|\^/| 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))); > end; exact_soln_y := proc(x) return c(2.0) - cos(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, #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_g, > array_tmp1, > array_tmp2, > 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_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_g, array_tmp1, array_tmp2, 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, #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_g, > array_tmp1, > array_tmp2, > 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_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_g, array_tmp1, array_tmp2, 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, #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_g, > array_tmp1, > array_tmp2, > 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_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_g, array_tmp1, array_tmp2, 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, #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_g, > array_tmp1, > array_tmp2, > 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_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_g, array_tmp1, array_tmp2, 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, #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_g, > array_tmp1, > array_tmp2, > 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)*17*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_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_g, array_tmp1, array_tmp2, 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)*17*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, #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_g, > array_tmp1, > array_tmp2, > 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_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_g, array_tmp1, array_tmp2, 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, #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_g, > array_tmp1, > array_tmp2, > 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_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_g, array_tmp1, array_tmp2, 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, #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_g, > array_tmp1, > array_tmp2, > 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 sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[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_tmp2[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_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1); > array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[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_tmp2[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_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2); > array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[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_tmp2[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_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3); > array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[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_tmp2[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_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4); > array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[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_tmp2[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_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1); > array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[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_tmp2[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_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_g, array_tmp1, array_tmp2, 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] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1); array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1); array_tmp2[2] := array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp2[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_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2); array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2); array_tmp2[3] := array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp2[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_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3); array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3); array_tmp2[4] := array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp2[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_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4); array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4); array_tmp2[5] := array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp2[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_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1) ; array_tmp2[kkk] := array_tmp1[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_tmp2[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, > #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_g, > array_tmp1, > array_tmp2, > 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:=16; > 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_g:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= 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_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_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_g); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > 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_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/sin_lg_hpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"Digits:=16;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_start := c(0.0);"); > omniout_str(ALWAYS,"x_end := c(5.0);"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := false;"); > omniout_str(ALWAYS,"glob_max_h := c(1.0);"); > omniout_str(ALWAYS,"glob_min_h := c(1.0);"); > omniout_str(ALWAYS,"glob_display_interval:= c(1.0);"); > omniout_str(ALWAYS,""); > 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,""); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(c(2.0) - cos(c(x)));"); > omniout_str(ALWAYS,""); > 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(0.0); > x_end := c(5.0); > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := false; > glob_max_h := c(1.0); > glob_min_h := c(1.0); > glob_display_interval:= c(1.0); > glob_type_given_pole := 3; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=100000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=false; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > glob_check_sign := c(my_check_sign(x_start,x_end)); > glob__pi := arccos(glob__m1); > glob_prec = expt(10.0,c(-Digits)); > if (glob_optimize) then # if number 9 > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > found_h := false; > glob_min_pole_est := glob_larger_float; > last_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > glob_min_h := float_abs(glob_min_h) * glob_check_sign; > glob_max_h := float_abs(glob_max_h) * glob_check_sign; > glob_h := float_abs(glob_min_h) * glob_check_sign; > glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign)); > display_max := c(x_end) - c(x_start)/glob__10; > if ((glob_display_interval) > (display_max)) then # if number 10 > glob_display_interval := c(display_max); > fi;# end if 10; > chk_data(); > min_value := glob_larger_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := glob_small_float; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > glob_h := glob_check_sign * float_abs(glob_min_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL"); > glob_h_reason := 2; > glob_h := glob_display_interval; > found_h := true; > fi;# end if 10; > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if ( not found_h) then # if number 10 > est_answer := est_size_answer(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (estimated_step_error < est_needed_step_err) then # if number 11 > omniout_str(ALWAYS,"Double H and LOOP"); > glob_h := glob_h*glob__2; > else > omniout_str(ALWAYS,"Found H for OPTIMAL"); > found_h := true; > glob_h_reason := 3; > glob_h := glob_h/glob__2; > fi;# end if 11; > fi;# end if 10; > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 10 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 10; > if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MAX H"); > glob_h := glob_check_sign * float_abs(glob_max_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > else > found_h := true; > glob_h := glob_h * glob_check_sign; > fi;# end if 9; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 10 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 10; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > track_estimated_error(); > atomall(); > track_estimated_error(); > display_alot(current_iter); > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (reached_interval()) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin ( 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,"2015-04-24T20:35:54-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sin_lg_h") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = 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,"sin_lg_h diffeq.mxt") > ; > logitem_str(html_log_file,"sin_lg_h 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_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_g, array_tmp1, array_tmp2, 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 := 16; 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_g := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := 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_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_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_g); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); 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_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/sin_lg_hpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) ; ") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "Digits:=16;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_start := c(0.0);"); omniout_str(ALWAYS, "x_end := c(5.0);"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := false;"); omniout_str(ALWAYS, "glob_max_h := c(1.0);"); omniout_str(ALWAYS, "glob_min_h := c(1.0);"); omniout_str(ALWAYS, "glob_display_interval:= c(1.0);"); omniout_str(ALWAYS, ""); 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, ""); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(c(2.0) - cos(c(x)));"); omniout_str(ALWAYS, ""); 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.); x_end := c(5.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := false; glob_max_h := c(1.0); glob_min_h := c(1.0); glob_display_interval := c(1.0); glob_type_given_pole := 3; glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 100000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := false; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; glob_check_sign := c(my_check_sign(x_start, x_end)); glob__pi := arccos(glob__m1); glob_prec = expt(10.0, c(-Digits)); if glob_optimize then omniout_str(ALWAYS, "START of Optimize"); found_h := false; glob_min_pole_est := glob_larger_float; last_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; glob_min_h := float_abs(glob_min_h)*glob_check_sign; glob_max_h := float_abs(glob_max_h)*glob_check_sign; glob_h := float_abs(glob_min_h)*glob_check_sign; glob_display_interval := c(float_abs(c(glob_display_interval))*glob_check_sign); display_max := c(x_end) - c(x_start)/glob__10; if display_max < glob_display_interval then glob_display_interval := c(display_max) end if; chk_data(); min_value := glob_larger_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := glob_small_float; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]*expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); glob_h := float_abs(glob_min_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if; if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL"); glob_h_reason := 2; glob_h := glob_display_interval; found_h := true end if; if glob_look_poles then check_for_pole() end if; if not found_h then est_answer := est_size_answer(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if estimated_step_error < est_needed_step_err then omniout_str(ALWAYS, "Double H and LOOP"); glob_h := glob_h*glob__2 else omniout_str(ALWAYS, "Found H for OPTIMAL"); found_h := true; glob_h_reason := 3; glob_h := glob_h/glob__2 end if end if; opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR MAX H"); glob_h := float_abs(glob_max_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if else found_h := true; glob_h := glob_check_sign*glob_h end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec - glob_orig_start_sec < glob_max_sec do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); track_estimated_error(); atomall(); track_estimated_error(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin ( 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, "2015-04-24T20:35:54-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sin_lg_h"); logitem_str(html_log_file, "diff ( y , x , 1 ) = 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, "sin_lg_h diffeq.mxt"); logitem_str(html_log_file, "sin_lg_h 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/sin_lg_hpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=16; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(0.0); x_end := c(5.0); array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := false; glob_max_h := c(1.0); glob_min_h := c(1.0); glob_display_interval:= c(1.0); 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))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 memory used=4.2MB, alloc=40.3MB, time=0.08 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (closed_form) = 1.000049999583335 y[1] (numeric) = 1.000049999583334 absolute error = 1e-15 relative error = 9.999500029164983e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (closed_form) = 1.000199993333422 y[1] (numeric) = 1.000199993333421 absolute error = 1e-15 relative error = 9.998000466559138e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (closed_form) = 1.000449966251012 y[1] (numeric) = 1.000449966251012 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (closed_form) = 1.000799893339022 y[1] (numeric) = 1.000799893339022 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (closed_form) = 1.001249739605034 y[1] (numeric) = 1.001249739605031 absolute error = 3e-15 relative error = 2.996255460883734e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (closed_form) = 1.001799460064796 y[1] (numeric) = 1.001799460064792 absolute error = 4e-15 relative error = 3.992815088701766e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (closed_form) = 1.00244899974672 y[1] (numeric) = 1.002448999746717 absolute error = 3e-15 relative error = 2.992670949602407e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (closed_form) = 1.003198293697381 y[1] (numeric) = 1.003198293697377 absolute error = 4e-15 relative error = 3.987247611095536e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (closed_form) = 1.004047266988006 y[1] (numeric) = 1.004047266988003 absolute error = 3e-15 relative error = 2.987907142060710e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.004995834721974 y[1] (numeric) = 1.004995834721971 absolute error = 3e-15 relative error = 2.985086998723663e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 1.006043902043303 y[1] (numeric) = 1.006043902043299 absolute error = 4e-15 relative error = 3.975969629034965e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 1.007191364146134 y[1] (numeric) = 1.007191364146128 absolute error = 6e-15 relative error = 5.957159893926033e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 1.008438106285212 y[1] (numeric) = 1.008438106285205 absolute error = 7e-15 relative error = 6.941427497009144e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 1.009784003787363 y[1] (numeric) = 1.009784003787357 absolute error = 6e-15 relative error = 5.941864772561262e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 1.011228922063958 y[1] (numeric) = 1.011228922063951 absolute error = 7e-15 relative error = 6.922270365559486e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 memory used=46.9MB, alloc=44.3MB, time=0.59 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (closed_form) = 1.012772716624373 y[1] (numeric) = 1.012772716624366 absolute error = 7e-15 relative error = 6.911718577225682e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (closed_form) = 1.014415233090439 y[1] (numeric) = 1.014415233090433 absolute error = 6e-15 relative error = 5.914737677707051e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (closed_form) = 1.016156307211879 y[1] (numeric) = 1.016156307211872 absolute error = 7e-15 relative error = 6.888703982172330e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (closed_form) = 1.01799576488273 y[1] (numeric) = 1.017995764882722 absolute error = 8e-15 relative error = 7.858578862478446e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 1.019933422158758 y[1] (numeric) = 1.019933422158751 absolute error = 7e-15 relative error = 6.863193075077417e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = 1.021969085275852 y[1] (numeric) = 1.021969085275843 absolute error = 9e-15 relative error = 8.806528621725090e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 1.024102550669394 y[1] (numeric) = 1.024102550669385 absolute error = 9e-15 relative error = 8.788182388684847e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = 1.026333604994625 y[1] (numeric) = 1.026333604994615 absolute error = 1.0e-14 relative error = 9.743420610350541e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = 1.02866202514797 y[1] (numeric) = 1.028662025147959 absolute error = 1.1e-14 relative error = 1.069350256068574e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (closed_form) = 1.031087578289355 y[1] (numeric) = 1.031087578289344 absolute error = 1.1e-14 relative error = 1.066834692960782e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (closed_form) = 1.033610021865487 y[1] (numeric) = 1.033610021865476 absolute error = 1.1e-14 relative error = 1.064231167200460e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (closed_form) = 1.03622910363411 y[1] (numeric) = 1.036229103634099 absolute error = 1.1e-14 relative error = 1.061541309872732e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (closed_form) = 1.038944561689229 y[1] (numeric) = 1.038944561689217 absolute error = 1.2e-14 relative error = 1.155018317867615e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (closed_form) = 1.041756124487303 y[1] (numeric) = 1.04175612448729 absolute error = 1.3e-14 relative error = 1.247892831577823e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 1.044663510874394 y[1] (numeric) = 1.04466351087438 absolute error = 1.4e-14 relative error = 1.340144444049918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 memory used=89.6MB, alloc=44.3MB, time=1.09 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (closed_form) = 1.047666430114287 y[1] (numeric) = 1.047666430114272 absolute error = 1.5e-14 relative error = 1.431753425406949e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (closed_form) = 1.050764581917559 y[1] (numeric) = 1.050764581917544 absolute error = 1.5e-14 relative error = 1.427531937993783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (closed_form) = 1.053957656471613 y[1] (numeric) = 1.0539576564716 absolute error = 1.3e-14 relative error = 1.233446137060264e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (closed_form) = 1.057245334471654 y[1] (numeric) = 1.057245334471642 absolute error = 1.2e-14 relative error = 1.135025108055630e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (closed_form) = 1.060627287152621 y[1] (numeric) = 1.06062728715261 absolute error = 1.1e-14 relative error = 1.037122100594903e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (closed_form) = 1.064103176322065 y[1] (numeric) = 1.064103176322054 absolute error = 1.1e-14 relative error = 1.033734345011550e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (closed_form) = 1.067672654393966 y[1] (numeric) = 1.067672654393955 absolute error = 1.1e-14 relative error = 1.030278330603479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (closed_form) = 1.07133536442349 y[1] (numeric) = 1.071335364423479 absolute error = 1.1e-14 relative error = 1.026755987460505e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (closed_form) = 1.075090940142687 y[1] (numeric) = 1.075090940142676 absolute error = 1.1e-14 relative error = 1.023169258457342e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 1.078939005997115 y[1] (numeric) = 1.078939005997105 absolute error = 1.0e-14 relative error = 9.268364517749893e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (closed_form) = 1.082879177183395 y[1] (numeric) = 1.082879177183385 absolute error = 1.0e-14 relative error = 9.234640586598345e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (closed_form) = 1.086911059687692 y[1] (numeric) = 1.08691105968768 absolute error = 1.2e-14 relative error = 1.104046176827755e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (closed_form) = 1.091034250325115 y[1] (numeric) = 1.091034250325106 absolute error = 9e-15 relative error = 8.249053590497373e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (closed_form) = 1.095248336780037 y[1] (numeric) = 1.095248336780027 absolute error = 1.0e-14 relative error = 9.130349404957224e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (closed_form) = 1.099552897647323 y[1] (numeric) = 1.099552897647313 absolute error = 1.0e-14 relative error = 9.094605654167862e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=132.4MB, alloc=44.3MB, time=1.61 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (closed_form) = 1.103947502474475 y[1] (numeric) = 1.103947502474465 absolute error = 1.0e-14 relative error = 9.058401760577574e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (closed_form) = 1.108431711804671 y[1] (numeric) = 1.108431711804662 absolute error = 9e-15 relative error = 8.119580037408736e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (closed_form) = 1.113005077220716 y[1] (numeric) = 1.113005077220707 absolute error = 9e-15 relative error = 8.086216482025304e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (closed_form) = 1.117667141389878 y[1] (numeric) = 1.11766714138987 absolute error = 8e-15 relative error = 7.157766121719905e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = 1.122417438109627 y[1] (numeric) = 1.122417438109619 absolute error = 8e-15 relative error = 7.127473013492718e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (closed_form) = 1.127255492354249 y[1] (numeric) = 1.127255492354241 absolute error = 8e-15 relative error = 7.096882698075989e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = 1.13218082032235 y[1] (numeric) = 1.132180820322343 absolute error = 7e-15 relative error = 6.182757978541792e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = 1.137192929485239 y[1] (numeric) = 1.137192929485234 absolute error = 5e-15 relative error = 4.396791318658037e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = 1.142291318636176 y[1] (numeric) = 1.142291318636172 absolute error = 4e-15 relative error = 3.501733695022517e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = 1.147475477940494 y[1] (numeric) = 1.147475477940491 absolute error = 3e-15 relative error = 2.614434955407016e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (closed_form) = 1.152744888986584 y[1] (numeric) = 1.152744888986581 absolute error = 3e-15 relative error = 2.602483887512526e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (closed_form) = 1.158099024837731 y[1] (numeric) = 1.158099024837728 absolute error = 3e-15 relative error = 2.590452056049654e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (closed_form) = 1.163537350084813 y[1] (numeric) = 1.16353735008481 absolute error = 3e-15 relative error = 2.578344390733416e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (closed_form) = 1.169059320899836 y[1] (numeric) = 1.169059320899835 absolute error = 1e-15 relative error = 8.553885864665024e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 memory used=175.1MB, alloc=44.3MB, time=2.09 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 1.174664385090322 y[1] (numeric) = 1.174664385090321 absolute error = 1e-15 relative error = 8.513069883557492e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (closed_form) = 1.18035198215452 y[1] (numeric) = 1.180351982154521 absolute error = 1e-15 relative error = 8.472049143973818e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (closed_form) = 1.186121543337466 y[1] (numeric) = 1.186121543337466 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (closed_form) = 1.191972491687848 y[1] (numeric) = 1.191972491687848 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (closed_form) = 