|\^/| 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(neg (c(0.1) * (c(5.0) + c(2.0)*c(x)))/exp(c(x))); > end; exact_soln_y := proc(x) return neg(c(0.1)*(c(5.0) + c(2.0)*c(x)))/exp(c(x)) end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if (rad_given < glob_least_given_sing) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])* (array_x[1] - array_given_rad_poles[1, 1]) + array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if rad_given < glob_least_given_sing then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if array_rad_test_poles[1, 1] < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if array_rad_test_poles[1, 2] < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if array_rad_test_poles[1, 3] < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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)*25*ATS_MAX_TERMS/float_abs(numeric_val)); > if (evalf(est_rel_err) > glob_prec) then # if number 6 > glob_est_digits := -int_trunc(log10(est_rel_err)) + 3; > else > glob_est_digits := Digits; > fi;# end if 6; > else > relerr := glob__m1 ; > glob_est_digits := -16; > fi;# end if 5; > array_est_digits[1] := glob_est_digits; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > array_est_rel_error[1] := est_rel_err; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," "); > omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," "); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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)*25*ATS_MAX_TERMS/float_abs(numeric_val)) ; if glob_prec < evalf(est_rel_err) then glob_est_digits := -int_trunc(log10(est_rel_err)) + 3 else glob_est_digits := Digits end if else relerr := glob__m1; glob_est_digits := -16 end if; array_est_digits[1] := glob_est_digits; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; array_est_rel_error[1] := est_rel_err; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Desired digits ", 32, glob_desired_digits_correct, 4, " "); omniout_int(INFO, "Estimated correct digits ", 32, glob_est_digits, 4, " "); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr((glob_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr((left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(glob_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(left_sec); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D2[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D3[1]; > #emit pre exp 1 $eq_no = 1 > array_tmp3[1] := exp(array_x[1]); > #emit pre div LINEAR - FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp2[1] / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D2[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre exp ID_LINEAR iii = 2 $eq_no = 1 > array_tmp3[2] := array_tmp3[1] * array_x[2] / c(1); > #emit pre div LINEAR - FULL $eq_no = 1 i = 2 > array_tmp4[2] := (array_tmp2[2] - array_tmp4[1] * array_tmp3[2]) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[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_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre exp ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := array_tmp3[2] * array_x[2] / c(2); > #emit pre div LINEAR FULL $eq_no = 1 i = 3 > array_tmp4[3] := neg( ats(3,array_tmp3,array_tmp4,2)) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre exp ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := array_tmp3[3] * array_x[2] / c(3); > #emit pre div LINEAR FULL $eq_no = 1 i = 4 > array_tmp4[4] := neg( ats(4,array_tmp3,array_tmp4,2)) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre exp ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := array_tmp3[4] * array_x[2] / c(4); > #emit pre div LINEAR FULL $eq_no = 1 i = 5 > array_tmp4[5] := neg( ats(5,array_tmp3,array_tmp4,2)) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit exp LINEAR $eq_no = 1 > array_tmp3[kkk] := array_tmp3[kkk - 1] * array_x[2] / c(kkk - 1); > #emit div LINEAR FULL $eq_no = 1 i = 1 > array_tmp4[kkk] := neg(ats(kkk,array_tmp3,array_tmp4,2)) / array_tmp3[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_0D2[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D3[1]; array_tmp3[1] := exp(array_x[1]); array_tmp4[1] := array_tmp2[1]/array_tmp3[1]; array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_0D2[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp3[1]*array_x[2]/c(1); array_tmp4[2] := (-array_tmp3[2]*array_tmp4[1] + array_tmp2[2])/array_tmp3[1]; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[3] := array_tmp3[2]*array_x[2]/c(2); array_tmp4[3] := neg(ats(3, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[4] := array_tmp3[3]*array_x[2]/c(3); array_tmp4[4] := neg(ats(4, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[5] := array_tmp3[4]*array_x[2]/c(4); array_tmp4[5] := neg(ats(5, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp3[kkk] := array_tmp3[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp4[kkk] := neg(ats(kkk, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_h, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_tmp5:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(30) ,(0..30+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 30) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=30) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_0D2); > array_const_0D2[1] := c(0.2); > zero_ats_ar(array_const_0D3); > array_const_0D3[1] := c(0.3); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_h := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 1000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/div_lin_exppostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := c(1.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_end := c(5.0) ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 3;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=100000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=false;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(neg (c(0.1) * (c(5.0) + c(2.0)*c(x)))/exp(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := c(1.0); > x_end := c(5.0) ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_type_given_pole := 3; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=100000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=false; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > glob_check_sign := c(my_check_sign(x_start,x_end)); > glob__pi := arccos(glob__m1); > glob_prec = expt(10.0,c(-Digits)); > if (glob_optimize) then # if number 9 > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > found_h := false; > glob_min_pole_est := glob_larger_float; > last_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > glob_min_h := float_abs(glob_min_h) * glob_check_sign; > glob_max_h := float_abs(glob_max_h) * glob_check_sign; > glob_h := float_abs(glob_min_h) * glob_check_sign; > glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign)); > display_max := c(x_end) - c(x_start)/glob__10; > if ((glob_display_interval) > (display_max)) then # if number 10 > glob_display_interval := c(display_max); > fi;# end if 10; > chk_data(); > min_value := glob_larger_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := glob_small_float; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > glob_h := glob_check_sign * float_abs(glob_min_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL"); > glob_h_reason := 2; > glob_h := glob_display_interval; > found_h := true; > fi;# end if 10; > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if ( not found_h) then # if number 10 > est_answer := est_size_answer(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (estimated_step_error < est_needed_step_err) then # if number 11 > omniout_str(ALWAYS,"Double H and LOOP"); > glob_h := glob_h*glob__2; > else > omniout_str(ALWAYS,"Found H for OPTIMAL"); > found_h := true; > glob_h_reason := 3; > glob_h := glob_h/glob__2; > fi;# end if 11; > fi;# end if 10; > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 10 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 10; > if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MAX H"); > glob_h := glob_check_sign * float_abs(glob_max_h); > glob_h_reason := 1; > found_h := true; > fi;# end if 10; > else > found_h := true; > glob_h := glob_h * glob_check_sign; > fi;# end if 9; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 10 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 10; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > track_estimated_error(); > atomall(); > track_estimated_error(); > display_alot(current_iter); > if (glob_look_poles) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (reached_interval()) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( 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,"2015-04-24T20:11:01-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"div_lin_exp") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( 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,"div_lin_exp diffeq.mxt") > ; > logitem_str(html_log_file,"div_lin_exp maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > fi;# end if 14 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 32; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_tmp5 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y_higher := Array(0 .. 2, 0 .. 