 relative error = 1.9603015901764422008974126988168e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = 3.5709145830635409588147420683494 y[1] (numeric) = 3.57091458306354095881474206835 absolute error = 6e-31 relative error = 1.6802418149281270064025063848036e-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) = 3.5709589634012719159052176575514 y[1] (numeric) = 3.570958963401271915905217657552 absolute error = 6e-31 relative error = 1.6802209326665327257654203123601e-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) = 3.5710132477601288237519952658272 y[1] (numeric) = 3.5710132477601288237519952658277 absolute error = 5e-31 relative error = 1.4001628258131454302480732101801e-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) = 3.5710784307033877279236095301669 y[1] (numeric) = 3.5710784307033877279236095301674 absolute error = 5e-31 relative error = 1.4001372686220057697928518513561e-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) = 3.5711555057044753159123571426651 y[1] (numeric) = 3.5711555057044753159123571426656 absolute error = 5e-31 relative error = 1.4001070499487137689559283042908e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=531.9MB, alloc=44.3MB, time=6.00 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = 3.5712454650476224023573102169489 y[1] (numeric) = 3.5712454650476224023573102169492 absolute error = 3e-31 relative error = 8.4004306882892888209205163341465e-30 % 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) = 3.5713492997286363328636217196688 y[1] (numeric) = 3.5713492997286363328636217196692 absolute error = 4e-31 relative error = 1.1200248601568975774327324930978e-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) = 3.5714679993558022290950516486574 y[1] (numeric) = 3.5714679993558022290950516486578 absolute error = 4e-31 relative error = 1.1199876355385218454302319063833e-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) = 3.5716025520509229849326226846549 y[1] (numeric) = 3.5716025520509229849326226846553 absolute error = 4e-31 relative error = 1.1199454423345839951999890192342e-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) = 3.5717539443505079096173230560574 y[1] (numeric) = 3.5717539443505079096173230560578 absolute error = 4e-31 relative error = 1.1198979723468506941272174883345e-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) = 3.5719231611071198989301998234959 y[1] (numeric) = 3.5719231611071198989301998234964 absolute error = 5e-31 relative error = 1.3998061476916672415891860889109e-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) = 3.5721111853908909996105141582696 y[1] (numeric) = 3.5721111853908909996105141582701 absolute error = 5e-31 relative error = 1.3997324664609668853288457120418e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = 3.5723189983912162153734467096874 y[1] (numeric) = 3.5723189983912162153734467096878 absolute error = 4e-31 relative error = 1.1197208317066277444310489997961e-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) = 3.5725475793186353850648297355354 y[1] (numeric) = 3.5725475793186353850648297355358 absolute error = 4e-31 relative error = 1.1196491890425401524125946081179e-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) = 3.5727979053069129446833256934694 y[1] (numeric) = 3.5727979053069129446833256934697 absolute error = 3e-31 relative error = 8.3967805610944342938240721480292e-30 % 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) = 3.573070951315325365212250149158 y[1] (numeric) = 3.5730709513153253652122501491582 absolute error = 2e-31 relative error = 5.5974259320648429026180660690392e-30 % 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) = 3.5733676900311660374358289551691 y[1] (numeric) = 3.5733676900311660374358289551693 absolute error = 2e-31 relative error = 5.5969611120051194341146487474844e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=572.6MB, alloc=44.3MB, time=6.45 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = 3.5736890917724773531701624163815 y[1] (numeric) = 3.5736890917724773531701624163816 absolute error = 1e-31 relative error = 2.7982288730775409154250723942655e-30 % 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) = 3.5740361243910197096197170167184 y[1] (numeric) = 3.5740361243910197096197170167185 absolute error = 1e-31 relative error = 2.7979571699779337764373483786398e-30 % 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) = 3.5744097531754871398780501645252 y[1] (numeric) = 3.5744097531754871398780501645252 absolute error = 0 relative error = 0 % 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) = 3.5748109407549792479290645117109 y[1] (numeric) = 3.5748109407549792479290645117108 absolute error = 1e-31 relative error = 2.7973507314733847850869577631407e-30 % 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) = 3.5752406470027391008748519351901 y[1] (numeric) = 3.57524064700273910087485193519 absolute error = 1e-31 relative error = 2.7970145193956055107142973617847e-30 % 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) = 3.5756998289401667045206862404778 y[1] (numeric) = 3.5756998289401667045206862404776 absolute error = 2e-31 relative error = 5.5933106683420842062876944724233e-30 % 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) = 3.5761894406411176608896175844488 y[1] (numeric) = 3.5761894406411176608896175844486 absolute error = 2e-31 relative error = 5.5925448950530206527491551294104e-30 % 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) = 3.5767104331364965777211663049197 y[1] (numeric) = 3.5767104331364965777211663049195 absolute error = 2e-31 relative error = 5.5917302711199791315206738835558e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = 3.5772637543191547705336610606025 y[1] (numeric) = 3.5772637543191547705336610606024 absolute error = 1e-31 relative error = 2.7954326789368252785566395547941e-30 % 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) = 3.577850348849101767400763396841 y[1] (numeric) = 3.5778503488491017674007633968408 absolute error = 2e-31 relative error = 5.5899487261767284674936588108806e-30 % 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) = 3.5784711580590400952127109352881 y[1] (numeric) = 3.5784711580590400952127109352879 absolute error = 2e-31 relative error = 5.5889789568257926281285867956611e-30 % 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) = 3.5791271198602327938649323141593 y[1] (numeric) = 3.5791271198602327938649323141591 absolute error = 2e-31 relative error = 5.5879546409575452039759128085161e-30 % 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) = 3.5798191686487130715441715408693 y[1] (numeric) = 3.5798191686487130715441715408691 absolute error = 2e-31 relative error = 5.5868743804591309346050511848546e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=613.4MB, alloc=44.3MB, time=6.92 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (closed_form) = 3.5805482352118454800684347845526 y[1] (numeric) = 3.5805482352118454800684347845523 absolute error = 3e-31 relative error = 8.3786051825733972727206851827285e-30 % 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) = 3.5813152466352479540853601861207 y[1] (numeric) = 3.5813152466352479540853601861205 absolute error = 2e-31 relative error = 5.5845404893608832780275838119920e-30 % 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) = 3.5821211262100840218475261400928 y[1] (numeric) = 3.5821211262100840218475261400926 absolute error = 2e-31 relative error = 5.5832841200320263031067157794857e-30 % 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) = 3.5829667933407344582663642838697 y[1] (numeric) = 3.5829667933407344582663642838694 absolute error = 3e-31 relative error = 8.3729494941894784091585967509288e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 3.5838531634528576130024317704992 y[1] (numeric) = 3.5838531634528576130024317704987 absolute error = 5e-31 relative error = 1.3951464448902694374083550754230e-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) = 3.5847811479018476074826176598346 y[1] (numeric) = 3.584781147901847607482617659834 absolute error = 6e-31 relative error = 1.6737423436607187311307380013305e-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) = 3.5857516538816995549482971259098 y[1] (numeric) = 3.5857516538816995549482971259093 absolute error = 5e-31 relative error = 1.3944077790739712675171249823249e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = 3.5867655843342909169364832683039 y[1] (numeric) = 3.5867655843342909169364832683035 absolute error = 4e-31 relative error = 1.1152108789798165780237662840877e-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) = 3.5878238378590880679827297947086 y[1] (numeric) = 3.5878238378590880679827297947082 absolute error = 4e-31 relative error = 1.1148819397963708406878221264903e-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) = 3.5889273086232870978140700058326 y[1] (numeric) = 3.5889273086232870978140700058322 absolute error = 4e-31 relative error = 1.1145391522388901297860637043418e-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) = 3.5900768862723978368768903735121 y[1] (numeric) = 3.5900768862723978368768903735115 absolute error = 6e-31 relative error = 1.6712733988908639605419972339789e-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) = 3.5912734558412800467226728609883 