1.197904242115707 y[1] (numeric) = 1.197904242115707 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (closed_form) = 1.203916201450944 y[1] (numeric) = 1.203916201450943 absolute error = 1e-15 relative error = 8.306225954886338e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (closed_form) = 1.210007768502635 y[1] (numeric) = 1.210007768502634 absolute error = 1e-15 relative error = 8.264409750339734e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (closed_form) = 1.216178334119151 y[1] (numeric) = 1.21617833411915 absolute error = 1e-15 relative error = 8.222478331882768e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (closed_form) = 1.222427281249072 y[1] (numeric) = 1.222427281249072 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (closed_form) = 1.228753985002893 y[1] (numeric) = 1.228753985002894 absolute error = 1e-15 relative error = 8.138325590029688e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = 1.235157812715512 y[1] (numeric) = 1.235157812715512 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (closed_form) = 1.241638124009492 y[1] (numeric) = 1.241638124009492 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (closed_form) = 1.248194270859105 y[1] (numeric) = 1.248194270859104 absolute error = 1e-15 relative error = 8.011573385220890e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (closed_form) = 1.25482559765513 y[1] (numeric) = 1.254825597655129 absolute error = 1e-15 relative error = 7.969234942837331e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (closed_form) = 1.261531441270412 y[1] (numeric) = 1.261531441270412 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 memory used=217.9MB, alloc=44.3MB, time=2.59 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (closed_form) = 1.268311131126179 y[1] (numeric) = 1.268311131126179 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (closed_form) = 1.275163989259095 y[1] (numeric) = 1.275163989259094 absolute error = 1e-15 relative error = 7.842128607952827e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (closed_form) = 1.282089330389057 y[1] (numeric) = 1.282089330389055 absolute error = 2e-15 relative error = 1.559953704156550e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (closed_form) = 1.289086461987723 y[1] (numeric) = 1.289086461987722 absolute error = 1e-15 relative error = 7.757431557058147e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (closed_form) = 1.296154684347764 y[1] (numeric) = 1.296154684347765 absolute error = 1e-15 relative error = 7.715128541954917e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (closed_form) = 1.303293290652835 y[1] (numeric) = 1.303293290652838 absolute error = 3e-15 relative error = 2.301861002059839e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (closed_form) = 1.310501567048253 y[1] (numeric) = 1.310501567048257 absolute error = 4e-15 relative error = 3.052266476116864e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (closed_form) = 1.317778792712386 y[1] (numeric) = 1.31777879271239 absolute error = 4e-15 relative error = 3.035410815624673e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (closed_form) = 1.325124239928733 y[1] (numeric) = 1.325124239928735 absolute error = 2e-15 relative error = 1.509292441973262e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (closed_form) = 1.332537174158692 y[1] (numeric) = 1.332537174158694 absolute error = 2e-15 relative error = 1.500896214218351e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (closed_form) = 1.340016854115018 y[1] (numeric) = 1.34001685411502 absolute error = 2e-15 relative error = 1.492518540985704e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (closed_form) = 1.347562531835948 y[1] (numeric) = 1.347562531835949 absolute error = 1e-15 relative error = 7.420805909745640e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (closed_form) = 1.355173452759999 y[1] (numeric) = 1.355173452759999 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (closed_form) = 1.36284885580142 y[1] (numeric) = 1.362848855801419 absolute error = 1e-15 relative error = 7.337570822642342e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (closed_form) = 1.370587973426303 y[1] (numeric) = 1.370587973426303 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 memory used=260.7MB, alloc=44.3MB, time=3.09 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (closed_form) = 1.378390031729336 y[1] (numeric) = 1.378390031729335 absolute error = 1e-15 relative error = 7.254840625518702e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (closed_form) = 1.386254250511188 y[1] (numeric) = 1.386254250511189 absolute error = 1e-15 relative error = 7.213683922925720e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (closed_form) = 1.394179843356537 y[1] (numeric) = 1.394179843356538 absolute error = 1e-15 relative error = 7.172675783293960e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (closed_form) = 1.402166017712702 y[1] (numeric) = 1.4021660177127 absolute error = 2e-15 relative error = 1.426364620690581e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (closed_form) = 1.410211974968902 y[1] (numeric) = 1.410211974968902 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (closed_form) = 1.418316910536116 y[1] (numeric) = 1.418316910536117 absolute error = 1e-15 relative error = 7.050610428257571e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (closed_form) = 1.426480013927543 y[1] (numeric) = 1.426480013927544 absolute error = 1e-15 relative error = 7.010262956623480e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (closed_form) = 1.434700468839646 y[1] (numeric) = 1.434700468839645 absolute error = 1e-15 relative error = 6.970096000657042e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (closed_form) = 1.442977453233783 y[1] (numeric) = 1.442977453233784 absolute error = 1e-15 relative error = 6.930115212534687e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (closed_form) = 1.451310139418412 y[1] (numeric) = 1.451310139418413 absolute error = 1e-15 relative error = 6.890326008476266e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 1.45969769413186 y[1] (numeric) = 1.45969769413186 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 1.468139278625644 y[1] (numeric) = 1.468139278625644 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = 1.47663404874835 y[1] (numeric) = 1.47663404874835 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = 1.485181155030045 y[1] (numeric) = 1.485181155030044 absolute error = 1e-15 relative error = 6.733185353269380e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 memory used=303.5MB, alloc=44.3MB, time=3.59 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = 1.493779742767222 y[1] (numeric) = 1.493779742767221 absolute error = 1e-15 relative error = 6.694427373526323e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = 1.502428952108273 y[1] (numeric) = 1.502428952108273 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (closed_form) = 1.511127918139472 y[1] (numeric) = 1.511127918139472 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = 1.519875770971466 y[1] (numeric) = 1.519875770971465 absolute error = 1e-15 relative error = 6.579485107265217e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = 1.52867163582626 y[1] (numeric) = 1.52867163582626 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (closed_form) = 1.537514633124699 y[1] (numeric) = 1.537514633124698 absolute error = 1e-15 relative error = 6.504003138934000e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 1.546403878574423 y[1] (numeric) = 1.546403878574421 absolute error = 2e-15 relative error = 1.293323191767814e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (closed_form) = 1.555338483258293 y[1] (numeric) = 1.55533848325829 absolute error = 3e-15 relative error = 1.928840591480301e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = 1.564317553723288 y[1] (numeric) = 1.564317553723284 absolute error = 4e-15 relative error = 2.557025579927463e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = 1.573340192069843 y[1] (numeric) = 1.57334019206984 absolute error = 3e-15 relative error = 1.906771348701950e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = 1.582405496041642 y[1] (numeric) = 1.58240549604164 absolute error = 2e-15 relative error = 1.263898542442479e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = 1.591512559115843 y[1] (numeric) = 1.591512559115841 absolute error = 2e-15 relative error = 1.256666174919217e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = 1.600660470593727 y[1] (numeric) = 1.600660470593726 absolute error = 1e-15 relative error = 6.247421101297477e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = 1.60984831569177 y[1] (numeric) = 1.60984831569177 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = 1.619075175633118 y[1] (numeric) = 1.619075175633119 absolute error = 1e-15 relative error = 6.176365464988142e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 memory used=346.5MB, alloc=44.3MB, time=4.09 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (closed_form) = 1.628340127739467 y[1] (numeric) = 1.628340127739468 absolute error = 1e-15 relative error = 6.141223095620961e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 1.637642245523326 y[1] (numeric) = 1.637642245523326 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = 1.64698059878067 y[1] (numeric) = 1.646980598780669 absolute error = 1e-15 relative error = 6.071716939108710e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = 1.656354253683953 y[1] (numeric) = 1.656354253683954 absolute error = 1e-15 relative error = 6.037355823948087e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (closed_form) = 1.665762272875497 y[1] (numeric) = 1.665762272875499 absolute error = 2e-15 relative error = 1.200651517066436e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = 1.675203715561224 y[1] (numeric) = 1.675203715561224 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (closed_form) = 1.684677637604731 y[1] (numeric) = 1.684677637604732 absolute error = 1e-15 relative error = 5.935853706836144e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (closed_form) = 1.694183091621711 y[1] (numeric) = 1.694183091621712 absolute error = 1e-15 relative error = 5.902549759499589e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (closed_form) = 1.703719127074681 y[1] (numeric) = 1.703719127074681 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (closed_form) = 1.713284790368044 y[1] (numeric) = 1.713284790368043 absolute error = 1e-15 relative error = 5.836741244782674e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (closed_form) = 1.722879124943442 y[1] (numeric) = 1.722879124943442 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 1.732501171375413 y[1] (numeric) = 1.732501171375411 absolute error = 2e-15 relative error = 1.154400373889631e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = 1.74214996746733 y[1] (numeric) = 1.742149967467328 absolute error = 2e-15 relative error = 1.148006794677683e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (closed_form) = 1.751824548347627 y[1] (numeric) = 1.751824548347624 absolute error = 3e-15 relative error = 1.712500263128342e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=389.2MB, alloc=44.3MB, time=4.64 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = 1.761523946566277 y[1] (numeric) = 1.761523946566273 absolute error = 4e-15 relative error = 2.270761069014795e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (closed_form) = 1.77124719219154 y[1] (numeric) = 1.771247192191537 absolute error = 3e-15 relative error = 1.693721809821553e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = 1.780993312906958 y[1] (numeric) = 1.780993312906954 absolute error = 4e-15 relative error = 2.245937686015875e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (closed_form) = 1.790761334108581 y[1] (numeric) = 1.790761334108577 absolute error = 4e-15 relative error = 2.233686825716030e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (closed_form) = 1.800550279002427 y[1] (numeric) = 1.800550279002423 absolute error = 4e-15 relative error = 2.221543073052173e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (closed_form) = 1.810359168702166 y[1] (numeric) = 1.810359168702162 absolute error = 4e-15 relative error = 2.209506306346697e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (closed_form) = 1.820187022327 y[1] (numeric) = 1.820187022326996 absolute error = 4e-15 relative error = 