31, []); array_y_higher_work := Array(0 .. 2, 0 .. 31, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y_set_initial := Array(0 .. 2, 0 .. 31, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 30 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 30 do term := 1; while term <= 30 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_0D2); array_const_0D2[1] := c(0.2); zero_ats_ar(array_const_0D3); array_const_0D3[1] := c(0.3); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_h := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 1000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/div_lin_exppostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 0.2 * x +\ 0.3 ) / exp ( x ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := c(1.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_end := c(5.0) ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 3;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=100000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=false;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(neg (c(0.1) * (c(5.0) + c(2.0)*c(x)))/exp(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := c(1.0); x_end := c(5.0); array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 3; glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 100000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := false; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; glob_check_sign := c(my_check_sign(x_start, x_end)); glob__pi := arccos(glob__m1); glob_prec = expt(10.0, c(-Digits)); if glob_optimize then omniout_str(ALWAYS, "START of Optimize"); found_h := false; glob_min_pole_est := glob_larger_float; last_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; glob_min_h := float_abs(glob_min_h)*glob_check_sign; glob_max_h := float_abs(glob_max_h)*glob_check_sign; glob_h := float_abs(glob_min_h)*glob_check_sign; glob_display_interval := c(float_abs(c(glob_display_interval))*glob_check_sign); display_max := c(x_end) - c(x_start)/glob__10; if display_max < glob_display_interval then glob_display_interval := c(display_max) end if; chk_data(); min_value := glob_larger_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := glob_small_float; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]*expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); glob_h := float_abs(glob_min_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if; if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL"); glob_h_reason := 2; glob_h := glob_display_interval; found_h := true end if; if glob_look_poles then check_for_pole() end if; if not found_h then est_answer := est_size_answer(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if estimated_step_error < est_needed_step_err then omniout_str(ALWAYS, "Double H and LOOP"); glob_h := glob_h*glob__2 else omniout_str(ALWAYS, "Found H for OPTIMAL"); found_h := true; glob_h_reason := 3; glob_h := glob_h/glob__2 end if end if; opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then omniout_str(ALWAYS, "SETTING H FOR MAX H"); glob_h := float_abs(glob_max_h)*glob_check_sign; glob_h_reason := 1; found_h := true end if else found_h := true; glob_h := glob_check_sign*glob_h end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec - glob_orig_start_sec < glob_max_sec do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); track_estimated_error(); atomall(); track_estimated_error(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = ( 0.2 * x \ + 0.3 ) / exp ( 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, "2015-04-24T20:11:01-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "div_lin_exp"); logitem_str(html_log_file, "diff ( y , x , 1 ) = \ ( 0.2 * x + 0.3 ) / exp ( 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, "div_lin_exp diffeq.mxt"); logitem_str(html_log_file, "div_lin_exp maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/div_lin_exppostode.ode################# diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := c(1.0); x_end := c(5.0) ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 3; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=100000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=false; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(neg (c(0.1) * (c(5.0) + c(2.0)*c(x)))/exp(c(x))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = -0.25751560882000962511686663911302 y[1] (numeric) = -0.25751560882000962511686663911302 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 32 h = 0.001 memory used=4.2MB, alloc=40.3MB, time=0.13 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = -0.25568172365920937046944649953742 y[1] (numeric) = -0.25568172365920937046944649953742 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (closed_form) = -0.25385883788184712199006451079643 y[1] (numeric) = -0.25385883788184712199006451079644 absolute error = 1e-32 relative error = 3.9391971079038322681806815016270e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (closed_form) = -0.25204691416181804305580601464985 y[1] (numeric) = -0.25204691416181804305580601464987 absolute error = 2e-32 relative error = 7.9350306931985243891494697441462e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = -0.25024591482681634489201125183874 y[1] (numeric) = -0.25024591482681634489201125183876 absolute error = 2e-32 relative error = 7.9921384586202246314109774214162e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (closed_form) = -0.24845580186892030181697720023953 y[1] (numeric) = -0.24845580186892030181697720023956 absolute error = 3e-32 relative error = 1.2074582188999283619144981195418e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (closed_form) = -0.24667653695500089706889794384017 y[1] (numeric) = -0.24667653695500089706889794384019 absolute error = 2e-32 relative error = 8.1077836777189838377566721486560e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (closed_form) = -0.24490808143695656104710871943071 y[1] (numeric) = -0.24490808143695656104710871943074 absolute error = 3e-32 relative error = 1.2249493697382338965873406609141e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (closed_form) = -0.24315039636177643227001891411732 y[1] (numeric) = -0.24315039636177643227001891411733 absolute error = 1e-32 relative error = 4.1126809372423516984917616274223e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 memory used=41.1MB, alloc=44.3MB, time=0.55 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (closed_form) = -0.24140344248143454020615485234121 y[1] (numeric) = -0.24140344248143454020615485234123 absolute error = 2e-32 relative error = 8.2848859959973964242671492733592e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = -0.23966718026261727836796977263054 y[1] (numeric) = -0.23966718026261727836796977263056 absolute error = 2e-32 relative error = 8.3449056220734253112733554266354e-30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (closed_form) = -0.23794156989628650566605335731524 y[1] (numeric) = -0.23794156989628650566605335731527 absolute error = 3e-32 relative error = 1.2608137373001422088609417421262e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (closed_form) = -0.23622657130708058399967521238963 y[1] (numeric) = -0.23622657130708058399967521238966 absolute error = 3e-32 relative error = 1.2699672113092549910090979662564e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (closed_form) = -0.23452214416255563040386515477689 y[1] (numeric) = -0.23452214416255563040386515477693 absolute error = 4e-32 relative error = 1.7055958678373066062771417779744e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (closed_form) = -0.23282824788226923277915751934655 y[1] (numeric) = -0.23282824788226923277915751934658 absolute error = 3e-32 relative error = 1.2885034471920971522520149345520e-29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (closed_form) = -0.23114484164670884929344596527355 y[1] (numeric) = -0.2311448416467088492934459652736 absolute error = 5e-32 relative error = 2.1631458285546353611306168684978e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (closed_form) = -0.22947188440606708296189744676165 y[1] (numeric) = -0.22947188440606708296189744676169 absolute error = 4e-32 relative error = 1.7431329377684069249441482164053e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (closed_form) = -0.22780933488886599467639555874577 y[1] (numeric) = -0.22780933488886599467639555874582 absolute error = 5e-32 relative error = 2.1948178736570162994213605397889e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=84.9MB, alloc=52.3MB, time=1.03 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (closed_form) = -0.22615715161043259006640870493178 y[1] (numeric) = -0.22615715161043259006640870493184 absolute error = 6e-32 relative error = 2.6530224480078838433820885024236e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (closed_form) = -0.22451529288122758802443914265516 y[1] (numeric) = -0.22451529288122758802443914265522 absolute error = 6e-32 relative error = 2.6724237458399335590657164256974e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = -0.22288371681502955151728342924159 y[1] (numeric) = -0.22288371681502955151728342924164 absolute error = 5e-32 relative error = 