y[1] (numeric) = 3.5912734558412800467226728609875 absolute error = 8e-31 relative error = 2.2276220673164934479007874055091e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=654.1MB, alloc=44.3MB, time=7.38 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = 3.5925178976656406715584311502276 y[1] (numeric) = 3.5925178976656406715584311502268 absolute error = 8e-31 relative error = 2.2268504229855804080866077285249e-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) = 3.5938110872940010011629336881296 y[1] (numeric) = 3.5938110872940010011629336881286 absolute error = 1.0e-30 relative error = 2.7825613971071607870113856191888e-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) = 3.5951538954001425483790614762808 y[1] (numeric) = 3.5951538954001425483790614762798 absolute error = 1.0e-30 relative error = 2.7815220963960972969629707988258e-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) = 3.5965471876960403965215898429283 y[1] (numeric) = 3.5965471876960403965215898429272 absolute error = 1.1e-30 relative error = 3.0584889967887881644296114061348e-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) = 3.5979918248452927232930981170161 y[1] (numeric) = 3.5979918248452927232930981170151 absolute error = 1.0e-30 relative error = 2.7793281604885198122383121422192e-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) = 3.5994886623770551581834737903903 y[1] (numeric) = 3.5994886623770551581834737903893 absolute error = 1.0e-30 relative error = 2.7781723844620005007021527432934e-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) = 3.6010385506004885798455500879914 y[1] (numeric) = 3.6010385506004885798455500879905 absolute error = 9e-31 relative error = 2.4992789923060422408619666650920e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = 3.602642334519728908595846117736 y[1] (numeric) = 3.6026423345197289085958461177352 absolute error = 8e-31 relative error = 2.2205923478291902963649700528994e-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) = 3.6043008537493873969903012560166 y[1] (numeric) = 3.6043008537493873969903012560158 absolute error = 8e-31 relative error = 2.2195705421421661242737914061222e-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) = 3.6060149424305898683755300055835 y[1] (numeric) = 3.6060149424305898683755300055826 absolute error = 9e-31 relative error = 2.4958299240805866082577178532563e-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) = 3.6077854291475632994217751323375 y[1] (numeric) = 3.6077854291475632994217751323366 absolute error = 9e-31 relative error = 2.4946051190540156255722655092729e-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) = 3.609613136844778087909794836203 y[1] (numeric) = 3.6096131368447780879097948362023 absolute error = 7e-31 relative error = 1.9392659918449916078376927215380e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=694.7MB, alloc=44.3MB, time=7.83 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 3.6114988827446542914758573873451 y[1] (numeric) = 3.6114988827446542914758573873442 absolute error = 9e-31 relative error = 2.4920400897812853462803549966915e-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) = 3.6134434782658400666223908224814 y[1] (numeric) = 3.6134434782658400666223908224806 absolute error = 8e-31 relative error = 2.2139546524301388692426143895391e-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) = 3.6154477289420704800822855624998 y[1] (numeric) = 3.615447728942070480082285562499 absolute error = 8e-31 relative error = 2.2127273299954220502396429165912e-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) = 3.6175124343416148065880960893144 y[1] (numeric) = 3.6175124343416148065880960893133 absolute error = 1.1e-30 relative error = 3.0407635632638796186251007305289e-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) = 3.6196383879873203682492377336896 y[1] (numeric) = 3.6196383879873203682492377336884 absolute error = 1.2e-30 relative error = 3.3152482965770878346544211093492e-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) = 3.6218263772772609110866109426036 y[1] (numeric) = 3.6218263772772609110866109426024 absolute error = 1.2e-30 relative error = 3.3132455148281025758030512444730e-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) = 3.6240771834059974538208734312552 y[1] (numeric) = 3.6240771834059974538208734312539 absolute error = 1.3e-30 relative error = 3.5871200700483641948446358433563e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = 3.6263915812864594827638656518757 y[1] (numeric) = 3.6263915812864594827638656518746 absolute error = 1.1e-30 relative error = 3.0333183147578781025457872668375e-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) = 3.6287703394724543046286016495393 y[1] (numeric) = 3.6287703394724543046286016495382 absolute error = 1.1e-30 relative error = 3.0313298916566775718284027840915e-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) = 3.631214220081812306257968981811 y[1] (numeric) = 3.6312142200818123062579689818101 absolute error = 9e-31 relative error = 2.4785097916358202072317604520970e-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) = 3.633723978720175806682119428834 y[1] (numeric) = 3.6337239787201758066821194288329 absolute error = 1.1e-30 relative error = 3.0271974603514823235716083803502e-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) = 3.636300364405439122555835676529 y[1] (numeric) = 3.6363003644054391225558356765279 absolute error = 1.1e-30 relative error = 3.0250526352760680013694414887032e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=735.1MB, alloc=44.3MB, time=8.28 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = 3.6389441194928474029063638339918 y[1] (numeric) = 3.6389441194928474029063638339908 absolute error = 1.0e-30 relative error = 2.7480498934931929211454786087253e-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) = 3.641655979600761723245819572184 y[1] (numeric) = 3.641655979600761723245819572183 absolute error = 1.0e-30 relative error = 2.7460034819368933630269667943324e-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) = 3.6444366735370978624768944279386 y[1] (numeric) = 3.6444366735370978624768944279376 absolute error = 1.0e-30 relative error = 2.7439082897534690466936755835295e-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) = 3.6472869232264461186528708877411 y[1] (numeric) = 3.6472869232264461186528708877401 absolute error = 1.0e-30 relative error = 2.7417640044490511784532723838833e-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) = 3.6502074436378794515496369653549 y[1] (numeric) = 3.650207443637879451549636965354 absolute error = 9e-31 relative error = 2.4656132943037330670677833898407e-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) = 3.6531989427134571711752833911776 y[1] (numeric) = 3.6531989427134571711752833911766 absolute error = 1.0e-30 relative error = 2.7373269720078207670655500948732e-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) = 3.6562621212974313217888523926325 y[1] (numeric) = 3.6562621212974313217888523926314 absolute error = 1.1e-30 relative error = 3.0085370345648604150387879886182e-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) = 3.6593976730661628407308417073819 y[1] (numeric) = 3.659397673066162840730841707381 absolute error = 9e-31 relative error = 2.4594211408728951527554741470987e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 3.6626062844587545003911777726652 y[1] (numeric) = 3.6626062844587545003911777726642 absolute error = 1.0e-30 relative error = 2.7302961943881883902276165714945e-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) = 3.665888634608407569962655604432 y[1] (numeric) = 3.665888634608407569962655604431 absolute error = 1.0e-30 relative error = 2.7278515516247279611869245007234e-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) = 3.6692453952745090612564674310893 y[1] (numeric) = 3.6692453952745090612564674310881 absolute error = 1.2e-30 relative error = 3.2704272152127993868462241290584e-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) = 3.6726772307754563497986447558221 y[1] (numeric) = 3.6726772307754563497986447558211 absolute error = 1.0e-30 relative error = 2.7228093762785084655733668130300e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=775.5MB, alloc=44.3MB, time=8.73 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = 3.6761847979222258886893249074626 y[1] (numeric) = 3.6761847979222258886893249074617 absolute error = 9e-31 relative error = 2.4481903099884386785059429946545e-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) = 3.6797687459526926582980969326635 y[1] (numeric) = 3.6797687459526926582980969326626 absolute error = 9e-31 relative error = 2.4458058702463104658480249523906e-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) = 3.6834297164667069197957236853138 y[1] (numeric) = 3.683429716466706919795723685313 absolute error = 8e-31 relative error = 2.1718888687453822007253480774416e-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) = 3.6871683433619347647927844159384 y[1] (numeric) = 3.6871683433619347647927844159377 absolute error = 7e-31 relative error = 1.8984758351492701550189198794412e-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) = 3.6909852527704688769768079664097 y[1] (numeric) = 3.6909852527704688769768079664089 absolute