2.197576375907922e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 1.830032857099759 y[1] (numeric) = 1.830032857099753 absolute error = 6e-15 relative error = 3.278629657780471e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (closed_form) = 1.839895688445169 y[1] (numeric) = 1.839895688445162 absolute error = 7e-15 relative error = 3.804563510834385e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = 1.849774530088314 y[1] (numeric) = 1.849774530088308 absolute error = 6e-15 relative error = 3.243638563730003e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = 1.859668394153263 y[1] (numeric) = 1.859668394153258 absolute error = 5e-15 relative error = 2.688651383074444e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (closed_form) = 1.869576291261854 y[1] (numeric) = 1.869576291261849 absolute error = 5e-15 relative error = 2.674402763540232e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = 1.879497230632633 y[1] (numeric) = 1.879497230632629 absolute error = 4e-15 relative error = 2.128228727771848e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (closed_form) = 1.88943022017993 y[1] (numeric) = 1.889430220179925 absolute error = 5e-15 relative error = 2.646300427820960e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = 1.899374266613068 y[1] (numeric) = 1.899374266613063 absolute error = 5e-15 relative error = 2.632445899625625e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=432.1MB, alloc=44.3MB, time=5.20 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (closed_form) = 1.90932837553569 y[1] (numeric) = 1.909328375535683 absolute error = 7e-15 relative error = 3.666210637044583e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (closed_form) = 1.919291551545199 y[1] (numeric) = 1.919291551545191 absolute error = 8e-15 relative error = 4.168204665705580e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = 1.929262798332297 y[1] (numeric) = 1.929262798332288 absolute error = 9e-15 relative error = 4.664994322069458e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (closed_form) = 1.939241118780614 y[1] (numeric) = 1.939241118780605 absolute error = 9e-15 relative error = 4.640990701382796e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = 1.949225515066421 y[1] (numeric) = 1.949225515066411 absolute error = 1.0e-14 relative error = 5.130242715737919e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (closed_form) = 1.959214988758409 y[1] (numeric) = 1.959214988758399 absolute error = 1.0e-14 relative error = 5.104085083759586e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = 1.969208540917534 y[1] (numeric) = 1.969208540917524 absolute error = 1.0e-14 relative error = 5.078182321584181e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (closed_form) = 1.979205172196908 y[1] (numeric) = 1.979205172196898 absolute error = 1.0e-14 relative error = 5.052533279761011e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (closed_form) = 1.989203882941733 y[1] (numeric) = 1.989203882941723 absolute error = 1.0e-14 relative error = 5.027136778564652e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (closed_form) = 1.999203673289267 y[1] (numeric) = 1.999203673289256 absolute error = 1.1e-14 relative error = 5.502190770739144e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (closed_form) = 2.009203543268808 y[1] (numeric) = 2.009203543268797 absolute error = 1.1e-14 relative error = 5.474806192161054e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = 2.019202492901693 y[1] (numeric) = 2.019202492901682 absolute error = 1.1e-14 relative error = 5.447695334504298e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = 2.029199522301289 y[1] (numeric) = 2.02919952230128 absolute error = 9e-15 relative error = 4.435246461024797e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (closed_form) = 2.039193631772988 y[1] (numeric) = 2.039193631772979 absolute error = 9e-15 relative error = 4.413509271395135e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=475.0MB, alloc=44.3MB, time=5.80 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = 2.04918382191417 y[1] (numeric) = 2.049183821914162 absolute error = 8e-15 relative error = 3.903993343323925e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (closed_form) = 2.059169093714148 y[1] (numeric) = 2.059169093714141 absolute error = 7e-15 relative error = 3.399429421006905e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (closed_form) = 2.069148448654062 y[1] (numeric) = 2.069148448654056 absolute error = 6e-15 relative error = 2.899743613805416e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (closed_form) = 2.079120888806734 y[1] (numeric) = 2.079120888806729 absolute error = 5e-15 relative error = 2.404862568077819e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = 2.089085416936459 y[1] (numeric) = 2.089085416936455 absolute error = 4e-15 relative error = 1.914713475845235e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (closed_form) = 2.099041036598728 y[1] (numeric) = 2.099041036598724 absolute error = 4e-15 relative error = 1.905632110214278e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (closed_form) = 2.108986752239871 y[1] (numeric) = 2.108986752239868 absolute error = 3e-15 relative error = 1.422484042070828e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (closed_form) = 2.118921569296612 y[1] (numeric) = 2.118921569296608 absolute error = 4e-15 relative error = 1.887752740809478e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = 2.128844494295525 y[1] (numeric) = 2.12884449429552 absolute error = 5e-15 relative error = 2.348691984500538e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = 2.138754534952378 y[1] (numeric) = 2.138754534952374 absolute error = 4e-15 relative error = 1.870247349394429e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (closed_form) = 2.148650700271364 y[1] (numeric) = 2.14865070027136 absolute error = 4e-15 relative error = 1.861633442557611e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (closed_form) = 2.158532000644198 y[1] (numeric) = 2.158532000644194 absolute error = 4e-15 relative error = 1.853111280632499e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (closed_form) = 2.168397447949077 y[1] (numeric) = 2.168397447949073 absolute error = 4e-15 relative error = 1.844680274726987e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = 2.178246055649492 y[1] (numeric) = 2.178246055649488 absolute error = 4e-15 relative error = 1.836339833888652e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (closed_form) = 2.18807683889288 y[1] (numeric) = 2.188076838892877 absolute error = 3e-15 relative error = 1.371067024098631e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=517.9MB, alloc=44.3MB, time=6.33 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (closed_form) = 2.197888814609109 y[1] (numeric) = 2.197888814609105 absolute error = 4e-15 relative error = 1.819928275448908e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = 2.207681001608784 y[1] (numeric) = 2.20768100160878 absolute error = 4e-15 relative error = 1.811855968813028e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (closed_form) = 2.217452420681365 y[1] (numeric) = 2.217452420681361 absolute error = 4e-15 relative error = 1.803871849827968e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = 2.227202094693087 y[1] (numeric) = 2.227202094693083 absolute error = 4e-15 relative error = 1.795975322370199e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = 2.236929048684675 y[1] (numeric) = 2.236929048684671 absolute error = 4e-15 relative error = 1.788165790216734e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (closed_form) = 2.246632309968834 y[1] (numeric) = 2.246632309968831 absolute error = 3e-15 relative error = 1.335331992996049e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = 2.256310908227523 y[1] (numeric) = 2.25631090822752 absolute error = 3e-15 relative error = 1.329603996089658e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (closed_form) = 2.26596387560898 y[1] (numeric) = 2.265963875608977 absolute error = 3e-15 relative error = 1.323939905791193e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (closed_form) = 2.275590246824513 y[1] (numeric) = 2.275590246824511 absolute error = 2e-15 relative error = 8.788928511145242e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (closed_form) = 2.285189059245021 y[1] (numeric) = 2.285189059245017 absolute error = 4e-15 relative error = 1.750402218940046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (closed_form) = 2.294759352997261 y[1] (numeric) = 2.294759352997256 absolute error = 5e-15 relative error = 2.178877708230859e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = 2.304300171059833 y[1] (numeric) = 2.304300171059828 absolute error = 5e-15 relative error = 2.169856194429875e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (closed_form) = 2.313810559358882 y[1] (numeric) = 2.313810559358877 absolute error = 5e-15 relative error = 2.160937497573447e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 2.323289566863503 y[1] (numeric) = 2.323289566863498 absolute error = 5e-15 relative error = 2.152120885538224e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=560.7MB, alloc=44.3MB, time=6.83 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = 2.332736245680845 y[1] (numeric) = 2.332736245680841 absolute error = 4e-15 relative error = 1.714724503212123e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (closed_form) = 2.342149651150898 y[1] (numeric) = 2.342149651150893 absolute error = 5e-15 relative error = 2.134791001737687e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (closed_form) = 2.35152884194096 y[1] (numeric) = 2.351528841940955 absolute error = 5e-15 relative error = 2.126276280699574e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (closed_form) = 2.360872880139767 y[1] (numeric) = 2.360872880139761 absolute error = 6e-15 relative error = 2.541432895635106e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = 2.370180831351287 y[1] (numeric) = 2.370180831351281 absolute error = 6e-15 relative error = 2.531452419425433e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (closed_form) = 2.379451764788154 y[1] (numeric) = 2.37945176478815 absolute error = 4e-15 relative error = 1.681059502526258e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (closed_form) = 2.388684753364752 y[1] (numeric) = 2.388684753364748 absolute error = 4e-15 relative error = 1.674561699431252e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (closed_form) = 2.397878873789916 y[1] (numeric) = 2.397878873789913 absolute error = 3e-15 relative error = 1.251105730481880e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = 2.407033206659266 y[1] (numeric) = 2.407033206659262 absolute error = 4e-15 relative error = 1.661796766631077e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 2.416146836547142 y[1] (numeric) = 2.416146836547139 absolute error = 3e-15 relative error = 1.241646391113890e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (closed_form) = 2.425218852098152 y[1] (numeric) = 2.425218852098149 absolute error = 3e-15 relative error = 1.237001764770459e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = 2.4342483461183 y[1] (numeric) = 2.434248346118295 absolute error = 5e-15 relative error = 2.054022141156262e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = 2.443234415665709 y[1] (numeric) = 2.443234415665704 absolute error = 5e-15 relative error = 2.046467570995495e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (closed_form) = 2.452176162140912 y[1] (numeric) = 2.452176162140907 absolute error = 5e-15 relative error = 2.039005222053325e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = 2.461072691376713 y[1] (numeric) = 2.461072691376708 absolute error = 5e-15 relative error = 2.031634424094569e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=603.4MB, alloc=44.3MB, time=7.33 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (closed_form) = 2.469923113727602 y[1] (numeric) = 2.469923113727596 absolute error = 6e-15 relative error = 2.429225414610099e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = 2.47872654415872 y[1] (numeric) = 2.478726544158714 absolute error = 6e-15 relative error = 2.420597792095860e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = 2.487482102334359 y[1] (numeric) = 2.487482102334353 absolute error = 6e-15 relative error = 2.412077656506290e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = 2.496188912705999 y[1] (numeric) = 2.496188912705994 absolute