2.2433222450922618172505185335146e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (closed_form) = -0.22126238133697643442524790517897 y[1] (numeric) = -0.22126238133697643442524790517903 absolute error = 6e-32 relative error = 2.7117126570477280439382124749668e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (closed_form) = -0.2196512441914665716012851395343 y[1] (numeric) = -0.21965124419146657160128513953436 absolute error = 6e-32 relative error = 2.7316030109849472853928590226317e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (closed_form) = -0.21805026294992111311686451636277 y[1] (numeric) = -0.21805026294992111311686451636281 absolute error = 4e-32 relative error = 1.8344394296459375730778296790628e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (closed_form) = -0.21645939501840987775742287432843 y[1] (numeric) = -0.21645939501840987775742287432849 absolute error = 6e-32 relative error = 2.7718824583657825652868573482263e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (closed_form) = -0.21487859764514257524366406998588 y[1] (numeric) = -0.21487859764514257524366406998593 absolute error = 5e-32 relative error = 2.3268953049745609174203640197815e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (closed_form) = -0.21330782792782732138203799037388 y[1] (numeric) = -0.21330782792782732138203799037392 absolute error = 4e-32 relative error = 1.8752241954071181728583553487355e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=128.6MB, alloc=52.3MB, time=1.53 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (closed_form) = -0.21174704282089834538472159813669 y[1] (numeric) = -0.21174704282089834538472159813673 absolute error = 4e-32 relative error = 1.8890464521779949731349980846429e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (closed_form) = -0.21019619914261476394268150194665 y[1] (numeric) = -0.21019619914261476394268150194669 absolute error = 4e-32 relative error = 1.9029839817826886044278933371645e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (closed_form) = -0.20865525358203227228129601694921 y[1] (numeric) = -0.20865525358203227228129601694926 absolute error = 5e-32 relative error = 2.3962972003646497958546713077252e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = -0.20712416270584957837297320734814 y[1] (numeric) = -0.2071241627058495783729732073482 absolute error = 6e-32 relative error = 2.8968131586467717529927551968513e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (closed_form) = -0.20560288296513138272167978906589 y[1] (numeric) = -0.20560288296513138272167978906593 absolute error = 4e-32 relative error = 1.9454980116588969503130315024801e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (closed_form) = -0.2040913707019096826667946600333 y[1] (numeric) = -0.20409137070190968266679466003335 absolute error = 5e-32 relative error = 2.4498831003016116286374710928180e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (closed_form) = -0.20258958215566515697476124460871 y[1] (numeric) = -0.20258958215566515697476124460876 absolute error = 5e-32 relative error = 2.4680439866636950038002465966274e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (closed_form) = -0.20109747346969036359321573543502 y[1] (numeric) = -0.20109747346969036359321573543507 absolute error = 5e-32 relative error = 2.4863564488062081990352777083846e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (closed_form) = -0.19961500069733646083023411024789 y[1] (numeric) = -0.19961500069733646083023411024794 absolute error = 5e-32 relative error = 2.5048217731798534663239213700846e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (closed_form) = -0.19814211980814513988772893629301 y[1] (numeric) = -0.19814211980814513988772893629308 absolute error = 7e-32 relative error = 3.5328177606951427454208793263085e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=172.5MB, alloc=52.3MB, time=2.00 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (closed_form) = -0.19667878669386743461953547666174 y[1] (numeric) = -0.19667878669386743461953547666181 absolute error = 7e-32 relative error = 3.5591026961619263943730672553812e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (closed_form) = -0.19522495717437105259809165153842 y[1] (numeric) = -0.19522495717437105259809165153849 absolute error = 7e-32 relative error = 3.5856071382040253649953833075485e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (closed_form) = -0.19378058700343785005561186637287 y[1] (numeric) = -0.19378058700343785005561186637294 absolute error = 7e-32 relative error = 3.6123329525654772681544937033413e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = -0.19234563187445305201309176707034 y[1] (numeric) = -0.19234563187445305201309176707041 absolute error = 7e-32 relative error = 3.6392820215272720654575336239231e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (closed_form) = -0.19092004742598779792020765098168 y[1] (numeric) = -0.19092004742598779792020765098175 absolute error = 7e-32 relative error = 3.6664562440534826519546241634257e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (closed_form) = -0.18950378924727657239807502829262 y[1] (numeric) = -0.18950378924727657239807502829268 absolute error = 6e-32 relative error = 3.1661636022332087343553322518006e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (closed_form) = -0.18809681288359106020182619962463 y[1] (numeric) = -0.18809681288359106020182619962468 absolute error = 5e-32 relative error = 2.6582055928264924660180609187995e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (closed_form) = -0.1866990738415119442980128237105 y[1] (numeric) = -0.18669907384151194429801282371057 absolute error = 7e-32 relative error = 3.7493490760121662156996576783042e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (closed_form) = -0.18531052759410014597992764447817 y[1] (numeric) = -0.18531052759410014597992764447824 absolute error = 7e-32 relative error = 3.7774432412888255340152246492489e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=216.1MB, alloc=52.3MB, time=2.48 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (closed_form) = -0.1839311295859689862190959999805 y[1] (numeric) = -0.18393112958596898621909599998055 absolute error = 5e-32 relative error = 2.7184087931472260758560542230320e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (closed_form) = -0.18256083523825872797047304114329 y[1] (numeric) = -0.18256083523825872797047304114335 absolute error = 6e-32 relative error = 3.2865756733471593767064271434727e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (closed_form) = -0.18119959995351493990939137501262 y[1] (numeric) = -0.18119959995351493990939137501268 absolute error = 6e-32 relative error = 3.3112655886322286575882821432040e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (closed_form) = -0.17984737912047210307716439149093 y[1] (numeric) = -0.17984737912047210307716439149099 absolute error = 6e-32 relative error = 3.3361620443636576005330495142962e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = -0.17850412811874386314662437661121 y[1] (numeric) = -0.17850412811874386314662437661127 absolute error = 6e-32 relative error = 3.3612668027535486169515415950895e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (closed_form) = -0.17716980232342131248595608940911 y[1] (numeric) = -0.17716980232342131248595608940917 absolute error = 6e-32 relative error = 3.3865816416316101127813015539738e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (closed_form) = -0.17584435710958066789620272820068 y[1] (numeric) = -0.17584435710958066789620272820072 absolute error = 4e-32 relative error = 2.2747389030558006004916599121591e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (closed_form) = -0.17452774785670169182203122564831 y[1] (numeric) = -0.17452774785670169182203122564833 absolute error = 2e-32 relative error = 1.1459495836972160816574490589962e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (closed_form) = -0.17321992995299818698403846064011 y[1] (numeric) = -0.17321992995299818698403846064011 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=260.0MB, alloc=52.3MB, time=2.97 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (closed_form) = -0.17192085879966187675138154803958 y[1] (numeric) = -0.17192085879966187675138154803957 absolute error = 1e-32 relative error = 5.8166298550502979326822713735610e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (closed_form) = -0.17063048981502096616317721615346 y[1] (numeric) = -0.17063048981502096616317721615344 absolute error = 2e-32 relative error = 1.1721234593935601137645161340924e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (closed_form) = -0.16934877843861466131332146670224 y[1] (numeric) = -0.16934877843861466131332146670223 absolute error = 1e-32 relative error = 5.9049732110260174123109825050111e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (closed_form) = -0.16807568013518490783354565347136 y[1] (numeric) = -0.16807568013518490783354565347134 absolute error = 2e-32 relative error = 1.1899401498130964010978926628039e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (closed_form) = -0.16681115039858659244109324873472 y[1] (numeric) = -0.1668111503985865924410932487347 absolute error = 2e-32 relative error = 