error = 8e-31 relative error = 2.1674429595716121428240187943082e-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) = 3.6948810629962158446189086674284 y[1] (numeric) = 3.6948810629962158446189086674277 absolute error = 7e-31 relative error = 1.8945129438953118289727174977533e-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) = 3.6988563844530662851664972095326 y[1] (numeric) = 3.6988563844530662851664972095319 absolute error = 7e-31 relative error = 1.8924768286279542540600189487896e-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) = 3.7029118196038539648580824921216 y[1] (numeric) = 3.7029118196038539648580824921208 absolute error = 8e-31 relative error = 2.1604619255707413594012945395714e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = 3.7070479629001100173973357395482 y[1] (numeric) = 3.7070479629001100173973357395473 absolute error = 9e-31 relative error = 2.4278078109782777795694877467963e-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) = 3.711265400722618286214344827445 y[1] (numeric) = 3.7112654007226182862143448274442 absolute error = 8e-31 relative error = 2.1555990036288767551445800137653e-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) = 3.7155647113227777347302956441934 y[1] (numeric) = 3.7155647113227777347302956441926 absolute error = 8e-31 relative error = 2.1531047422269012202024177572077e-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) = 3.7199464647647777883356895241677 y[1] (numeric) = 3.7199464647647777883356895241668 absolute error = 9e-31 relative error = 2.4193896566113873323996578510201e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=815.9MB, alloc=44.3MB, time=9.19 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = 3.7244112228685923904997118766176 y[1] (numeric) = 3.7244112228685923904997118766167 absolute error = 9e-31 relative error = 2.4164893352104328268272279890277e-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) = 3.7289595391537984735576362784329 y[1] (numeric) = 3.728959539153798473557636278432 absolute error = 9e-31 relative error = 2.4135418755555451318272194915107e-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) = 3.7335919587842244622823675054308 y[1] (numeric) = 3.73359195878422446228236750543 absolute error = 8e-31 relative error = 2.1427087074092190917731397233040e-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) = 3.7383090185134343453436402545917 y[1] (numeric) = 3.738309018513434345343640254591 absolute error = 7e-31 relative error = 1.8725043770682180509366544196803e-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) = 3.7431112466310527662022978483548 y[1] (numeric) = 3.7431112466310527662022978483542 absolute error = 6e-31 relative error = 1.6029446106899002299530033914065e-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) = 3.7479991629099365008858325512774 y[1] (numeric) = 3.7479991629099365008858325512768 absolute error = 6e-31 relative error = 1.6008541462270808212506086893620e-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) = 3.7529732785541976054533863232516 y[1] (numeric) = 3.7529732785541976054533863232511 absolute error = 5e-31 relative error = 1.3322770051606147550990845316309e-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) = 3.7580340961480834307921516098051 y[1] (numeric) = 3.7580340961480834307921516098045 absolute error = 6e-31 relative error = 1.5965794472567161716134648926945e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = 3.763182109605718616701092683734 y[1] (numeric) = 3.7631821096057186167010926837335 absolute error = 5e-31 relative error = 1.3286627790978382915623677322994e-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) = 3.7684178041217140910206976339462 y[1] (numeric) = 3.7684178041217140910206976339458 absolute error = 4e-31 relative error = 1.0614534289762118321451805086799e-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) = 3.7737416561226480128676889961174 y[1] (numeric) = 3.773741656122648012867688996117 absolute error = 4e-31 relative error = 1.0599559706240788059063983268718e-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) = 3.7791541332194235118399371415703 y[1] (numeric) = 3.77915413321942351183993714157 absolute error = 3e-31 relative error = 7.9382843203707335470141685757076e-30 % 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) = 3.7846556941605079873779541813793 y[1] (numeric) = 3.7846556941605079873779541813792 absolute error = 1e-31 relative error = 2.6422482804524035644949541528128e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=856.4MB, alloc=44.3MB, time=9.63 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = 3.7902467887860586443140651156711 y[1] (numeric) = 3.7902467887860586443140651156709 absolute error = 2e-31 relative error = 5.2767012583910415709793133527985e-30 % 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) = 3.7959278579829388520174727180567 y[1] (numeric) = 3.7959278579829388520174727180565 absolute error = 2e-31 relative error = 5.2688040311249486989765544245266e-30 % 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) = 3.8016993336406298254618154062839 y[1] (numeric) = 3.8016993336406298254618154062836 absolute error = 3e-31 relative error = 7.8912079486493827967257229459864e-30 % 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) = 3.8075616386080420370103712000129 y[1] (numeric) = 3.8075616386080420370103712000125 absolute error = 4e-31 relative error = 1.0505411020640256929539611937189e-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) = 3.8135151866512306777417388751072 y[1] (numeric) = 3.8135151866512306777417388751068 absolute error = 4e-31 relative error = 1.0489010281122094035837095443122e-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) = 3.8195603824120193967346267482207 y[1] (numeric) = 3.8195603824120193967346267482204 absolute error = 3e-31 relative error = 7.8543070396638837981719212717470e-30 % 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) = 3.8256976213675364559033405104733 y[1] (numeric) = 3.8256976213675364559033405104731 absolute error = 2e-31 relative error = 5.2278046984933394946325075481023e-30 % 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) = 3.8319272897906673467347668028599 y[1] (numeric) = 3.8319272897906673467347668028597 absolute error = 2e-31 relative error = 5.2193057141991259216600886863098e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = 3.8382497647114278236322227921709 y[1] (numeric) = 3.8382497647114278236322227921708 absolute error = 1e-31 relative error = 2.6053541621859078576119796170120e-30 % 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) = 3.8446654138792612165306483308824 y[1] (numeric) = 3.8446654138792612165306483308822 absolute error = 2e-31 relative error = 5.2020131395049100462647971819867e-30 % 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) = 3.8511745957262637930204603803759 y[1] (numeric) = 3.8511745957262637930204603803757 absolute error = 2e-31 relative error = 5.1932207961161916022194573459458e-30 % 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) = 3.8577776593313418474132118826338 y[1] (numeric) = 3.8577776593313418474132118826337 absolute error = 1e-31 relative error = 2.5921659782055124748130825253090e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=896.7MB, alloc=44.3MB, time=10.08 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = 3.8644749443853041010102795216412 y[1] (numeric) = 3.8644749443853041010102795216409 absolute error = 3e-31 relative error = 7.7630209618998829216244519185319e-30 % 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) = 3.87126678115689290430546393624 y[1] (numeric) = 3.8712667811568929043054639362397 absolute error = 3e-31 relative error = 7.7494013448059946340300331647360e-30 % 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) = 3.8781534904597576379729748872755 y[1] (numeric) = 3.8781534904597576379729748872751 absolute error = 4e-31 relative error = 1.0314186918697220976843804526845e-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) = 3.8851353836203736152731805064138 y[1] (numeric) = 3.8851353836203736152731805064134 absolute error = 4e-31 relative error = 1.0295651515424385263380505100962e-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) = 3.8922127624469096939591458928251 y[1] (numeric) = 3.8922127624469096939591458928248 absolute error = 3e-31 relative error = 7.7076978651958274181147578882405e-30 % 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) = 3.8993859191990477108968268336072 y[1] (numeric) = 3.8993859191990477108968268336068 absolute error = 4e-31 relative error = 1.0258025450380707372036937666771e-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) = 3.9066551365587567574303062412621 y[1] (numeric) = 3.9066551365587567574303062412616 absolute error = 5e-31 relative error = 1.2798672586196934073661845093036e-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) = 3.9140206876020252180401820952345 y[1] (numeric) = 3.914020687602025218040182095234 absolute error = 5e-31 relative error = 1.2774587563724181240275481252939e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = 3.9214828357715533990676844927907 y[1] (numeric) = 3.9214828357715533990676844927902 absolute error = 5e-31 relative error = 1.2750278936299992486805476518269e-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) = 