error = 5e-15 relative error = 2.003053524734928e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 2.504846104599858 y[1] (numeric) = 2.504846104599853 absolute error = 5e-15 relative error = 1.996130616894221e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = 2.51345281230396 y[1] (numeric) = 2.513452812303954 absolute error = 6e-15 relative error = 2.387154423838215e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = 2.522008175154707 y[1] (numeric) = 2.522008175154702 absolute error = 5e-15 relative error = 1.982547102446758e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = 2.530511337622945 y[1] (numeric) = 2.530511337622939 absolute error = 6e-15 relative error = 2.371062287211938e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = 2.538961449399511 y[1] (numeric) = 2.538961449399504 absolute error = 7e-15 relative error = 2.757032802390744e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = 2.547357665480271 y[1] (numeric) = 2.547357665480264 absolute error = 7e-15 relative error = 2.747945486752149e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = 2.555699146250613 y[1] (numeric) = 2.555699146250605 absolute error = 8e-15 relative error = 3.130258900675595e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = 2.56398505756941 y[1] (numeric) = 2.563985057569402 absolute error = 8e-15 relative error = 3.120142988502354e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = 2.572214570852437 y[1] (numeric) = 2.572214570852428 absolute error = 9e-15 relative error = 3.498930494362833e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (closed_form) = 2.580386863155222 y[1] (numeric) = 2.580386863155213 absolute error = 9e-15 relative error = 3.487849100655807e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=646.2MB, alloc=44.3MB, time=7.83 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 2.588501117255346 y[1] (numeric) = 2.588501117255337 absolute error = 9e-15 relative error = 3.476915632759290e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = 2.59655652173416 y[1] (numeric) = 2.596556521734152 absolute error = 8e-15 relative error = 3.081003603440547e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = 2.60455227105793 y[1] (numeric) = 2.604552271057922 absolute error = 8e-15 relative error = 3.071545189895736e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = 2.612487565658385 y[1] (numeric) = 2.612487565658378 absolute error = 7e-15 relative error = 2.679438590260198e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = 2.62036161201268 y[1] (numeric) = 2.620361612012673 absolute error = 7e-15 relative error = 2.671387020749153e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = 2.628173622722739 y[1] (numeric) = 2.628173622722733 absolute error = 6e-15 relative error = 2.282954196071762e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = 2.635922816594002 y[1] (numeric) = 2.635922816593997 absolute error = 5e-15 relative error = 1.896868894841440e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = 2.64360841871354 y[1] (numeric) = 2.643608418713536 absolute error = 4e-15 relative error = 1.513083394531828e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = 2.651229660527546 y[1] (numeric) = 2.651229660527543 absolute error = 3e-15 relative error = 1.131550406464242e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = 2.658785779918188 y[1] (numeric) = 2.658785779918184 absolute error = 4e-15 relative error = 1.504446138614101e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 2.666276021279824 y[1] (numeric) = 2.666276021279819 absolute error = 5e-15 relative error = 1.875274712780854e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = 2.673699635594561 y[1] (numeric) = 2.673699635594556 absolute error = 5e-15 relative error = 1.870067951326975e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = 2.681055880507153 y[1] (numeric) = 2.681055880507149 absolute error = 4e-15 relative error = 1.491949507312527e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = 2.688344020399238 y[1] (numeric) = 2.688344020399235 absolute error = 3e-15 relative error = 1.115928607810573e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=689.1MB, alloc=44.3MB, time=8.33 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = 2.695563326462902 y[1] (numeric) = 2.695563326462899 absolute error = 3e-15 relative error = 1.112939907791585e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = 2.702713076773554 y[1] (numeric) = 2.702713076773551 absolute error = 3e-15 relative error = 1.109995739385455e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = 2.70979255636212 y[1] (numeric) = 2.709792556362119 absolute error = 1e-15 relative error = 3.690319384973490e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = 2.716801057286543 y[1] (numeric) = 2.716801057286542 absolute error = 1e-15 relative error = 3.680799509842539e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = 2.723737878702569 y[1] (numeric) = 2.723737878702566 absolute error = 3e-15 relative error = 1.101427572549318e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = 2.730602326933837 y[1] (numeric) = 2.730602326933834 absolute error = 3e-15 relative error = 1.098658699001647e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 2.737393715541246 y[1] (numeric) = 2.737393715541241 absolute error = 5e-15 relative error = 1.826554934941605e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = 2.744111365391592 y[1] (numeric) = 2.744111365391588 absolute error = 4e-15 relative error = 1.457666788034745e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (closed_form) = 2.750754604725491 y[1] (numeric) = 2.750754604725485 absolute error = 6e-15 relative error = 2.181219651397717e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (closed_form) = 2.757322769224544 y[1] (numeric) = 2.757322769224536 absolute error = 8e-15 relative error = 2.901365081118117e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = 2.763815202077774 y[1] (numeric) = 2.763815202077767 absolute error = 7e-15 relative error = 2.532730840592221e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = 2.770231254047307 y[1] (numeric) = 2.770231254047298 absolute error = 9e-15 relative error = 3.248826243964652e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = 2.776570283533293 y[1] (numeric) = 2.776570283533283 absolute error = 1.0e-14 relative error = 3.601565593100929e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = 2.782831656638065 y[1] (numeric) = 2.782831656638054 absolute error = 1.1e-14 relative error = 3.952808274895465e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = 2.789014747229531 y[1] (numeric) = 2.789014747229521 absolute error = 1.0e-14 relative error = 3.585495562522036e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=731.9MB, alloc=44.3MB, time=8.83 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = 2.795118937003784 y[1] (numeric) = 2.795118937003773 absolute error = 1.1e-14 relative error = 3.935431818079056e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 2.801143615546934 y[1] (numeric) = 2.801143615546922 absolute error = 1.2e-14 relative error = 4.283964568398952e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = 2.807088180396146 y[1] (numeric) = 2.807088180396133 absolute error = 1.3e-14 relative error = 4.631133460925120e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = 2.81295203709989 y[1] (numeric) = 2.812952037099877 absolute error = 1.3e-14 relative error = 4.621479438164470e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = 2.818734599277382 y[1] (numeric) = 2.81873459927737 absolute error = 1.2e-14 relative error = 4.257229468526888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = 2.824435288677222 y[1] (numeric) = 2.824435288677212 absolute error = 1.0e-14 relative error = 3.540530753205302e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = 2.830053535235222 y[1] (numeric) = 2.830053535235212 absolute error = 1.0e-14 relative error = 3.533502061178798e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = 2.835588777131408 y[1] (numeric) = 2.835588777131397 absolute error = 1.1e-14 relative error = 3.879264895076933e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = 2.841040460846202 y[1] (numeric) = 2.841040460846191 absolute error = 1.1e-14 relative error = 3.871820958411714e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = 2.846408041215776 y[1] (numeric) = 2.846408041215765 absolute error = 1.1e-14 relative error = 3.864519717735764e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = 2.851690981486566 y[1] (numeric) = 2.851690981486554 absolute error = 1.2e-14 relative error = 4.208029578907770e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 2.856888753368947 y[1] (numeric) = 2.856888753368934 absolute error = 1.3e-14 relative error = 4.550404696252148e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = 2.862000837090064 y[1] (numeric) = 2.862000837090051 absolute error = 1.3e-14 relative error = 4.542276798639142e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = 2.867026721445802 y[1] (numeric) = 2.867026721445791 absolute error = 1.1e-14 relative error = 3.836727407428157e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=774.6MB, alloc=44.3MB, time=9.33 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (closed_form) = 2.871965903851917 y[1] (numeric) = 2.871965903851906 absolute error = 1.1e-14 relative error = 3.830129036436909e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = 2.876817890394281 y[1] (numeric) = 2.876817890394272 absolute error = 9e-15 relative error = 3.128456629128689e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = 2.881582195878286 y[1] (numeric) = 2.881582195878275 absolute error = 1.1e-14 relative error = 3.817347294737597e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = 2.886258343877352 y[1] (numeric) = 2.886258343877343 absolute error = 9e-15 relative error = 3.118223986806929e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = 2.890845866780576 y[1] (numeric) = 2.890845866780569 absolute error = 7e-15 relative error = 2.421436604572637e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = 2.895344305839492 y[1] (numeric) = 2.895344305839483 absolute error = 9e-15 relative error = 3.108438599806005e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = 2.899753211213941 y[1] (numeric) = 2.899753211213933 absolute error = 8e-15 relative error = 2.758855467100565e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 2.904072142017061 y[1] (numeric) = 2.904072142017053 absolute error = 8e-15 relative error = 2.754752502272032e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = 2.90830066635937 y[1] (numeric) = 2.908300666359361 absolute error = 9e-15 relative error = 3.094590632978212e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = 2.912438361391958 y[1] (numeric) = 2.912438361391948 absolute error = 1.0e-14 relative error = 3.433549060664290e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = 2.916484813348769 y[1] (numeric) = 2.916484813348762 absolute error = 7e-15 relative error = 2.400149648632133e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = 2.920439617587981 y[1] (numeric) = 2.920439617587972 absolute error = 9e-15 relative error = 3.081727814469654e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = 2.924302378632464 y[1] (numeric) = 2.924302378632456 absolute error = 8e-15 relative error = 2.735695206643152e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = 2.928072710209333 y[1] (numeric) = 2.928072710209325 absolute error = 8e-15 relative error = 2.732172589876727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (closed_form) = 2.931750235288572 y[1] (numeric) = 2.931750235288563 absolute error = 9e-15 relative error = 3.069838587090326e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=817.4MB, alloc=44.3MB, time=9.81 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = 2.935334586120739 y[1] (numeric) = 2.93533458612073 absolute error = 9e-15 relative error = 3.066089992791644e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = 2.938825404273736 y[1] (numeric) = 2.938825404273728 absolute error = 8e-15 relative error = 2.722176005544984e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 2.942222340668658 y[1] (numeric) = 2.942222340668651 absolute error = 7e-15 relative error = 2.379153982771118e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = 2.945525055614696 y[1] (numeric) = 2.94552505561469 absolute error = 6e-15 relative error = 2.036988274319015e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = 2.948733218843107 y[1] (numeric) = 2.948733218843102 absolute error = 5e-15 relative error = 1.695643392914900e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = 2.951846509540242 y[1] (numeric) = 2.951846509540238 absolute error = 4e-15 relative error = 1.355084008288429e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = 2.954864616379626 y[1] (numeric) = 2.954864616379621 absolute error = 5e-15 relative error = 1.692124902198100e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = 2.95778723755309 y[1] (numeric) = 2.957787237553085 absolute error = 5e-15 relative error = 1.690452895501837e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = 2.960614080800952 y[1] (numeric) = 2.960614080800947 absolute error = 5e-15 relative error = 1.688838823142840e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = 2.963344863441243 y[1] (numeric) = 2.963344863441239 absolute error = 4e-15 relative error = 1.349826019019238e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = 2.965979312397975 y[1] (numeric) = 2.96597931239797 absolute error = 5e-15 relative error = 1.685783841815651e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = 2.968517164228447 y[1] (numeric) = 2.968517164228443 absolute error = 4e-15 relative error = 1.347474101952733e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 2.97095816514959 y[1] (numeric) = 2.970958165149587 absolute error = 3e-15 relative error = 1.009775241937460e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = 2.973302071063349 y[1] (numeric) = 2.973302071063345 absolute error = 4e-15 relative error = 1.345305624655039e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=860.1MB, alloc=44.3MB, time=10.33 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = 2.975548647581083 y[1] (numeric) = 2.97554864758108 absolute error = 3e-15 relative error = 1.008217426537050e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = 2.977697670047013 y[1] (numeric) = 2.97769767004701 absolute error = 3e-15 relative error = 1.007489789906252e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = 2.979748923560684 y[1] (numeric) = 2.979748923560681 absolute error = 3e-15 relative error = 1.006796235843628e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = 2.981702202998454 y[1] (numeric) = 2.981702202998451 absolute error = 3e-15 relative error = 1.006136695000307e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = 2.983557313034006 y[1] (numeric) = 2.983557313034002 absolute error = 4e-15 relative error = 1.340681468569600e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = 2.985314068157884 y[1] (numeric) = 2.985314068157881 absolute error = 3e-15 relative error = 1.004919392568695e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = 2.986972292696038 y[1] (numeric) = 2.986972292696034 absolute error = 4e-15 relative error = 1.339148679008872e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = 2.988531820827396 y[1] (numeric) = 2.988531820827392 absolute error = 4e-15 relative error = 1.338449860939601e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = 2.989992496600446 y[1] (numeric) = 2.98999249660044 absolute error = 6e-15 relative error = 2.006693999005638e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = 2.991354173948826 y[1] (numeric) = 2.99135417394882 absolute error = 6e-15 relative error = 2.005780543224516e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = 2.992616716705937 y[1] (numeric) = 2.992616716705932 absolute error = 5e-15 relative error = 1.670778610601243e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = 2.993779998618556 y[1] (numeric) = 2.99377999861855 absolute error = 6e-15 relative error = 2.004155282876039e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = 2.99484390335946 y[1] (numeric) = 2.994843903359454 absolute error = 6e-15 relative error = 2.003443315783341e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = 2.995808324539061 y[1] (numeric) = 2.995808324539055 absolute error = 6e-15 relative error = 2.002798360246618e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = 2.996673165716047 y[1] (numeric) = 2.99667316571604 absolute error = 7e-15 relative error = 2.335923743731782e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=902.9MB, alloc=44.3MB, time=10.83 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (closed_form) = 2.997438340407018 y[1] (numeric) = 2.997438340407013 absolute error = 5e-15 relative error = 1.668091027127203e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = 2.998103772095146 y[1] (numeric) = 2.99810377209514 absolute error = 6e-15 relative error = 2.001264951482002e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = 2.998669394237814 y[1] (numeric) = 2.998669394237808 absolute error = 6e-15 relative error = 2.000887464129752e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = 2.99913515027328 y[1] (numeric) = 2.999135150273273 absolute error = 7e-15 relative error = 2.334006188204677e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = 2.999500993626328 y[1] (numeric) = 2.999500993626322 absolute error = 6e-15 relative error = 2.000332726259956e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = 2.999766887712928 y[1] (numeric) = 2.999766887712923 absolute error = 5e-15 relative error = 1.666796183556811e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = 2.999932805943894 y[1] (numeric) = 2.999932805943888 absolute error = 6e-15 relative error = 2.000044797040769e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = 2.99999873172754 y[1] (numeric) = 2.999998731727534 absolute error = 6e-15 relative error = 2.000000845515331e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = 2.999964658471342 y[1] (numeric) = 2.999964658471338 absolute error = 4e-15 relative error = 1.333349040864446e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = 2.999830589582598 y[1] (numeric) = 2.999830589582594 absolute error = 4e-15 relative error = 1.333408631104254e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = 2.999596538468086 y[1] (numeric) = 2.999596538468081 absolute error = 5e-15 relative error = 1.666890842110897e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = 2.999262528532721 y[1] (numeric) = 2.999262528532717 absolute error = 4e-15 relative error = 1.333661179022182e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = 2.998828593177219 y[1] (numeric) = 2.998828593177214 absolute error = 5e-15 relative error = 1.667317702444129e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = 2.998294775794753 y[1] (numeric) = 2.998294775794749 absolute error = 4e-15 relative error = 1.334091641786531e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop memory used=945.5MB, alloc=44.3MB, time=11.33 x[1] = 3.21 y[1] (closed_form) = 2.997661129766618 y[1] (numeric) = 2.997661129766614 absolute error = 4e-15 relative error = 1.334373642264034e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = 2.996927718456887 y[1] (numeric) = 2.996927718456883 absolute error = 4e-15 relative error = 1.334700191588068e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = 2.996094615206081 y[1] (numeric) = 2.996094615206077 absolute error = 4e-15 relative error = 1.335071322413784e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = 2.99516190332383 y[1] (numeric) = 2.995161903323827 absolute error = 3e-15 relative error = 1.001615303890852e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = 2.994129676080546 y[1] (numeric) = 2.994129676080541 absolute error = 5e-15 relative error = 1.669934351856540e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = 2.992998036698093 y[1] (numeric) = 2.992998036698088 absolute error = 5e-15 relative error = 1.670565746683901e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = 2.991767098339465 y[1] (numeric) = 2.99176709833946 absolute error = 5e-15 relative error = 1.671253087439585e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = 2.990436984097473 y[1] (numeric) = 2.990436984097467 absolute error = 6e-15 relative error = 2.006395731428805e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = 2.989007826982433 y[1] (numeric) = 2.989007826982428 absolute error = 5e-15 relative error = 1.672795887271989e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = 2.987479769908865 y[1] (numeric) = 2.98747976990886 absolute error = 5e-15 relative error = 1.673651500626740e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = 2.985852965681203 y[1] (numeric) = 2.985852965681199 absolute error = 4e-15 relative error = 1.339650694784773e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = 2.984127576978514 y[1] (numeric) = 2.98412757697851 absolute error = 4e-15 relative error = 1.340425265614842e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = 2.982303776338232 y[1] (numeric) = 2.982303776338227 absolute error = 5e-15 relative error = 1.676556238056728e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = 2.980381746138899 y[1] (numeric) = 2.980381746138894 absolute error = 5e-15 relative error = 1.677637439055426e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = 2.978361678581934 y[1] (numeric) = 2.978361678581931 absolute error = 3e-15 relative error = 1.007265175876279e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=988.3MB, alloc=44.3MB, time=11.84 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = 2.97624377567241 y[1] (numeric) = 2.976243775672408 absolute error = 2e-15 relative error = 6.719879656188944e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = 2.974028249198852 y[1] (numeric) = 2.97402824919885 absolute error = 2e-15 relative error = 6.724885685059524e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = 2.971715320712062 y[1] (numeric) = 2.971715320712059 absolute error = 3e-15 relative error = 1.009517963948566e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = 2.969305221502961 y[1] (numeric) = 2.969305221502958 absolute error = 3e-15 relative error = 1.010337360495902e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = 2.966798192579461 y[1] (numeric) = 2.966798192579458 absolute error = 3e-15 relative error = 1.011191124325066e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = 2.964194484642366 y[1] (numeric) = 2.964194484642363 absolute error = 3e-15 relative error = 1.012079340793306e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (closed_form) = 2.961494358060299 y[1] (numeric) = 2.961494358060296 absolute error = 3e-15 relative error = 1.013002098698888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (closed_form) = 2.958698082843669 y[1] (numeric) = 2.958698082843666 absolute error = 3e-15 relative error = 1.013959490289268e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = 2.955805938617666 y[1] (numeric) = 2.955805938617663 absolute error = 3e-15 relative error = 1.014951611269515e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = 2.952818214594305 y[1] (numeric) = 2.952818214594302 absolute error = 3e-15 relative error = 1.015978560810990e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (closed_form) = 2.949735209543496 y[1] (numeric) = 2.949735209543494 absolute error = 2e-15 relative error = 6.780269610401816e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = 2.946557231763177 y[1] (numeric) = 2.946557231763174 absolute error = 3e-15 relative error = 1.018137359648312e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = 2.943284599048476 y[1] (numeric) = 2.943284599048473 absolute error = 3e-15 relative error = 1.019269424699827e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = 2.939917638659938 y[1] (numeric) = 2.939917638659936 absolute error = 2e-15 relative error = 6.802911665619423e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = 2.936456687290796 y[1] (numeric) = 2.936456687290794 absolute error = 2e-15 relative error = 6.810929678125850e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 memory used=1031.1MB, alloc=44.3MB, time=12.34 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = 2.932902091033304 y[1] (numeric) = 2.932902091033301 absolute error = 3e-15 relative error = 1.022877650492266e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (closed_form) = 2.929254205344123 y[1] (numeric) = 2.92925420534412 absolute error = 3e-15 relative error = 1.024151469861103e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = 2.925513395008784 y[1] (numeric) = 2.925513395008781 absolute error = 3e-15 relative error = 1.025461037067305e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = 2.921680034105203 y[1] (numeric) = 2.9216800341052 absolute error = 3e-15 relative