1.1989606181727682635809992104166e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = -0.16555514475561743495784699946755 y[1] (numeric) = -0.16555514475561743495784699946753 absolute error = 2e-32 relative error = 1.2080566888768572691839722820546e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (closed_form) = -0.16430761876976878185456235273505 y[1] (numeric) = -0.16430761876976878185456235273502 absolute error = 3e-32 relative error = 1.8258435138078787224525122063190e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (closed_form) = -0.16306852804489849622460239810636 y[1] (numeric) = -0.16306852804489849622460239810634 absolute error = 2e-32 relative error = 1.2264782321756959241276924575012e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (closed_form) = -0.16183782822882712314378325339081 y[1] (numeric) = -0.16183782822882712314378325339079 absolute error = 2e-32 relative error = 1.2358050165948488463769139068093e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (closed_form) = -0.16061547501685849362421627326992 y[1] (numeric) = -0.16061547501685849362421627326992 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=303.8MB, alloc=52.3MB, time=3.47 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (closed_form) = -0.15940142415522591481799217667387 y[1] (numeric) = -0.15940142415522591481799217667387 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (closed_form) = -0.15819563144446507876883736050089 y[1] (numeric) = -0.15819563144446507876883736050088 absolute error = 1e-32 relative error = 6.3212870726525225170919116257858e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (closed_form) = -0.15699805274271480684415687584571 y[1] (numeric) = -0.15699805274271480684415687584571 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (closed_form) = -0.15580864396894673200386144658671 y[1] (numeric) = -0.15580864396894673200386144658671 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (closed_form) = -0.15462736110612500627378393582625 y[1] (numeric) = -0.15462736110612500627378393582627 absolute error = 2e-32 relative error = 1.2934321491959919373639282115163e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = -0.15345416020429710618807670371751 y[1] (numeric) = -0.15345416020429710618807670371753 absolute error = 2e-32 relative error = 1.3033208075540951811406815864307e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (closed_form) = -0.15228899738361679454452440312886 y[1] (numeric) = -0.15228899738361679454452440312888 absolute error = 2e-32 relative error = 1.3132925124997634337004399884705e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (closed_form) = -0.15113182883730028257701184377505 y[1] (numeric) = -0.15113182883730028257701184377507 absolute error = 2e-32 relative error = 1.3233479773166004757455415812842e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (closed_form) = -0.14998261083451662258828410634347 y[1] (numeric) = -0.14998261083451662258828410634349 absolute error = 2e-32 relative error = 1.3334879216142602358513231011367e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=347.6MB, alloc=52.3MB, time=3.95 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (closed_form) = -0.14884129972321334720148186880219 y[1] (numeric) = -0.1488412997232133472014818688022 absolute error = 1e-32 relative error = 6.7185653569245177027560127787266e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (closed_form) = -0.14770785193287835767860966986642 y[1] (numeric) = -0.14770785193287835767860966986643 absolute error = 1e-32 relative error = 6.7701207953008593374899996527559e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (closed_form) = -0.14658222397723905021600403622931 y[1] (numeric) = -0.14658222397723905021600403622933 absolute error = 2e-32 relative error = 1.3644219235686827816620517897769e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (closed_form) = -0.14546437245689965575894191986325 y[1] (numeric) = -0.14546437245689965575894191986326 absolute error = 1e-32 relative error = 6.8745355519702588947497118452325e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (closed_form) = -0.14435425406191775567772175258403 y[1] (numeric) = -0.14435425406191775567772175258404 absolute error = 1e-32 relative error = 6.9274023581672265322068593248210e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (closed_form) = -0.14325182557432092261383751862116 y[1] (numeric) = -0.14325182557432092261383751862117 absolute error = 1e-32 relative error = 6.9807138302833488682499612200646e-30 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = -0.1421570438705644229352520595717 y[1] (numeric) = -0.14215704387056442293525205957173 absolute error = 3e-32 relative error = 2.1103421387487021222317525417539e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (closed_form) = -0.14106986592393090453228417382358 y[1] (numeric) = -0.14106986592393090453228417382362 absolute error = 4e-32 relative error = 2.8354744465107238165796013577701e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (closed_form) = -0.13999024880687298113830282854031 y[1] (numeric) = -0.13999024880687298113830282854037 absolute error = 6e-32 relative error = 4.2860128124191341160165080874304e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (closed_form) = -0.13891814969329961197034163770439 y[1] (numeric) = -0.13891814969329961197034163770444 absolute error = 5e-32 relative error = 3.5992417197024926695704582967512e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=391.5MB, alloc=52.3MB, time=4.44 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (closed_form) = -0.13785352586080716325200088210822 y[1] (numeric) = -0.13785352586080716325200088210826 absolute error = 4e-32 relative error = 2.9016305350353257222175182382602e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (closed_form) = -0.13679633469285602610270824316572 y[1] (numeric) = -0.13679633469285602610270824316575 absolute error = 3e-32 relative error = 2.1930412146902867946024903002195e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (closed_form) = -0.13574653368089365335170060303866 y[1] (numeric) = -0.13574653368089365335170060303871 absolute error = 5e-32 relative error = 3.6833353047185401622809313606133e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (closed_form) = -0.13470408042642486606012701260046 y[1] (numeric) = -0.1347040804264248660601270126005 absolute error = 4e-32 relative error = 2.9694720362868243089377717731574e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (closed_form) = -0.13366893264303026890863805380436 y[1] (numeric) = -0.13366893264303026890863805380442 absolute error = 6e-32 relative error = 4.4887019604048962652750809187122e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (closed_form) = -0.13264104815833360212892140943797 y[1] (numeric) = -0.13264104815833360212892140943802 absolute error = 5e-32 relative error = 3.7695721418240759399018066610251e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = -0.13162038491591884632409062081129 y[1] (numeric) = -0.13162038491591884632409062081134 absolute error = 5e-32 relative error = 3.7988036603859485318593924589163e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (closed_form) = -0.1306069009771978853328776762566 y[1] (numeric) = -0.13060690097719788533287767625667 absolute error = 7e-32 relative error = 5.3595942845486402241909983482950e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (closed_form) = -0.12960055452322952124448469998359 y[1] (numeric) = -0.12960055452322952124448469998367 absolute error = 8e-32 relative error = 6.1728130943807690813996369528883e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=435.4MB, alloc=52.3MB, time=4.92 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (closed_form) = -0.12860130385649062476300039214676 y[1] (numeric) = -0.12860130385649062476300039214684 absolute error = 8e-32 relative error = 6.2207767418341246657146900532676e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (closed_form) = -0.12760910740260019335078788544181 y[1] (numeric) = -0.12760910740260019335078788544189 absolute error = 8e-32 relative error = 6.2691450185921370280467280413298e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (closed_form) = -0.12662392371199707894752706788881 y[1] (numeric) = -0.12662392371199707894752706788888 absolute error = 7e-32 relative error = 5.5281812431601183528130532061742e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (closed_form) = -0.1256457114615721365639905432976 y[1] (numeric) = -0.12564571146157213656399054329768 absolute error = 8e-32 relative error = 6.3671094754768006021896282260824e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (closed_form) = -0.12467442945625553468551203393797 y[1] (numeric) = -0.12467442945625553468551203393806 absolute error = 9e-32 relative error = 7.2188018339059865233669470844608e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (closed_form) = -0.12371003663055995818785213165665 y[1] (numeric) = -0.12371003663055995818785213165673 absolute error = 8e-32 relative error = 6.4667348081794751861718167438791e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (closed_form) = -0.12275249205008042436618079563696 y[1] (numeric) = -0.12275249205008042436618079563704 absolute error = 8e-32 relative error = 