3.9290418348504094782188933306545 y[1] (numeric) = 3.929041834850409478218893330654 absolute error = 5e-31 relative error = 1.2725748948891925307107378472538e-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) = 3.9366979289366514092321528933972 y[1] (numeric) = 3.9366979289366514092321528933968 absolute error = 4e-31 relative error = 1.0160799919643433824658957127370e-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) = 3.9444513524189173194970682648417 y[1] (numeric) = 3.9444513524189173194970682648413 absolute error = 4e-31 relative error = 1.0140827310614485632919707511390e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=937.1MB, alloc=44.3MB, time=10.53 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = 3.9523023299529868415649803953237 y[1] (numeric) = 3.9523023299529868415649803953233 absolute error = 4e-31 relative error = 1.0120683252608310783053260010744e-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) = 3.9602510764393157223982366186717 y[1] (numeric) = 3.9602510764393157223982366186713 absolute error = 4e-31 relative error = 1.0100369705843051650543455358048e-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) = 3.968297797001545956878610595298 y[1] (numeric) = 3.9682977970015459568786105952976 absolute error = 4e-31 relative error = 1.0079888669198184403995783098596e-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) = 3.9764426869659935945436126770238 y[1] (numeric) = 3.9764426869659935945436126770233 absolute error = 5e-31 relative error = 1.2574052724031527915031510583100e-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) = 3.9846859318421162707529236251939 y[1] (numeric) = 3.9846859318421162707529236251934 absolute error = 5e-31 relative error = 1.2548040386431422121665150661852e-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) = 3.9930277073039624155155580356046 y[1] (numeric) = 3.9930277073039624155155580356042 absolute error = 4e-31 relative error = 1.0017461167833331116450496934885e-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) = 4.0014681791726039950414158127892 y[1] (numeric) = 4.0014681791726039950414158127887 absolute error = 5e-31 relative error = 1.2495413623491229489767355771155e-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) = 4.0100075033995545427284272052687 y[1] (numeric) = 4.0100075033995545427284272052685 absolute error = 2e-31 relative error = 4.9875218395588156564222352113463e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = 4.0186458260511741377683744258176 y[1] (numeric) = 4.0186458260511741377683744258173 absolute error = 3e-31 relative error = 7.4652012888328553989810151370607e-30 % 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) = 4.027383283294062890860533466737 y[1] (numeric) = 4.0273832832940628908605334667367 absolute error = 3e-31 relative error = 7.4490054434209469119633792715829e-30 % 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) = 4.0362200013814443976723926912916 y[1] (numeric) = 4.0362200013814443976723926912915 absolute error = 1e-31 relative error = 2.4775656422537376118355715728516e-30 % 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) = 4.0451560966405405216907550451568 y[1] (numeric) = 4.0451560966405405216907550451569 absolute error = 1e-31 relative error = 2.4720924881749049290474277162039e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=977.5MB, alloc=44.3MB, time=10.98 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = 4.0541916754609387689744177984351 y[1] (numeric) = 4.0541916754609387689744177984351 absolute error = 0 relative error = 0 % 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) = 4.0633268342839534180612607282068 y[1] (numeric) = 4.0633268342839534180612607282068 absolute error = 0 relative error = 0 % 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) = 4.0725616595929814689078863372732 y[1] (numeric) = 4.0725616595929814689078863372732 absolute error = 0 relative error = 0 % 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) = 4.0818962279048543752588814626402 y[1] (numeric) = 4.0818962279048543752588814626402 absolute error = 0 relative error = 0 % 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) = 4.0913306057621864252652564819142 y[1] (numeric) = 4.0913306057621864252652564819141 absolute error = 1e-31 relative error = 2.4441926022590563975761584658500e-30 % 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) = 4.1008648497267205355076239454585 y[1] (numeric) = 4.1008648497267205355076239454584 absolute error = 1e-31 relative error = 2.4385100134832277417394024067024e-30 % 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) = 4.1104990063736721238391691632832 y[1] (numeric) = 4.110499006373672123839169163283 absolute error = 2e-31 relative error = 4.8655893041181445577026439925834e-30 % 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) = 4.1202331122870716266564150260244 y[1] (numeric) = 4.1202331122870716266564150260243 absolute error = 1e-31 relative error = 2.4270471421091922987640197587677e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = 4.1300671940561061263421727608608 y[1] (numeric) = 4.1300671940561061263421727608608 absolute error = 0 relative error = 0 % 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) = 4.140001268272460454714885693655 y[1] (numeric) = 4.140001268272460454714885693655 absolute error = 0 relative error = 0 % 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) = 4.1500353415286580383718053432053 y[1] (numeric) = 4.1500353415286580383718053432054 absolute error = 1e-31 relative error = 2.4096180338349885047418608238948e-30 % 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) = 4.160169410417401651840082905726 y[1] (numeric) = 4.1601694104174016518400829057261 absolute error = 1e-31 relative error = 2.4037482644238450625552180771673e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1018.0MB, alloc=44.3MB, time=11.44 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = 4.1704034615319141444599116498647 y[1] (numeric) = 4.1704034615319141444599116498646 absolute error = 1e-31 relative error = 2.3978495347610085623257641331443e-30 % 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) = 4.1807374714672791069273158461397 y[1] (numeric) = 4.1807374714672791069273158461396 absolute error = 1e-31 relative error = 2.3919224941169008871042064679910e-30 % 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) = 4.1911714068227813434310491703005 y[1] (numeric) = 4.1911714068227813434310491703004 absolute error = 1e-31 relative error = 2.3859677949990457184006344219886e-30 % 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) = 4.2017052242052469153383392777164 y[1] (numeric) = 4.2017052242052469153383392777163 absolute error = 1e-31 relative error = 2.3799860928824442435202427436440e-30 % 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) = 4.2123388702333824224278933347958 y[1] (numeric) = 4.2123388702333824224278933347957 absolute error = 1e-31 relative error = 2.3739780459414831582264273072245e-30 % 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) = 4.2230722815431130877456572625241 y[1] (numeric) = 4.2230722815431130877456572625241 absolute error = 0 relative error = 0 % 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) = 4.233905384793919112279291505415 y[1] (numeric) = 4.2339053847939191122792915054151 absolute error = 1e-31 relative error = 2.3618855621845076902562167175992e-30 % 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) = 4.2448380966761696658211761562575 y[1] (numeric) = 4.2448380966761696658211761562576 absolute error = 1e-31 relative error = 2.3558024528262426908665240110949e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = 4.2558703239194537806269707748284 y[1] (numeric) = 4.2558703239194537806269707748284 absolute error = 0 relative error = 0 % 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) = 4.2670019633019073147873054328283 y[1] (numeric) = 4.2670019633019073147873054328284 absolute error = 1e-31 relative error = 2.3435658305302870874440513397096e-30 % 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) = 4.2782329016605350526240382595053 y[1] (numeric) = 4.2782329016605350526240382595053 absolute error = 0 relative error = 0 % 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) = 4.2895630159025269099096415838683 y[1] (numeric) = 4.2895630159025269099096415838683 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1058.4MB, alloc=44.3MB, time=11.89 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = 4.3009921730175671122986248744605 y[1] (numeric) = 4.3009921730175671122986248744605 absolute error = 0 relative error = 0 % 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) = 4.3125202300911351160634089488972 y[1] (numeric) = 4.3125202300911351160634089488972 absolute error = 0 relative error = 0 % 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) = 4.3241470343187969410536619294145 y[1] (numeric) = 4.3241470343187969410536619294144 absolute error = 1e-31 relative error = 2.3125948124877642280196186928703e-30 % 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) = 4.3358724230214854867577104152688 y[1] (numeric) = 4.3358724230214854867577104152687 absolute error = 1e-31 relative error = 2.3063409215881458933484981498023e-30 % 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) = 4.3476962236617683034471532851407 y[1] (numeric) = 