error = 1.026806482907285e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = 2.917754505966276 y[1] (numeric) = 2.917754505966273 absolute error = 3e-15 relative error = 1.028187941742716e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = 2.913737203141545 y[1] (numeric) = 2.913737203141543 absolute error = 2e-15 relative error = 6.864037010076378e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = 2.909628527357944 y[1] (numeric) = 2.909628527357943 absolute error = 1e-15 relative error = 3.436864845795415e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = 2.90542888947963 y[1] (numeric) = 2.905428889479628 absolute error = 2e-15 relative error = 6.883665290318653e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = 2.901138709466888 y[1] (numeric) = 2.901138709466887 absolute error = 1e-15 relative error = 3.446922398907840e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = 2.896758416334147 y[1] (numeric) = 2.896758416334145 absolute error = 2e-15 relative error = 6.904269229779277e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = 2.892288448107068 y[1] (numeric) = 2.892288448107067 absolute error = 1e-15 relative error = 3.457469813062648e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (closed_form) = 2.88772925177875 y[1] (numeric) = 2.887729251778749 absolute error = 1e-15 relative error = 3.462928525532758e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = 2.883081283265026 y[1] (numeric) = 2.883081283265025 absolute error = 1e-15 relative error = 3.468511296592797e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = 2.878345007358874 y[1] (numeric) = 2.878345007358873 absolute error = 1e-15 relative error = 3.474218682761678e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 memory used=1073.9MB, alloc=44.3MB, time=12.84 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = 2.873520897683938 y[1] (numeric) = 2.873520897683938 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = 2.868609436647165 y[1] (numeric) = 2.868609436647164 absolute error = 1e-15 relative error = 3.486009587867777e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = 2.863611115390566 y[1] (numeric) = 2.863611115390566 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = 2.858526433742102 y[1] (numeric) = 2.858526433742101 absolute error = 1e-15 relative error = 3.498305939018021e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = 2.8533559001657 y[1] (numeric) = 2.853355900165698 absolute error = 2e-15 relative error = 7.009290358359629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = 2.848100031710408 y[1] (numeric) = 2.848100031710406 absolute error = 2e-15 relative error = 7.022225265026639e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = 2.842759353958694 y[1] (numeric) = 2.842759353958691 absolute error = 3e-15 relative error = 1.055312682665995e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = 2.83733440097388 y[1] (numeric) = 2.837334400973876 absolute error = 4e-15 relative error = 1.409773905616148e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = 2.831825715246746 y[1] (numeric) = 2.831825715246741 absolute error = 5e-15 relative error = 1.765645383146164e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = 2.826233847641272 y[1] (numeric) = 2.82623384764127 absolute error = 2e-15 relative error = 7.076555259817467e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = 2.820559357339561 y[1] (numeric) = 2.820559357339558 absolute error = 3e-15 relative error = 1.063618814542408e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = 2.814802811785912 y[1] (numeric) = 2.814802811785911 absolute error = 1e-15 relative error = 3.552646728264168e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = 2.808964786630086 y[1] (numeric) = 2.808964786630084 absolute error = 2e-15 relative error = 7.120060776551775e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = 2.803045865669731 y[1] (numeric) = 2.803045865669728 absolute error = 3e-15 relative error = 1.070264328080558e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = 2.797046640792012 y[1] (numeric) = 2.797046640792008 absolute error = 4e-15 relative error = 1.430079835517995e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=1116.7MB, alloc=44.3MB, time=13.34 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (closed_form) = 2.790967711914417 y[1] (numeric) = 2.790967711914414 absolute error = 3e-15 relative error = 1.074895989370726e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = 2.784809686924768 y[1] (numeric) = 2.784809686924766 absolute error = 2e-15 relative error = 7.181819315662379e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = 2.778573181620432 y[1] (numeric) = 2.778573181620429 absolute error = 3e-15 relative error = 1.079690835513799e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (closed_form) = 2.772258819646744 y[1] (numeric) = 2.772258819646741 absolute error = 3e-15 relative error = 1.082150042679737e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = 2.765867232434637 y[1] (numeric) = 2.765867232434635 absolute error = 2e-15 relative error = 7.231005076984526e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = 2.759399059137508 y[1] (numeric) = 2.759399059137506 absolute error = 2e-15 relative error = 7.247954924740499e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = 2.752854946567295 y[1] (numeric) = 2.752854946567292 absolute error = 3e-15 relative error = 1.089777724663948e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = 2.746235549129803 y[1] (numeric) = 2.7462355491298 absolute error = 3e-15 relative error = 1.092404473808012e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = 2.739541528759258 y[1] (numeric) = 2.739541528759254 absolute error = 4e-15 relative error = 1.460098325945658e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = 2.732773554852121 y[1] (numeric) = 2.732773554852115 absolute error = 6e-15 relative error = 2.195571597707692e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = 2.72593230420014 y[1] (numeric) = 2.725932304200135 absolute error = 5e-15 relative error = 1.834234838589336e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = 2.719018460922681 y[1] (numeric) = 2.719018460922677 absolute error = 4e-15 relative error = 1.471119103267370e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = 2.71203271639831 y[1] (numeric) = 2.712032716398305 absolute error = 5e-15 relative error = 1.843635576284715e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = 2.704975769195658 y[1] (numeric) = 2.704975769195652 absolute error = 6e-15 relative error = 2.218134472156155e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=1159.5MB, alloc=44.3MB, time=13.84 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = 2.697848325003564 y[1] (numeric) = 2.697848325003559 absolute error = 5e-15 relative error = 1.853328800459305e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = 2.690651096560508 y[1] (numeric) = 2.690651096560502 absolute error = 6e-15 relative error = 2.229943528415807e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = 2.683384803583336 y[1] (numeric) = 2.683384803583331 absolute error = 5e-15 relative error = 1.863318296102409e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = 2.676050172695292 y[1] (numeric) = 2.676050172695288 absolute error = 4e-15 relative error = 1.494740285818796e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = 2.668647937353351 y[1] (numeric) = 2.668647937353349 absolute error = 2e-15 relative error = 7.494431813225663e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = 2.66117883777488 y[1] (numeric) = 2.661178837774877 absolute error = 3e-15 relative error = 1.127319952126337e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = 2.653643620863612 y[1] (numeric) = 2.65364362086361 absolute error = 2e-15 relative error = 7.536807068875030e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (closed_form) = 2.646043040134959 y[1] (numeric) = 2.646043040134956 absolute error = 3e-15 relative error = 1.133768406067570e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = 2.638377855640659 y[1] (numeric) = 2.638377855640657 absolute error = 2e-15 relative error = 7.580415351516638e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (closed_form) = 2.630648833892776 y[1] (numeric) = 2.630648833892773 absolute error = 3e-15 relative error = 1.140403067619127e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (closed_form) = 2.622856747787042 y[1] (numeric) = 2.622856747787041 absolute error = 1e-15 relative error = 3.812636739859012e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = 2.615002376525574 y[1] (numeric) = 2.615002376525573 absolute error = 1e-15 relative error = 3.824088302851377e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = 2.607086505538955 y[1] (numeric) = 2.607086505538952 absolute error = 3e-15 relative error = 1.150709803309660e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = 2.599109926407685 y[1] (numeric) = 2.599109926407682 absolute error = 3e-15 relative error = 1.154241292189745e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = 2.591073436783031 y[1] (numeric) = 2.591073436783027 absolute error = 4e-15 relative error = 1.543761725629141e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=1202.5MB, alloc=44.3MB, time=14.34 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = 2.582977840307259 y[1] (numeric) = 2.582977840307255 absolute error = 4e-15 relative error = 1.548600199963070e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = 2.574823946533269 y[1] (numeric) = 2.574823946533266 absolute error = 3e-15 relative error = 1.165128203828920e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = 2.566612570843644 y[1] (numeric) = 2.566612570843639 absolute error = 5e-15 relative error = 1.948093006634228e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = 2.55834453436911 y[1] (numeric) = 2.558344534369104 absolute error = 6e-15 relative error = 2.345266604788868e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = 2.550020663906425 y[1] (numeric) = 2.55002066390642 absolute error = 5e-15 relative error = 1.960768424652844e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = 2.541641791835698 y[1] (numeric) = 2.541641791835693 absolute error = 5e-15 relative error = 1.967232367700704e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = 2.533208756037155 y[1] (numeric) = 2.533208756037148 absolute error = 7e-15 relative error = 2.763293780395148e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = 2.524722399807346 y[1] (numeric) = 2.524722399807338 absolute error = 8e-15 relative error = 3.168665196859051e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = 2.516183571774825 y[1] (numeric) = 2.516183571774817 absolute error = 8e-15 relative error = 3.179418262538408e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = 2.507593125815277 y[1] (numeric) = 2.507593125815269 absolute error = 8e-15 relative error = 3.190310229215919e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (closed_form) = 2.498951920966141 y[1] (numeric) = 2.498951920966132 absolute error = 9e-15 relative error = 3.601509866792649e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 2.4902608213407 y[1] (numeric) = 2.49026082134069 absolute error = 1.0e-14 relative error = 4.015643628291203e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = 2.481520696041674 y[1] (numeric) = 2.481520696041663 absolute error = 1.1e-14 relative error = 4.432765770419055e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = 2.47273241907431 y[1] (numeric) = 2.472732419074299 absolute error = 1.1e-14 relative error = 4.448520153311999e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=1245.2MB, alloc=44.3MB, time=14.84 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = 2.46389686925898 y[1] (numeric) = 2.46389686925897 absolute error = 1.0e-14 relative error = 4.058611431657654e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = 2.455014930143305 y[1] (numeric) = 2.455014930143294 absolute error = 1.1e-14 relative error = 4.480624482132133e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = 2.446087489913793 y[1] (numeric) = 2.446087489913783 absolute error = 1.0e-14 relative error = 4.088161213053106e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = 2.437115441307028 y[1] (numeric) = 2.437115441307018 absolute error = 1.0e-14 relative error = 4.103211456670673e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (closed_form) = 2.428099681520394 y[1] (numeric) = 2.428099681520385 absolute error = 