6.5171792982713287406994840387653e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = -0.12180175491295142270459954547524 y[1] (numeric) = -0.1218017549129514227045995454753 absolute error = 6e-32 relative error = 4.9260373992871001514869516403832e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (closed_form) = -0.12085778455126207916745810743713 y[1] (numeric) = -0.1208577845512620791674581074372 absolute error = 7e-32 relative error = 5.7919314225315254962803052673565e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=479.2MB, alloc=52.3MB, time=5.41 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (closed_form) = -0.11992054043243003607313785931741 y[1] (numeric) = -0.11992054043243003607313785931747 absolute error = 6e-32 relative error = 5.0033130090676474188965234582259e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (closed_form) = -0.11898998216053472901445341435182 y[1] (numeric) = -0.11898998216053472901445341435188 absolute error = 6e-32 relative error = 5.0424412972052811368763905007524e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (closed_form) = -0.11806606947761073281585761798056 y[1] (numeric) = -0.11806606947761073281585761798063 absolute error = 7e-32 relative error = 5.9288837436291835076277534064305e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (closed_form) = -0.11714876226490183916473533023783 y[1] (numeric) = -0.11714876226490183916473533023791 absolute error = 8e-32 relative error = 6.8289240495004587395557486991159e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (closed_form) = -0.11623802054407651932076635185884 y[1] (numeric) = -0.11623802054407651932076635185891 absolute error = 7e-32 relative error = 6.0221259509023181375750074456898e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (closed_form) = -0.11533380447840541619217373726719 y[1] (numeric) = -0.11533380447840541619217373726726 absolute error = 7e-32 relative error = 6.0693393681560626714935549650354e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (closed_form) = -0.11443607437390150106921363007176 y[1] (numeric) = -0.11443607437390150106921363007184 absolute error = 8e-32 relative error = 6.9908025452369891216069728627682e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (closed_form) = -0.11354479068042352142208666220373 y[1] (numeric) = -0.11354479068042352142208666220383 absolute error = 1.0e-31 relative error = 8.8070971288726145696878439176928e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = -0.11265991399274335740115558598682 y[1] (numeric) = -0.11265991399274335740115558598692 absolute error = 1.0e-31 relative error = 8.8762716440952718189670950113895e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (closed_form) = -0.11178140505157789602055238104201 y[1] (numeric) = -0.11178140505157789602055238104212 absolute error = 1.1e-31 relative error = 9.8406349382747582603515282356284e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=523.1MB, alloc=52.3MB, time=5.89 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (closed_form) = -0.11090922474458602346058013925996 y[1] (numeric) = -0.11090922474458602346058013926006 absolute error = 1.0e-31 relative error = 9.0163825624325670319271097937734e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (closed_form) = -0.11004333410733132748840626037928 y[1] (numeric) = -0.11004333410733132748840626037938 absolute error = 1.0e-31 relative error = 9.0873291700217379533180064306144e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (closed_form) = -0.10918369432421109366906551679945 y[1] (numeric) = -0.10918369432421109366906551679956 absolute error = 1.1e-31 relative error = 1.0074764430791740801834469794951e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (closed_form) = -0.10833026672935217081842176419004 y[1] (numeric) = -0.10833026672935217081842176419014 absolute error = 1.0e-31 relative error = 9.2310305345998858776774060348404e-29 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (closed_form) = -0.10748301280747427303516846429221 y[1] (numeric) = -0.10748301280747427303516846429232 absolute error = 1.1e-31 relative error = 1.0234175347971888811433353089004e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (closed_form) = -0.10664189419472127763888913389901 y[1] (numeric) = -0.10664189419472127763888913389913 absolute error = 1.2e-31 relative error = 1.1252613328574947814444229467355e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (closed_form) = -0.10580687267946107043437295382424 y[1] (numeric) = -0.10580687267946107043437295382436 absolute error = 1.2e-31 relative error = 1.1341418280411387598224368482486e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (closed_form) = -0.1049779102030544819175267316456 y[1] (numeric) = -0.10497791020305448191752673164574 absolute error = 1.4e-31 relative error = 1.3336138977162311663588767807461e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = -0.10415496886059385033409576029894 y[1] (numeric) = -0.1041549688605938503340957602991 absolute error = 1.6e-31 relative error = 1.5361725105419780300377493050024e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=566.9MB, alloc=52.3MB, time=6.38 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (closed_form) = -0.10333801090161173989777110837224 y[1] (numeric) = -0.10333801090161173989777110837238 absolute error = 1.4e-31 relative error = 1.3547773832543979346017288877905e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (closed_form) = -0.10252699873076033496790231405919 y[1] (numeric) = -0.10252699873076033496790231405934 absolute error = 1.5e-31 relative error = 1.4630292689431542837063788181801e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (closed_form) = -0.10172189490846202357774950233917 y[1] (numeric) = -0.10172189490846202357774950233932 absolute error = 1.5e-31 relative error = 1.4746087863874606771765193331826e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (closed_form) = -0.10092266215153167639080898000512 y[1] (numeric) = -0.10092266215153167639080898000528 absolute error = 1.6e-31 relative error = 1.5853723691886552417055205351922e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (closed_form) = -0.10012926333377111994405680477866 y[1] (numeric) = -0.10012926333377111994405680477883 absolute error = 1.7e-31 relative error = 1.6978053601904730236774344605969e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (closed_form) = -0.099341661486536295911814973424912 y[1] (numeric) = -0.099341661486536295911814973425078 absolute error = 1.66e-31 relative error = 1.6710008421038726120882781064698e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (closed_form) = -0.098559819799277591091207751429108 y[1] (numeric) = -0.098559819799277591091207751429273 absolute error = 1.65e-31 relative error = 1.6741102036918435206539104656790e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (closed_form) = -0.097783701620053815868707858622811 y[1] (numeric) = -0.097783701620053815868707858622976 absolute error = 1.65e-31 relative error = 1.6873977694270599778014680954497e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (closed_form) = -0.097013270456020302075953723274113 y[1] (numeric) = -0.097013270456020302075953723274278 absolute error = 1.65e-31 relative error = 1.7007982436258614019657635426986e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = -0.096248489973891584380743066046067 y[1] (numeric) = -0.096248489973891584380743066046233 absolute error = 1.66e-31 relative error = 1.7247023828117121279510042875488e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=610.9MB, alloc=52.3MB, time=6.86 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (closed_form) = -0.095489324000379122684781018840141 y[1] (numeric) = -0.095489324000379122684781018840303 absolute error = 1.62e-31 relative error = 1.6965247340043669069020413273688e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (closed_form) = -0.094735736522604516412302114226203 y[1] (numeric) = -0.094735736522604516412302114226365 absolute error = 1.62e-31 relative error = 1.7100199559998757790755832539089e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (closed_form) = -0.093987691688488655072026890256781 y[1] (numeric) = -0.093987691688488655072026890256952 absolute error = 1.71e-31 relative error = 1.8193871657871941674986767327888e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (closed_form) = -0.093245153807117243058000285592435 y[1] (numeric) = -0.093245153807117243058000285592602 absolute error = 1.67e-31 relative error = 1.7909777954299773562971305651499e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (closed_form) = -0.092508087349083130321647698895804 y[1] (numeric) = -0.092508087349083130321647698895976 absolute error = 1.72e-31 relative error = 1.8592968996424152417668223677595e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (closed_form) = -0.091776456946805874296845163117692 y[1] (numeric) = -0.091776456946805874296845163117859 absolute error = 1.67e-31 relative error = 1.8196387783502482985358457468994e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (closed_form) = -0.09105022739482895229091436644959 y[1] (numeric) = -0.091050227394828952290914366449758 absolute error = 1.68e-31 relative error = 