4.3476962236617683034471532851405 absolute error = 2e-31 relative error = 4.6001373994697731386393341814618e-30 % 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) = 4.3596182538611011916411200989301 y[1] (numeric) = 4.3596182538611011916411200989298 absolute error = 3e-31 relative error = 6.8813364503716497726346905636547e-30 % 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) = 4.3716383214180659045446056247285 y[1] (numeric) = 4.371638321418065904544605624728 absolute error = 5e-31 relative error = 1.1437359709066936296450061210613e-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) = 4.3837562243275901297058346922217 y[1] (numeric) = 4.3837562243275901297058346922212 absolute error = 5e-31 relative error = 1.1405743714152201666150259802064e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = 4.3959717508011478279105082340292 y[1] (numeric) = 4.3959717508011478279105082340287 absolute error = 5e-31 relative error = 1.1374049433071926588733805765623e-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) = 4.4082846792879379092958746500094 y[1] (numeric) = 4.408284679287937909295874650009 absolute error = 4e-31 relative error = 9.0738241538568525927588010550420e-30 % 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) = 4.4206947784970391288346639253275 y[1] (numeric) = 4.4206947784970391288346639253271 absolute error = 4e-31 relative error = 9.0483514479593450183491535400755e-30 % 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) = 4.4332018074205389857177984602343 y[1] (numeric) = 4.4332018074205389857177984602338 absolute error = 5e-31 relative error = 1.1278530094503531901513054463050e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1098.7MB, alloc=44.3MB, time=12.36 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = 4.445805515357634313765216359047 y[1] (numeric) = 4.4458055153576343137652163590466 absolute error = 4e-31 relative error = 8.9972446751940916998950670610795e-30 % 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) = 4.4585056419397011528258498543986 y[1] (numeric) = 4.4585056419397011528258498543983 absolute error = 3e-31 relative error = 6.7287119069223179803154308201010e-30 % 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) = 4.4713019171563313942005103587744 y[1] (numeric) = 4.4713019171563313942005103587742 absolute error = 2e-31 relative error = 4.4729701484170062006753782978989e-30 % 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) = 4.4841940613823335964448349870275 y[1] (numeric) = 4.4841940613823335964448349870272 absolute error = 3e-31 relative error = 6.6901654097351798348240833734055e-30 % 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) = 4.4971817854056952714932148600522 y[1] (numeric) = 4.4971817854056952714932148600521 absolute error = 1e-31 relative error = 2.2236148052658471727491754125785e-30 % 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) = 4.510264790456503844898394624218 y[1] (numeric) = 4.5102647904565038448983946242179 absolute error = 1e-31 relative error = 2.2171647263724965863119221125137e-30 % 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) = 4.5234427682368233981148199464733 y[1] (numeric) = 4.5234427682368233981148199464731 absolute error = 2e-31 relative error = 4.4214110854763237279174441368848e-30 % 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) = 4.5367154009515242051764018526177 y[1] (numeric) = 4.5367154009515242051764018526174 absolute error = 3e-31 relative error = 6.6127136812919414936959825721257e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = 4.5500823613400619808407213272332 y[1] (numeric) = 4.5500823613400619808407213272327 absolute error = 5e-31 relative error = 1.0988812076200376892096626442562e-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) = 4.5635433127092036623013423733282 y[1] (numeric) = 4.5635433127092036623013423733276 absolute error = 6e-31 relative error = 1.3147678435066777405681442916910e-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) = 4.5770979089666964519173336942424 y[1] (numeric) = 4.5770979089666964519173336942417 absolute error = 7e-31 relative error = 1.5293533455525940973877029195361e-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) = 4.5907457946558767540837834877278 y[1] (numeric) = 4.590745794655876754083783487727 absolute error = 8e-31 relative error = 1.7426362420922680690665489085801e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1139.1MB, alloc=44.3MB, time=12.81 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = 4.604486604991215545378460985316 y[1] (numeric) = 4.6044866049912155453784609853153 absolute error = 7e-31 relative error = 1.5202563500591081908294965638338e-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) = 4.6183199658947966234772311138702 y[1] (numeric) = 4.6183199658947966234772311138698 absolute error = 4e-31 relative error = 8.6611582340311115401002631755830e-30 % 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) = 4.6322454940337240870437291772895 y[1] (numeric) = 4.632245494033724087043729177289 absolute error = 5e-31 relative error = 1.0793901157527033591588431732833e-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) = 4.6462627968584553058764793868963 y[1] (numeric) = 4.6462627968584553058764793868958 absolute error = 5e-31 relative error = 1.0761337054332617889094321653820e-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) = 4.6603714726420555480483865639633 y[1] (numeric) = 4.6603714726420555480483865639629 absolute error = 4e-31 relative error = 8.5830067913713366046162795234196e-30 % 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) = 4.674571110520370338608599145451 y[1] (numeric) = 4.6745711105203703386085991454506 absolute error = 4e-31 relative error = 8.5569347549292548817651365863077e-30 % 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) = 4.6888612905331115326443501606522 y[1] (numeric) = 4.6888612905331115326443501606519 absolute error = 3e-31 relative error = 6.3981419242600535006830306842104e-30 % 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) = 4.7032415836658529941297082747341 y[1] (numeric) = 4.7032415836658529941297082747338 absolute error = 3e-31 relative error = 6.3785794257706544416424578227161e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = 4.7177115518929316810283503064616 y[1] (numeric) = 4.7177115518929316810283503064612 absolute error = 4e-31 relative error = 8.4786870837727297264710313880245e-30 % 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) = 4.732270748221249846577595727932 y[1] (numeric) = 4.7322707482212498465775957279316 absolute error = 4e-31 relative error = 8.4526017483329893279385562101668e-30 % 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) = 4.746918716734973976570076455602 y[1] (numeric) = 4.7469187167349739765700764556016 absolute error = 4e-31 relative error = 8.4265188403126488124370789048250e-30 % 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) = 4.7616549926411259927765627558659 y[1] (numeric) = 4.7616549926411259927765627558655 absolute error = 4e-31 relative error = 8.4004406160920486887403254363706e-30 % 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) = 4.7764791023160621634275955254717 y[1] (numeric) = 4.7764791023160621634275955254714 absolute error = 3e-31 relative error = 6.2807769818260756286917816631284e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1179.5MB, alloc=44.3MB, time=13.27 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = 4.7913905633528350729016090798401 y[1] (numeric) = 4.7913905633528350729016090798398 absolute error = 3e-31 relative error = 6.2612303470846941963292013941461e-30 % 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) = 4.8063888846094339144620438135202 y[1] (numeric) = 4.8063888846094339144620438135201 absolute error = 1e-31 relative error = 2.0805640658876061300904611855733e-30 % 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) = 4.8214735662578982820543751314638 y[1] (numeric) = 4.8214735662578982820543751314638 absolute error = 0 relative error = 0 % 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) = 4.8366440998343005498248069716278 y[1] (numeric) = 4.8366440998343005498248069716277 absolute error = 1e-31 relative error = 2.0675492745770960856945302265922e-30 % 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) = 4.8518999682895918411643298936456 y[1] (numeric) = 4.8518999682895918411643298936455 absolute error = 1e-31 relative error = 2.0610482626098397828514903938712e-30 % 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) = 4.8672406460413065027236108273902 y[1] (numeric) = 4.8672406460413065027236108273901 absolute error = 1e-31 relative error = 2.0545522046733691814591776084990e-30 % 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) = 4.8826655990261199129943999105103 y[1] (numeric) = 4.8826655990261199129943999105102 absolute error = 1e-31 relative error = 2.0480616165879896475719208232212e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = 4.8981742847532543697203943020784 y[1] (numeric) = 4.8981742847532543697203943020782 absolute error = 2e-31 relative error = 4.0831540156206386215007899511529e-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) = 4.9137661523587277155933226437975 y[1] (numeric) = 4.9137661523587277155933226437972 absolute error = 3e-31 relative error = 