9e-15 relative error = 3.706602355947967e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = 2.419041112122356 y[1] (numeric) = 2.419041112122347 absolute error = 9e-15 relative error = 3.720482448561534e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = 2.409940638962306 y[1] (numeric) = 2.409940638962296 absolute error = 1.0e-14 relative error = 4.149479799762159e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 2.400799172079975 y[1] (numeric) = 2.400799172079964 absolute error = 1.1e-14 relative error = 4.581807644689395e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = 2.391617625614435 y[1] (numeric) = 2.391617625614425 absolute error = 1.0e-14 relative error = 4.181270405812000e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = 2.38239691771268 y[1] (numeric) = 2.382396917712669 absolute error = 1.1e-14 relative error = 4.617198720421873e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = 2.373137970437818 y[1] (numeric) = 2.373137970437808 absolute error = 1.0e-14 relative error = 4.213830010968603e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = 2.363841709676858 y[1] (numeric) = 2.36384170967685 absolute error = 8e-15 relative error = 3.384321364349568e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = 2.354509065048132 y[1] (numeric) = 2.354509065048123 absolute error = 9e-15 relative error = 3.822452898399020e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = 2.345140969808323 y[1] (numeric) = 2.345140969808316 absolute error = 7e-15 relative error = 2.984895189721638e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=1288.0MB, alloc=44.3MB, time=15.34 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = 2.335738360759151 y[1] (numeric) = 2.335738360759144 absolute error = 7e-15 relative error = 2.996911005787862e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = 2.326302178153683 y[1] (numeric) = 2.326302178153677 absolute error = 6e-15 relative error = 2.579200611316120e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = 2.316833365602318 y[1] (numeric) = 2.316833365602311 absolute error = 7e-15 relative error = 3.021365327316139e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = 2.30733286997842 y[1] (numeric) = 2.307332869978413 absolute error = 7e-15 relative error = 3.033805867839723e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = 2.297801641323633 y[1] (numeric) = 2.297801641323628 absolute error = 5e-15 relative error = 2.175992875137727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = 2.288240632752882 y[1] (numeric) = 2.288240632752875 absolute error = 7e-15 relative error = 3.059118826842353e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = 2.278650800359054 y[1] (numeric) = 2.278650800359047 absolute error = 7e-15 relative error = 3.071993303623788e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = 2.269033103117399 y[1] (numeric) = 2.269033103117393 absolute error = 6e-15 relative error = 2.644298133754271e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = 2.259388502789626 y[1] (numeric) = 2.259388502789619 absolute error = 7e-15 relative error = 3.098183420583590e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (closed_form) = 2.249717963827731 y[1] (numeric) = 2.249717963827724 absolute error = 7e-15 relative error = 3.111501135942396e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = 2.24002245327755 y[1] (numeric) = 2.240022453277543 absolute error = 7e-15 relative error = 3.124968675987046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = 2.230302940682059 y[1] (numeric) = 2.230302940682052 absolute error = 7e-15 relative error = 3.138587082640575e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = 2.220560397984419 y[1] (numeric) = 2.220560397984412 absolute error = 7e-15 relative error = 3.152357398769172e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = 2.21079579943078 y[1] (numeric) = 2.210795799430773 absolute error = 7e-15 relative error = 3.166280667713549e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = 2.20101012147286 y[1] (numeric) = 2.201010121472855 absolute error = 5e-15 relative error = 2.271684237714512e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=1330.8MB, alloc=44.3MB, time=15.84 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = 2.191204342670301 y[1] (numeric) = 2.191204342670297 absolute error = 4e-15 relative error = 1.825480135332982e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = 2.181379443592812 y[1] (numeric) = 2.181379443592807 absolute error = 5e-15 relative error = 2.292127586828643e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (closed_form) = 2.171536406722112 y[1] (numeric) = 2.171536406722108 absolute error = 4e-15 relative error = 1.842013786928820e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = 2.161676216353686 y[1] (numeric) = 2.161676216353683 absolute error = 3e-15 relative error = 1.387811910638679e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = 2.151799858498355 y[1] (numeric) = 2.151799858498352 absolute error = 3e-15 relative error = 1.394181707072686e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = 2.141908320783674 y[1] (numeric) = 2.14190832078367 absolute error = 4e-15 relative error = 1.867493562253166e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = 2.13200259235517 y[1] (numeric) = 2.132002592355167 absolute error = 3e-15 relative error = 1.407127744946114e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = 2.122083663777433 y[1] (numeric) = 2.122083663777429 absolute error = 4e-15 relative error = 1.884939820364936e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = 2.112152526935054 y[1] (numeric) = 2.11215252693505 absolute error = 4e-15 relative error = 1.893802625042616e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = 2.102210174933442 y[1] (numeric) = 2.102210174933437 absolute error = 5e-15 relative error = 2.378449148243850e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (closed_form) = 2.092257601999512 y[1] (numeric) = 2.092257601999506 absolute error = 6e-15 relative error = 2.867715712570942e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = 2.082295803382262 y[1] (numeric) = 2.082295803382255 absolute error = 7e-15 relative error = 3.361674162061863e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = 2.072325775253254 y[1] (numeric) = 2.072325775253248 absolute error = 6e-15 relative error = 2.895297675514727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = 2.062348514606992 y[1] (numeric) = 2.062348514606986 absolute error = 6e-15 relative error = 2.909304590132953e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=1373.7MB, alloc=44.3MB, time=16.34 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = 2.052365019161226 y[1] (numeric) = 2.052365019161219 absolute error = 7e-15 relative error = 3.410699332061704e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = 2.042376287257181 y[1] (numeric) = 2.042376287257176 absolute error = 5e-15 relative error = 2.448128697535347e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = 2.032383317759724 y[1] (numeric) = 2.032383317759719 absolute error = 5e-15 relative error = 2.460165834027535e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (closed_form) = 2.022387109957478 y[1] (numeric) = 2.022387109957473 absolute error = 5e-15 relative error = 2.472325884288853e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = 2.012388663462891 y[1] (numeric) = 2.012388663462887 absolute error = 4e-15 relative error = 1.987687603604790e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = 2.002388978112282 y[1] (numeric) = 2.002388978112278 absolute error = 4e-15 relative error = 1.997613872091391e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = 1.992389053865852 y[1] (numeric) = 1.992389053865849 absolute error = 3e-15 relative error = 1.505730015018438e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = 1.982389890707693 y[1] (numeric) = 1.982389890707691 absolute error = 2e-15 relative error = 1.008883272344584e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = 1.972392488545789 y[1] (numeric) = 1.972392488545787 absolute error = 2e-15 relative error = 1.013996966432662e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = 1.962397847112023 y[1] (numeric) = 1.962397847112023 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = 1.952406965862212 y[1] (numeric) = 1.952406965862211 absolute error = 1e-15 relative error = 5.121882975655053e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = 1.942420843876154 y[1] (numeric) = 1.942420843876153 absolute error = 1e-15 relative error = 5.148214935772995e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = 1.932440479757725 y[1] (numeric) = 1.932440479757726 absolute error = 1e-15 relative error = 5.174803625130915e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = 1.922466871535021 y[1] (numeric) = 1.922466871535021 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = 1.912501016560553 y[1] (numeric) = 1.912501016560554 absolute error = 1e-15 relative error = 5.228755390668512e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 memory used=1416.4MB, alloc=44.3MB, time=16.84 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = 1.902543911411514 y[1] (numeric) = 1.902543911411514 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = 1.89259655179012 y[1] (numeric) = 1.892596551790118 absolute error = 2e-15 relative error = 1.056749257050211e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = 1.882659932424045 y[1] (numeric) = 1.882659932424044 absolute error = 1e-15 relative error = 5.311633730433919e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = 1.872735046966944 y[1] (numeric) = 1.872735046966943 absolute error = 1e-15 relative error = 5.339783658236045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = 1.862822887899092 y[1] (numeric) = 1.862822887899092 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = 1.852924446428137 y[1] (numeric) = 1.852924446428136 absolute error = 1e-15 relative error = 5.396874124725860e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = 1.843040712389977 y[1] (numeric) = 1.843040712389974 absolute error = 3e-15 relative error = 1.627744834844005e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = 1.833172674149778 y[1] (numeric) = 1.833172674149776 absolute error = 2e-15 relative error = 1.091004698140395e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = 1.823321318503142 y[1] (numeric) = 1.823321318503141 absolute error = 1e-15 relative error = 5.484496834715624e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = 1.813487630577425 y[1] (numeric) = 1.813487630577424 absolute error = 1e-15 relative error = 5.514236673792995e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = 1.803672593733223 y[1] (numeric) = 1.803672593733222 absolute error = 1e-15 relative error = 5.544243470097920e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (closed_form) = 1.793877189466042 y[1] (numeric) = 1.793877189466039 absolute error = 3e-15 relative error = 1.672355285867126e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = 1.784102397308146 y[1] (numeric) = 1.784102397308143 absolute error = 3e-15 relative error = 1.681517834697381e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = 1.774349194730605 y[1] (numeric) = 1.774349194730601 absolute error = 4e-15 relative error = 2.254347685269083e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 memory used=1459.2MB, alloc=44.3MB, time=17.33 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = 1.764618557045549 y[1] (numeric) = 1.764618557045544 absolute error = 5e-15 relative error = 2.833473545904084e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = 1.754911457308638 y[1] (numeric) = 1.754911457308632 absolute error = 6e-15 relative error = 3.418975911868341e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = 1.745228866221757 y[1] (numeric) = 1.745228866221752 absolute error = 5e-15 relative error = 2.864953758657735e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = 1.735571752035945 y[1] (numeric) = 1.73557175203594 absolute error = 5e-15 relative error = 2.880895010036120e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 1.725941080454573 y[1] (numeric) = 1.725941080454568 absolute error = 5e-15 relative error = 2.896970271246522e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) ; Iterations = 5000 Total Elapsed Time = 17 Seconds Elapsed Time(since restart) = 17 Seconds Time to Timeout = 2 Minutes 42 Seconds Percent Done = 100 % > quit memory used=1475.3MB, alloc=44.3MB, time=17.52