1.8451354247748016421893580616163e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (closed_form) = -0.090329363650095037466215141194639 y[1] (numeric) = -0.090329363650095037466215141194804 absolute error = 1.65e-31 relative error = 1.8266485374473951577686710085372e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (closed_form) = -0.08961383083219974552842338090745 y[1] (numeric) = -0.089613830832199745528423380907615 absolute error = 1.65e-31 relative error = 1.8412336406972655086091412015355e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=654.8MB, alloc=52.3MB, time=7.36 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = -0.088903594223624253307668775678096 y[1] (numeric) = -0.088903594223624253307668775678266 absolute error = 1.70e-31 relative error = 1.9121836578664002866127038375955e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (closed_form) = -0.088198619269947184566493579309495 y[1] (numeric) = -0.088198619269947184566493579309663 absolute error = 1.68e-31 relative error = 1.9047917233920276811223418158908e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (closed_form) = -0.087498871580036152593121672564968 y[1] (numeric) = -0.087498871580036152593121672565141 absolute error = 1.73e-31 relative error = 1.9771683551570725323509704599155e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (closed_form) = -0.086804316926219343438848690815511 y[1] (numeric) = -0.086804316926219343438848690815678 absolute error = 1.67e-31 relative error = 1.9238674516838166438411241203144e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (closed_form) = -0.086114921244437518033542432632324 y[1] (numeric) = -0.086114921244437518033542432632495 absolute error = 1.71e-31 relative error = 1.9857185900991057789289428407418e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (closed_form) = -0.085430650634376805862352781350995 y[1] (numeric) = -0.085430650634376805862352781351163 absolute error = 1.68e-31 relative error = 1.9665073220500296595305440812499e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (closed_form) = -0.084751471359582657408857581611753 y[1] (numeric) = -0.084751471359582657408857581611925 absolute error = 1.72e-31 relative error = 2.0294632912063579006704395440112e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (closed_form) = -0.084077349847555317164111821258835 y[1] (numeric) = -0.084077349847555317164111821259007 absolute error = 1.72e-31 relative error = 2.0457352701037968539346607321032e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (closed_form) = -0.083408252689827173666529330407187 y[1] (numeric) = -0.083408252689827173666529330407363 absolute error = 1.76e-31 relative error = 2.1101029493387973927592880068997e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=698.6MB, alloc=52.3MB, time=7.84 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (closed_form) = -0.082744146642022337773326904860512 y[1] (numeric) = -0.082744146642022337773326904860685 absolute error = 1.73e-31 relative error = 2.0907823335039440550709920716376e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = -0.08208499862389879516952867446716 y[1] (numeric) = -0.082084998623898795169528674467332 absolute error = 1.72e-31 relative error = 2.0953889612409974313480702636009e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (closed_form) = -0.081430775719373473994402434001873 y[1] (numeric) = -0.081430775719373473994402434002045 absolute error = 1.72e-31 relative error = 2.1122235233610686641144111586594e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (closed_form) = -0.080781445176530563406828561525371 y[1] (numeric) = -0.080781445176530563406828561525547 absolute error = 1.76e-31 relative error = 2.1787181402287327145577068863292e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (closed_form) = -0.08013697440761341391964523592534 y[1] (numeric) = -0.080136974407613413919645235925511 absolute error = 1.71e-31 relative error = 2.1338464705469856568324810807285e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (closed_form) = -0.079497330989000345407640125180843 y[1] (numeric) = -0.079497330989000345407640125181016 absolute error = 1.73e-31 relative error = 2.1761736884466870831914511574533e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (closed_form) = -0.078862482661164683833747651948313 y[1] (numeric) = -0.078862482661164683833747651948487 absolute error = 1.74e-31 relative error = 2.2063723348350174018017605475040e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (closed_form) = -0.078232397328619342942351248972236 y[1] (numeric) = -0.078232397328619342942351248972411 absolute error = 1.75e-31 relative error = 2.2369249310474687225525820843694e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (closed_form) = -0.077607043059846262436580269093602 y[1] (numeric) = -0.077607043059846262436580269093776 absolute error = 1.74e-31 relative error = 2.2420645490361076712925669478246e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (closed_form) = -0.076986388087211009487339556331622 y[1] (numeric) = -0.076986388087211009487339556331794 absolute error = 1.72e-31 relative error = 2.2341611845090920195078095477461e-28 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 32 h = 0.001 memory used=742.5MB, alloc=52.3MB, time=8.33 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (closed_form) = -0.076370400806862845814733715220247 y[1] (numeric) = -0.076370400806862845814733715220424 absolute error = 1.77e-31 relative error = 2.3176518406342357805917583116491e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = -0.075759049778620558036774781573376 y[1] (numeric) = -0.075759049778620558036774781573549 absolute error = 1.73e-31 relative error = 2.2835555686816592537361693946441e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (closed_form) = -0.075152303725844344495027483586668 y[1] (numeric) = -0.075152303725844344495027483586843 absolute error = 1.75e-31 relative error = 2.3286045979162544365056817649702e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (closed_form) = -0.074550131535294047341395902981914 y[1] (numeric) = -0.07455013153529404734139590298209 absolute error = 1.76e-31 relative error = 2.3608274911852683017901614527841e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (closed_form) = -0.073952502256974014303843441863639 y[1] (numeric) = -0.073952502256974014303843441863809 absolute error = 1.70e-31 relative error = 2.2987727908012514299428720749003e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (closed_form) = -0.073359385103964870240727832094713 y[1] (numeric) = -0.073359385103964870240727832094885 absolute error = 1.72e-31 relative error = 2.3446216153017329412119478027003e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (closed_form) = -0.072770749452242474342896566532256 y[1] (numeric) = -0.072770749452242474342896566532429 absolute error = 1.73e-31 relative error = 2.3773288210194309207328822201614e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (closed_form) = -0.072186564840484334649006375337096 y[1] (numeric) = -0.072186564840484334649006375337267 absolute error = 1.71e-31 relative error = 2.3688618564669280933219636457346e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (closed_form) = -0.071606800969863747401992618097381 y[1] (numeric) = -0.071606800969863747401992618097555 absolute error = 1.74e-31 relative error = 2.4299367887308523789853964386106e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=786.3MB, alloc=52.3MB, time=8.81 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (closed_form) = -0.071031427703831924692518628200816 y[1] (numeric) = -0.071031427703831924692518628200989 absolute error = 1.73e-31 relative error = 2.4355416411075063868634982184131e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (closed_form) = -0.070460415067888369807887457414605 y[1] (numeric) = -0.070460415067888369807887457414781 absolute error = 1.76e-31 relative error = 2.4978564181097230233509406705813e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = -0.069893733249339755731613768890206 y[1] (numeric) = -0.069893733249339755731613768890379 absolute error = 1.73e-31 relative error = 2.4751861426951925974551305695846e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (closed_form) = -0.069331352597047558318954677142431 y[1] (numeric) = -0.069331352597047558318954677142606 absolute error = 1.75e-31 relative error = 2.5241105711163103611183681033940e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (closed_form) = -0.06877324362116469180651611804696 y[1] (numeric) = -0.068773243621164691806516118047136 absolute error = 1.76e-31 relative error = 2.5591347845899288221563413760618e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (closed_form) = -0.068219376992861390498924862781868 y[1] (numeric) = -0.068219376992861390498924862782042 absolute error = 1.74e-31 relative error = 2.5505949727187878233723069497976e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (closed_form) = -0.067669723544040576711832513748314 y[1] (numeric) = -0.067669723544040576711832513748488 absolute error = 1.74e-31 relative error = 2.5713124110335387806304605279561e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (closed_form) = -0.067124254267042951337551526835848 y[1] (numeric) = -0.067124254267042951337551526836025 absolute error = 1.77e-31 relative error = 