6.1052966441228115004188023689696e-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) = 4.9294406426604392774168875977093 y[1] (numeric) = 4.929440642660439277416887597709 absolute error = 3e-31 relative error = 6.0858832015084123810314074149749e-30 % 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) = 4.9451971882140876101905548624369 y[1] (numeric) = 4.9451971882140876101905548624366 absolute error = 3e-31 relative error = 6.0664921656711981431329183962960e-30 % 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) = 4.9610352133699144543853782538038 y[1] (numeric) = 4.9610352133699144543853782538035 absolute error = 3e-31 relative error = 6.0471249869685375804740021380149e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1220.0MB, alloc=44.3MB, time=13.72 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = 4.9769541343302692320634197407623 y[1] (numeric) = 4.976954134330269232063419740762 absolute error = 3e-31 relative error = 6.0277830959028903732853427193190e-30 % 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) = 4.9929533592079883254391227481598 y[1] (numeric) = 4.9929533592079883254391227481595 absolute error = 3e-31 relative error = 6.0084679030045609569651427543814e-30 % 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) = 5.0090322880855833000034318256493 y[1] (numeric) = 5.0090322880855833000034318256488 absolute error = 5e-31 relative error = 9.9819679978764214023395583451251e-30 % 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) = 5.025190313075232153437669625635 y[1] (numeric) = 5.0251903130752321534376696256345 absolute error = 5e-31 relative error = 9.9498719222440421250689805268244e-30 % 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) = 5.0414268183795675912422723433438 y[1] (numeric) = 5.0414268183795675912422723433433 absolute error = 5e-31 relative error = 9.9178271948160835568647058839245e-30 % 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) = 5.0577411803532562503034774729765 y[1] (numeric) = 5.057741180353256250303477472976 absolute error = 5e-31 relative error = 9.8858360317496053905053965065873e-30 % 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) = 5.0741327675653627125269230597523 y[1] (numeric) = 5.0741327675653627125269230597518 absolute error = 5e-31 relative error = 9.8539006152160015049938809495632e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = 5.0906009408624920721887649260472 y[1] (numeric) = 5.0906009408624920721887649260466 absolute error = 6e-31 relative error = 1.1786427711977419219781449284946e-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) = 5.1071450534327047428001953906352 y[1] (numeric) = 5.1071450534327047428001953906345 absolute error = 7e-31 relative error = 1.3706287812003765356449032480324e-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) = 5.1237644508701971120579391906727 y[1] (numeric) = 5.123764450870197112057939190672 absolute error = 7e-31 relative error = 1.3661830217060722765990515144489e-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) = 5.1404584712407415768691319229587 y[1] (numeric) = 5.140458471240741576869131922958 absolute error = 7e-31 relative error = 1.3617462409555124412280768059195e-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) = 5.1572264451478794145016116973683 y[1] (numeric) = 5.1572264451478794145016116973677 absolute error = 6e-31 relative error = 1.1634160461666434963514767123532e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1260.4MB, alloc=44.3MB, time=14.17 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = 5.1740676957998598706276695153856 y[1] (numeric) = 5.174067695799859870627669515385 absolute error = 6e-31 relative error = 1.1596292033191999308499648987936e-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) = 5.1909815390773187704082363861256 y[1] (numeric) = 5.1909815390773187704082363861249 absolute error = 7e-31 relative error = 1.3484925629776423316087461483058e-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) = 5.2079672836016898848127974157074 y[1] (numeric) = 5.2079672836016898848127974157068 absolute error = 6e-31 relative error = 1.1520809700345432323340691330941e-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) = 5.225024230804342211095410160473 y[1] (numeric) = 5.2250242308043422110954101604725 absolute error = 5e-31 relative error = 9.5693336128898642529545813860586e-30 % 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) = 5.2421516749964362537563938505644 y[1] (numeric) = 5.2421516749964362537563938505638 absolute error = 6e-31 relative error = 1.1445681796309487650508912301062e-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) = 5.2593489034394923204198066883598 y[1] (numeric) = 5.2593489034394923204198066883592 absolute error = 6e-31 relative error = 1.1408256250267288834521778889789e-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) = 5.2766151964166637758559301912485 y[1] (numeric) = 5.2766151964166637758559301912478 absolute error = 7e-31 relative error = 1.3266080127945813724462233034339e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = 5.2939498273047081268827525106807 y[1] (numeric) = 5.2939498273047081268827525106799 absolute error = 8e-31 relative error = 1.5111590137742228299155486047909e-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) = 5.3113520626466487410979362833252 y[1] (numeric) = 5.3113520626466487410979362833243 absolute error = 9e-31 relative error = 1.6944837950575049240852245680407e-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) = 5.3288211622251199333299490479899 y[1] (numeric) = 5.3288211622251199333299490479891 absolute error = 8e-31 relative error = 1.5012701226887287627968755903442e-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) = 5.3463563791363880853608318169022 y[1] (numeric) = 5.3463563791363880853608318169015 absolute error = 7e-31 relative error = 1.3093029165277473699920421142200e-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) = 5.363956959865041396870317585315 y[1] (numeric) = 5.3639569598650413968703175853141 absolute error = 9e-31 relative error = 1.6778658120005575932560513270831e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1300.8MB, alloc=44.3MB, time=14.62 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = 5.3816221443593407986884466192346 y[1] (numeric) = 5.3816221443593407986884466192336 absolute error = 1.0e-30 relative error = 1.8581757937950616597868198922609e-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) = 5.3993511661072244933281454781476 y[1] (numeric) = 5.3993511661072244933281454781467 absolute error = 9e-31 relative error = 1.6668669481056811551056533328711e-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) = 5.4171432522129585224070534208273 y[1] (numeric) = 5.4171432522129585224070534208266 absolute error = 7e-31 relative error = 1.2921939985878033183305375382021e-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) = 5.4349976234744256959657292715176 y[1] (numeric) = 5.434997623474425695965729271517 absolute error = 6e-31 relative error = 1.1039563244858211693168289426257e-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) = 5.4529134944610451548537141522107 y[1] (numeric) = 5.4529134944610451548537141522101 absolute error = 6e-31 relative error = 1.1003292104477127340210596883064e-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) = 5.4708900735923147742921442269604 y[1] (numeric) = 5.4708900735923147742921442269598 absolute error = 6e-31 relative error = 1.0967136826531517630433281275819e-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) = 5.4889265632169685544380089817521 y[1] (numeric) = 5.4889265632169685544380089817513 absolute error = 8e-31 relative error = 1.4574798747737905741129953438151e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = 5.5070221596927410822769628863557 y[1] (numeric) = 5.5070221596927410822769628863549 absolute error = 8e-31 relative error = 1.4526907225022592208313069517886e-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) = 5.5251760534667310884649713203402 y[1] (numeric) = 5.5251760534667310884649713203395 absolute error = 7e-31 relative error = 1.2669279552835065718083876711432e-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) = 5.5433874291563560628300760061255 y[1] (numeric) = 5.5433874291563560628300760061248 absolute error = 7e-31 relative error = 1.2627657888716835911011170544845e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = 5.5616554656308898331401917272407 y[1] (numeric) = 5.56165546563088983314019172724 absolute error = 7e-31 relative error = 1.2586180577451412955444437283281e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = 5.5799793360935749534470053079295 y[1] (numeric) = 5.5799793360935749534470053079289 absolute error = 6e-31 relative error = 1.0752727991642479082247580592132e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1341.3MB, alloc=44.3MB, time=15.08 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = 5.5983582081643016908355692264027 y[1] (numeric) = 5.598358208164301690835569226402 absolute error = 7e-31 relative error = 1.2503665788644302942267691325888e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = 5.6167912439628453427498138283373 y[1] (numeric) = 5.6167912439628453427498138283364 absolute error = 9e-31 relative error = 1.6023383474815027916496846303183e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = 5.6352776001926535612316097892908 y[1] (numeric) = 5.6352776001926535612316097892901 absolute error = 7e-31 relative error = 1.2421748308833429244298544155449e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = 5.6538164282251753054107794572422 y[1] (numeric) = 5.6538164282251753054107794572416 absolute error = 6e-31 relative error = 1.0612300693115176598782340867051e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = 5.6724068741847229894210819669533 y[1] (numeric) = 5.6724068741847229894210819669526 absolute error = 7e-31 relative error = 1.2340440584149894485252784860864e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (closed_form) = 5.6910480790338593395980987485076 y[1] (numeric) = 5.6910480790338593395980987485069 absolute error = 7e-31 relative error = 1.2300019087500583647178360281911e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 5.7097391786593004223444551186229 y[1] (numeric) = 5.7097391786593004223444551186222 absolute error = 7e-31 relative error = 1.2259754396773802817016826825214e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = 5.7284793039583262524311770505132 y[1] (numeric) = 5.7284793039583262524311770505123 absolute error = 9e-31 relative error = 1.5710975849700780422269690715664e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = 5.7472675809256903407463615868448 y[1] (numeric) = 5.7472675809256903407463615868441 absolute error = 7e-31 relative error = 1.2179700877738733811363150798798e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = 5.7661031307410194906088104104552 y[1] (numeric) = 5.7661031307410194906088104104546 absolute error = 6e-31 relative error = 1.0405641147852521516929623014224e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = 5.7849850698566951027398281302941 y[1] (numeric) = 5.7849850698566951027398281302936 absolute error = 5e-31 relative error = 8.6430646572504626174809298410975e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = 5.8039125100862072008359222794552 y[1] (numeric) = 5.8039125100862072008359222794547 absolute error = 5e-31 relative error = 8.6148783106410636529904436796539e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1381.7MB, alloc=44.3MB, time=15.53 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = 5.822884558692972342413475864514 y[1] (numeric) = 5.8228845586929723424134758645134 absolute error = 6e-31 relative error = 1.0304171308089239689165699219395e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = 5.8419003184796065332083226779057 y[1] (numeric) = 5.8419003184796065332083226779051 absolute error = 6e-31 relative error = 1.0270630570364713038960820243432e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = 5.860958887877644217913179263164 y[1] (numeric) = 5.8609588878776442179131792631632 absolute error = 8e-31 relative error = 1.3649643604473294646736259580449e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = 5.8800593610376943754286253662208 y[1] (numeric) = 5.88005936103769437542862536622 absolute error = 8e-31 relative error = 1.3605304825678129158614798583960e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 5.899200827920024703093237603664 y[1] (numeric) = 5.8992008279200247030932376036632 absolute error = 8e-31 relative error = 1.3561158932134011714306263734630e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = 5.9183823743855648315499399031558 y[1] (numeric) = 5.9183823743855648315499399031551 absolute error = 7e-31 relative error = 1.1827556175308336084136186961280e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = 5.9376030822873194700029198405699 y[1] (numeric) = 5.9376030822873194700029198405693 absolute error = 6e-31 relative error = 1.0105087721169539023696659254475e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = 5.9568620295621823406267625493371 y[1] (numeric) = 5.9568620295621823406267625493366 absolute error = 5e-31 relative error = 8.3936810609116796676275921936521e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = 5.9761582903231417208108726455763 y[1] (numeric) = 5.9761582903231417208108726455759 absolute error = 4e-31 relative error = 6.6932631394268386139560616569141e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = 5.9954909349518683727617974225641 y[1] (numeric) = 5.9954909349518683727617974225637 absolute error = 4e-31 relative error = 6.6716805068976588885811367734760e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = 6.0148590301916766017476474330366 y[1] (numeric) = 6.0148590301916766017476474330364 absolute error = 2e-31 relative error = 3.3250987096471746202935270030207e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = 6.0342616392408491469562573075772 y[1] (numeric) = 6.034261639240849146956257307577 absolute error = 2e-31 relative error = 3.3144071629144895720930035472915e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1422.1MB, alloc=44.3MB, time=15.98 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = 6.0536978218463165725557714761559 y[1] (numeric) = 6.0536978218463165725557714761557 absolute error = 2e-31 relative error = 3.3037658285197001126429909318082e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = 6.0731666343976817910966146332443 y[1] (numeric) = 6.0731666343976817910966146332439 absolute error = 4e-31 relative error = 6.5863498250558175948746622207591e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = 6.0926671300215803168808602577823 y[1] (numeric) = 6.0926671300215803168808602577819 absolute error = 4e-31 relative error = 6.5652692238675312973713663545438e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = 6.1121983586763668133522935335094 y[1] (numeric) = 6.1121983586763668133522935335089 absolute error = 5e-31 relative error = 8.1803627869871356177115455287770e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = 6.1317593672471184659313348565068 y[1] (numeric) = 6.1317593672471184659313348565063 absolute error = 5e-31 relative error = 8.1542665009125642962464957719128e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = 6.1513491996409456800367096510664 y[1] (numeric) = 6.1513491996409456800367096510659 absolute error = 5e-31 relative error = 8.1282980980690383413871358315631e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = 6.1709668968826005733034876438366 y[1] (numeric) = 6.1709668968826005733034876438362 absolute error = 4e-31 relative error = 6.4819663868569572619574320181841e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = 6.1906114972103737012279432702555 y[1] (numeric) = 6.1906114972103737012279432702551 absolute error = 4e-31 relative error = 6.4613972332175720683807639059766e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (closed_form) = 6.2102820361722694266465863988873 y[1] (numeric) = 6.210282036172269426646586398887 absolute error = 3e-31 relative error = 4.8306984812062758211163566455495e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = 6.2299775467224503155925613446698 y[1] (numeric) = 6.2299775467224503155925613446695 absolute error = 3e-31 relative error = 4.8154266648653974917962181768930e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = 6.2496970593179409151701985931512 y[1] (numeric) = 6.249697059317940915170198593151 absolute error = 2e-31 relative error = 3.2001551131476274896093732225415e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = 6.2694396020155812431505179934839 y[1] (numeric) = 6.2694396020155812431505179934839 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1462.4MB, alloc=44.3MB, time=16.42 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = 6.2892042005692202940195181752062 y[1] (numeric) = 6.2892042005692202940195181752061 absolute error = 1e-31 relative error = 1.5900262864886665263160255792903e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = 6.3089898785271398422096416782592 y[1] (numeric) = 6.3089898785271398422096416782592 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = 6.3287956573296988002152788818011 y[1] (numeric) = 6.328795657329698800215278881801 absolute error = 1e-31 relative error = 1.5800794560997546992026543885161e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = 6.3486205564071883672378692086186 y[1] (numeric) = 6.3486205564071883672378692086185 absolute error = 1e-31 relative error = 1.5751453266344209509385222667088e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (closed_form) = 6.3684635932778881829272807804022 y[1] (numeric) = 6.3684635932778881829272807804022 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = 6.3883237836463136806858075749921 y[1] (numeric) = 6.3883237836463136806858075749922 absolute error = 1e-31 relative error = 1.5653558489942758588029213502943e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = 6.4082001415016448158813262073901 y[1] (numeric) = 6.4082001415016448158813262073903 absolute error = 2e-31 relative error = 3.1210011482745863186061166237430e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = 6.4280916792163263261788146856254 y[1] (numeric) = 6.4280916792163263261788146856258 absolute error = 4e-31 relative error = 6.2226866068712566455251122975649e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = 6.4479974076448296640463665993177 y[1] (numeric) = 6.447997407644829664046366599318 absolute error = 3e-31 relative error = 4.6526073295922249397268380066626e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = 6.4679163362225667253247514756035 y[1] (numeric) = 6.4679163362225667253247514756038 absolute error = 3e-31 relative error = 4.6382789202126243226015426890432e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = 6.4878474730649454825700921787708 y[1] (numeric) = 6.4878474730649454825700921787711 absolute error = 3e-31 relative error = 4.6240297917835606542709691404197e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = 6.5077898250665576176888711718273 y[1] (numeric) = 6.5077898250665576176888711718278 absolute error = 5e-31 relative error = 7.6830999992364736775415841572295e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=1502.7MB, alloc=44.3MB, time=16.88 x[1] = 4.62 y[1] (closed_form) = 6.5277423980004882351846582243842 y[1] (numeric) = 6.5277423980004882351846582243848 absolute error = 6e-31 relative error = 9.1915391787486268950608443357330e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = 6.5477041966177377251279927125974 y[1] (numeric) = 6.5477041966177377251279927125981 absolute error = 7e-31 relative error = 1.0690770061995010139587062190955e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = 6.5676742247467458337459747992399 y[1] (numeric) = 6.5676742247467458337459747992406 absolute error = 7e-31 relative error = 1.0658263123990326962537821716757e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = 6.5876514853930079893074429838229 y[1] (numeric) = 6.5876514853930079893074429838237 absolute error = 8e-31 relative error = 1.2143933263225344594248223589714e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = 6.607634980838773921754162833204 y[1] (numeric) = 6.6076349808387739217541628332047 absolute error = 7e-31 relative error = 1.0593805529965003028864393629657e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = 6.6276237127428186062991456798947 y[1] (numeric) = 6.6276237127428186062991456798953 absolute error = 6e-31 relative error = 9.0530184875521867020980452655997e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = 6.6476166822402755539808796320554 y[1] (numeric) = 6.6476166822402755539808796320561 absolute error = 7e-31 relative error = 1.0530089706738279838477170105351e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (closed_form) = 6.667612890042522465927611603558 y[1] (numeric) = 6.6676128900425224659276116035587 absolute error = 7e-31 relative error = 1.0498509909676771512461797509928e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = 6.6876113365371092628494917036729 y[1] (numeric) = 6.6876113365371092628494917036736 absolute error = 7e-31 relative error = 1.0467115458334406910278239173672e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = 6.7076110218877184970389038522753 y[1] (numeric) = 6.707611021887718497038903852276 absolute error = 7e-31 relative error = 1.0435906281920913577104445420422e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = 6.7276109461341481509210826531746 y[1] (numeric) = 6.7276109461341481509210826531753 absolute error = 7e-31 relative error = 1.0404882291866733680172379136102e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = 6.7476101092923068239584801849428 y[1] (numeric) = 6.7476101092923068239584801849435 absolute error = 7e-31 relative error = 1.0374043382204494282723873742468e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = 6.767607511454211308473521317219 y[1] (numeric) = 6.7676075114542113084735213172197 absolute error = 7e-31 relative error = 1.0343389429946200606871001279221e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1543.1MB, alloc=44.3MB, time=17.33 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = 6.7876021528879765547154963123733 y[1] (numeric) = 6.7876021528879765547154963123741 absolute error = 8e-31 relative error = 1.1786194623378411514347420684764e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = 6.8075930341377880262584087164105 y[1] (numeric) = 6.8075930341377880262584087164112 absolute error = 7e-31 relative error = 1.0282635822819248731436393211134e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = 6.8275791561238464485775487727873 y[1] (numeric) = 6.827579156123846448577548772788 absolute error = 7e-31 relative error = 1.0252535840205535340596278158428e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = 6.8475595202422749564132217146596 y[1] (numeric) = 6.8475595202422749564132217146603 absolute error = 7e-31 relative error = 1.0222620160229482042713442621858e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = 6.8675331284649786492901502413476 y[1] (numeric) = 6.8675331284649786492901502413483 absolute error = 7e-31 relative error = 1.0192888580305443913624842670012e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = 6.8874989834394465693202152576495 y[1] (numeric) = 6.8874989834394465693202152576502 absolute error = 7e-31 relative error = 1.0163340882998393136188789602666e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = 6.9074560885884861211739226395384 y[1] (numeric) = 6.9074560885884861211739226395392 absolute error = 8e-31 relative error = 1.1581687812994510557688190890583e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = 6.9274034482098799608617106191698 y[1] (numeric) = 6.9274034482098799608617106191706 absolute error = 8e-31 relative error = 1.1548338507795862846931160676869e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = 6.9473400675759553877192667889538 y[1] (numeric) = 6.9473400675759553877192667889547 absolute error = 9e-31 relative error = 1.2954598324622177919823838896624e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = 6.9672649530330562827406304097327 y[1] (numeric) = 6.9672649530330562827406304097335 absolute error = 8e-31 relative error = 1.1482267509458447735696981666685e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = 6.9871771121009076461481397184653 y[1] (numeric) = 6.987177112100907646148139718466 absolute error = 7e-31 relative error = 1.0018352029286454944301298100941e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = 7.0070755535718627978282707459854 y[1] (numeric) = 7.0070755535718627978282707459861 absolute error = 7e-31 relative error = 9.9899022730413460030388192918696e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1583.6MB, alloc=44.3MB, time=17.78 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = 7.026959287610023315996029785628 y[1] (numeric) = 7.0269592876100233159960297856289 absolute error = 9e-31 relative error = 1.2807815772988544106174963650191e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = 7.0468273258502218021766327470316 y[1] (numeric) = 7.0468273258502218021766327470324 absolute error = 8e-31 relative error = 1.1352626692941954452344742981953e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = 7.0666786814968575743104585897138 y[1] (numeric) = 7.0666786814968575743104585897146 absolute error = 8e-31 relative error = 1.1320735469332882044378450672147e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = 7.0865123694225754044943291441219 y[1] (numeric) = 7.0865123694225754044943291441226 absolute error = 7e-31 relative error = 9.8779196804963389594630883318112e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = 7.1063274062667774335675731995194 y[1] (numeric) = 7.1063274062667774335675731995203 absolute error = 9e-31 relative error = 1.2664769698147133926635738079866e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (closed_form) = 7.1261228105339584114335092408118 y[1] (numeric) = 7.1261228105339584114335092408127 absolute error = 9e-31 relative error = 1.2629588682777181170960716276690e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = 7.1458976026918544296742604464858 y[1] (numeric) = 7.1458976026918544296742604464866 absolute error = 8e-31 relative error = 1.1195234587445537728464264251128e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = 7.1656508052693953316674308040397 y[1] (numeric) = 7.1656508052693953316674308040406 absolute error = 9e-31 relative error = 1.2559919879687245828370406728132e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = 7.1853814429544510050452574116347 y[1] (numeric) = 7.1853814429544510050452574116358 absolute error = 1.1e-30 relative error = 1.5308860200853960871072374698936e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = 7.2050885426913617819484480229353 y[1] (numeric) = 7.2050885426913617819484480229364 absolute error = 1.1e-30 relative error = 1.5266987955558282714863510454598e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = 7.2247711337782431941159535140125 y[1] (numeric) = 7.2247711337782431941159535140135 absolute error = 1.0e-30 relative error = 1.3841268899504131417726958740187e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = 7.2444282479640553524162533206808 y[1] (numeric) = 7.244428247964055352416253320682 absolute error = 1.2e-30 relative error = 1.6564454211238038266376112758347e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=1624.1MB, alloc=44.3MB, time=18.23 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 7.264058919545427243963091597697 y[1] (numeric) = 7.2640589195454272439630915976981 absolute error = 1.1e-30 relative error = 1.5143048978309170640492531916565e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 Finished! diff ( y , x , 1 ) = 1.0 - sin ( x ) ; Iterations = 4900 Total Elapsed Time = 18 Seconds Elapsed Time(since restart) = 18 Seconds Time to Timeout = 2 Minutes 41 Seconds Percent Done = 100 % > quit memory used=1629.5MB, alloc=44.3MB, time=18.30