2.6369008033345775000072833849236e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (closed_form) = -0.066582940314342039736777032691134 y[1] (numeric) = -0.066582940314342039736777032691308 absolute error = 1.74e-31 relative error = 2.6132820085525752245869873177116e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=830.2MB, alloc=52.3MB, time=9.30 x[1] = 2.77 y[1] (closed_form) = -0.066045752998229422046492180032814 y[1] (numeric) = -0.066045752998229422046492180032988 absolute error = 1.74e-31 relative error = 2.6345373033246309367834830467518e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (closed_form) = -0.065512663790490373429666667710763 y[1] (numeric) = -0.065512663790490373429666667710936 absolute error = 1.73e-31 relative error = 2.6407108181901187440530761428471e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (closed_form) = -0.064983644322070136276123323056813 y[1] (numeric) = -0.064983644322070136276123323056988 absolute error = 1.75e-31 relative error = 2.6929853169309780779058917222562e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = -0.064458666382731042895358671474977 y[1] (numeric) = -0.064458666382731042895358671475151 absolute error = 1.74e-31 relative error = 2.6994042812932893185289196093405e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (closed_form) = -0.063937701920700703820560384657685 y[1] (numeric) = -0.063937701920700703820560384657862 absolute error = 1.77e-31 relative error = 2.7683197031311166619340302480630e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (closed_form) = -0.063420723042311473467974474582547 y[1] (numeric) = -0.063420723042311473467974474582722 absolute error = 1.75e-31 relative error = 2.7593504394966897033071052803444e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (closed_form) = -0.062907702011631401566552439288916 y[1] (numeric) = -0.062907702011631401566552439289089 absolute error = 1.73e-31 relative error = 2.7500607154273881994046381626219e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (closed_form) = -0.062398611250086875488874642174957 y[1] (numeric) = -0.062398611250086875488874642175133 absolute error = 1.76e-31 relative error = 2.8205755941363993275788091517432e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (closed_form) = -0.061893423336077155375129370651819 y[1] (numeric) = -0.061893423336077155375129370651994 absolute error = 1.75e-31 relative error = 2.8274409552330251111518975531337e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (closed_form) = -0.061392111004581000746862516048042 y[1] (numeric) = -0.061392111004581000746862516048216 absolute error = 1.74e-31 relative error = 2.8342403796314536684382853316182e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=874.1MB, alloc=52.3MB, time=9.78 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (closed_form) = -0.060894647146755584155742699869714 y[1] (numeric) = -0.060894647146755584155742699869887 absolute error = 1.73e-31 relative error = 2.8409722053741680189078910721210e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (closed_form) = -0.060401004809527884304159729033937 y[1] (numeric) = -0.060401004809527884304159729034112 absolute error = 1.75e-31 relative error = 2.8973027940819096139253108240148e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (closed_form) = -0.05991115719517874800854593487176 y[1] (numeric) = -0.059911157195178748008545934871936 absolute error = 1.76e-31 relative error = 2.9376832002531126369143387286087e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = -0.059425077660919807352342253300909 y[1] (numeric) = -0.059425077660919807352342253301085 absolute error = 1.76e-31 relative error = 2.9617125787240543758435381083764e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (closed_form) = -0.058942739718463435392992350814033 y[1] (numeric) = -0.05894273971846343539299235081421 absolute error = 1.77e-31 relative error = 3.0029143681720631756207061053841e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (closed_form) = -0.058464117033585920845713629427383 y[1] (numeric) = -0.058464117033585920845713629427558 absolute error = 1.75e-31 relative error = 2.9932890271731570266428413664396e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (closed_form) = -0.057989183425684039265544837310934 y[1] (numeric) = -0.057989183425684039265544837311112 absolute error = 1.78e-31 relative error = 3.0695379635430745937574132972744e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (closed_form) = -0.05751791286732519538779382717967 y[1] (numeric) = -0.057517912867325195387793827179845 absolute error = 1.75e-31 relative error = 3.0425304270630808516520141485449e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (closed_form) = -0.05705027948379130846499949777876 y[1] (numeric) = -0.057050279483791308464999497778934 absolute error = 1.74e-31 relative error = 3.0499412373507400032298859650917e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=917.9MB, alloc=52.3MB, time=10.27 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (closed_form) = -0.056586257552616609655379007825856 y[1] (numeric) = -0.056586257552616609655379007826031 absolute error = 1.75e-31 relative error = 3.0926236787664677608934028786981e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (closed_form) = -0.056125821503119517772960904431163 y[1] (numeric) = -0.05612582150311951777296090443134 absolute error = 1.77e-31 relative error = 3.1536286732152722130683796260012e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (closed_form) = -0.055668945915928757002718781136344 y[1] (numeric) = -0.055668945915928757002718781136521 absolute error = 1.77e-31 relative error = 3.1795105347837087266250152379845e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (closed_form) = -0.055215605522503877514536309949837 y[1] (numeric) = -0.055215605522503877514536309950015 absolute error = 1.78e-31 relative error = 3.2237263055542089107294029093380e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = -0.054765775204650337277276657215067 y[1] (numeric) = -0.054765775204650337277276657215248 absolute error = 1.81e-31 relative error = 3.3049838028154253282800580613449e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (closed_form) = -0.054319429994029300778126850819468 y[1] (numeric) = -0.05431942999402930077812685081965 absolute error = 1.82e-31 relative error = 3.3505506228619322772121933968893e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (closed_form) = -0.053876545071662307792275780226237 y[1] (numeric) = -0.053876545071662307792275780226419 absolute error = 1.82e-31 relative error = 3.3780933754738362078664493885705e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (closed_form) = -0.053437095767430962823403986271071 y[1] (numeric) = -0.053437095767430962823403986271253 absolute error = 1.82e-31 relative error = 3.4058737172413106274316559224811e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (closed_form) = -0.053001057559571793345960614651822 y[1] (numeric) = -0.053001057559571793345960614652004 absolute error = 1.82e-31 relative error = 3.4338937443924923854031316715448e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (closed_form) = -0.052568406074166422525329754966104 y[1] (numeric) = -0.052568406074166422525329754966289 absolute error = 1.85e-31 relative error = 3.5192240704234353355067425409615e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=961.8MB, alloc=52.3MB, time=10.75 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (closed_form) = -0.052139117084627199671302200085871 y[1] (numeric) = -0.052139117084627199671302200086056 absolute error = 1.85e-31 relative error = 3.5481997077113100105216370092774e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (closed_form) = -0.051713166511178429293332153328767 y[1] (numeric) = -0.051713166511178429293332153328954 absolute error = 1.87e-31 relative error = 3.6161003592688078347768674089423e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (closed_form) = -0.051290530420333337272439615438391 y[1] (numeric) = -0.051290530420333337272439615438576 absolute error = 1.85e-31 relative error = 3.6069036230255012555658439320068e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (closed_form) = -0.050871185024366910343891386852752 y[1] (numeric) = -0.050871185024366910343891386852937 absolute error = 1.85e-31 relative error = 3.6366363376710491097589337283201e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = -0.050455106680784742796535303239736 y[1] (numeric) = -0.050455106680784742796535303239921 absolute error = 1.85e-31 relative error = 3.6666258813095555177617636254755e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (closed_form) = -0.050042271891788022038457095912319 y[1] (numeric) = -0.050042271891788022038457095912504 absolute error = 1.85e-31 relative error = 3.6968745224047002571155616842428e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (closed_form) = -0.049632657303734782454065817198494 y[1] (numeric) = -0.049632657303734782454065817198678 absolute error = 1.84e-31 relative error = 3.7072365252173245632880189907133e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (closed_form) = -0.04922623970659755478438578971336 y[1] (numeric) = -0.049226239706597554784385789713541 absolute error = 1.81e-31 relative error = 3.6769007967866667166220336889127e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (closed_form) = -0.048822996033417536099839176219681 y[1] (numeric) = -0.048822996033417536099839176219865 absolute error = 1.84e-31 relative error = 3.7687158705717035747894960662436e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1005.6MB, alloc=52.3MB, time=11.23 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = -0.048422903359755403302747066360455 y[1] (numeric) = -0.04842290335975540330274706636064 absolute error = 1.85e-31 relative error = 3.8205061482074354325887753976804e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (closed_form) = -0.048025938903138890994766817864003 y[1] (numeric) = -0.048025938903138890994766817864187 absolute error = 1.84e-31 relative error = 3.8312629425340413959318987318717e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (closed_form) = -0.047632080022507252472132432586239 y[1] (numeric) = -0.047632080022507252472132432586425 absolute error = 1.86e-31 relative error = 3.9049312965570834912533376109481e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (closed_form) = -0.047241304217652720568490875210256 y[1] (numeric) = -0.04724130421765272056849087521044 absolute error = 1.84e-31 relative error = 3.8948967020949535274426470414748e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (closed_form) = -0.046853589128659083050953005632225 y[1] (numeric) = -0.04685358912865908305095300563241 absolute error = 1.85e-31 relative error = 3.9484701906612414646720678249489e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = -0.046468912535337485289330358844645 y[1] (numeric) = -0.046468912535337485289330358844828 absolute error = 1.83e-31 relative error = 3.9381166895359743875188844405416e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (closed_form) = -0.046087252356659570961040090634769 y[1] (numeric) = -0.046087252356659570961040090634953 absolute error = 1.84e-31 relative error = 3.9924272025605394489906341248870e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (closed_form) = -0.045708586650188069624466240332695 y[1] (numeric) = -0.04570858665018806962446624033288 absolute error = 1.85e-31 relative error = 4.0473795747792786072351447250417e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (closed_form) = -0.04533289361150493809130672120713 y[1] (numeric) = -0.045332893611504938091306721207312 absolute error = 1.82e-31 relative error = 4.0147448243588538399268938443646e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1049.4MB, alloc=52.3MB, time=11.72 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (closed_form) = -0.044960151573637160653257211739887 y[1] (numeric) = -0.044960151573637160653257211740069 absolute error = 1.82e-31 relative error = 4.0480290575069488803503571164965e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = -0.044590339006480311369934810557736 y[1] (numeric) = -0.044590339006480311369934810557917 absolute error = 1.81e-31 relative error = 4.0591752391408210766291299897019e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (closed_form) = -0.044223434516219979802879653366151 y[1] (numeric) = -0.044223434516219979802879653366332 absolute error = 1.81e-31 relative error = 4.0928526239547046736791032646329e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (closed_form) = -0.043859416844751159784449635604978 y[1] (numeric) = -0.043859416844751159784449635605157 absolute error = 1.79e-31 relative error = 4.0812216139034616493226323344781e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (closed_form) = -0.043498264869095699040104098021788 y[1] (numeric) = -0.043498264869095699040104098021968 absolute error = 1.80e-31 relative error = 4.1380960951360836262932306737877e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (closed_form) = -0.04313995760081790573762311711766 y[1] (numeric) = -0.043139957600817905737623117117841 absolute error = 1.81e-31 relative error = 4.1956462190998620008926824933828e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (closed_form) = -0.042784474185438406316900297500158 y[1] (numeric) = -0.042784474185438406316900297500338 absolute error = 1.80e-31 relative error = 4.2071336256193273593338853274497e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (closed_form) = -0.04243179390184634725875313500178 y[1] (numeric) = -0.04243179390184634725875313500196 absolute error = 1.80e-31 relative error = 4.2421020524462814781939907674660e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (closed_form) = -0.042081896161710031780394553883857 y[1] (numeric) = -0.042081896161710031780394553884035 absolute error = 1.78e-31 relative error = 4.2298474221786784258310493470142e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (closed_form) = -0.041734760508886080798484516553766 y[1] (numeric) = -0.041734760508886080798484516553943 absolute error = 1.77e-31 relative error = 4.2410690235616307893915316687930e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1093.3MB, alloc=52.3MB, time=12.20 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (closed_form) = -0.041390366618827205877717963286282 y[1] (numeric) = -0.041390366618827205877717963286461 absolute error = 1.79e-31 relative error = 4.3246778084487514673411282670132e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (closed_form) = -0.041048694297988680283394924794674 y[1] (numeric) = -0.041048694297988680283394924794853 absolute error = 1.79e-31 relative error = 4.3606746343883272036217938899135e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (closed_form) = -0.040709723483233592680054437771227 y[1] (numeric) = -0.040709723483233592680054437771406 absolute error = 1.79e-31 relative error = 4.3969839312153919092575699119820e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (closed_form) = -0.040373434241236966464733626417377 y[1] (numeric) = -0.040373434241236966464733626417556 absolute error = 1.79e-31 relative error = 4.4336084696300478748995482033685e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (closed_form) = -0.04003980676788882619243845861026 y[1] (numeric) = -0.040039806767888826192438458610439 absolute error = 1.79e-31 relative error = 4.4705510453051097547096133871849e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (closed_form) = -0.039708821387696291042688390025546 y[1] (numeric) = -0.039708821387696291042688390025727 absolute error = 1.81e-31 relative error = 4.5581811213385077677390162114890e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (closed_form) = -0.039380458553184773789232155135719 y[1] (numeric) = -0.039380458553184773789232155135899 absolute error = 1.80e-31 relative error = 4.5707949224842901717536402932808e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (closed_form) = -0.039054698844298362269938724810878 y[1] (numeric) = -0.03905469884429836226993872481106 absolute error = 1.82e-31 relative error = 4.6601306727671868060215557439250e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (closed_form) = -0.03873152296779945891016185029374 y[1] (numeric) = -0.038731522967799458910161850293922 absolute error = 1.82e-31 relative error = 4.6990148089790019214655286184387e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1137.1MB, alloc=52.3MB, time=12.69 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (closed_form) = -0.038410911756667752430278084209698 y[1] (numeric) = -0.03841091175666775243027808420988 absolute error = 1.82e-31 relative error = 4.7382369143686522697286686522092e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (closed_form) = -0.038092846169498594466329608519083 y[1] (numeric) = -0.038092846169498594466329608519265 absolute error = 1.82e-31 relative error = 4.7777999887477458960669846409523e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (closed_form) = -0.037777307289900852451490929142885 y[1] (numeric) = -0.037777307289900852451490929143066 absolute error = 1.81e-31 relative error = 4.7912361410784669856154798153747e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (closed_form) = -0.037464276325894308745152223607566 y[1] (numeric) = -0.037464276325894308745152223607747 absolute error = 1.81e-31 relative error = 4.8312690848614531140880064005198e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (closed_form) = -0.03715373460930667465550490141511 y[1] (numeric) = -0.037153734609306674655504901415291 absolute error = 1.81e-31 relative error = 4.8716502365999335155005102038444e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (closed_form) = -0.036845663595170286680363110870559 y[1] (numeric) = -0.036845663595170286680363110870739 absolute error = 1.80e-31 relative error = 4.8852424528892002516240352989451e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (closed_form) = -0.036540044861118550989298119352908 y[1] (numeric) = -0.036540044861118550989298119353089 absolute error = 1.81e-31 relative error = 4.9534695616260196272070229242048e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (closed_form) = -0.036236860106782200887743550836343 y[1] (numeric) = -0.036236860106782200887743550836525 absolute error = 1.82e-31 relative error = 5.0225102137350009188490761514757e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (closed_form) = -0.035936091153185430740294416559987 y[1] (numeric) = -0.035936091153185430740294416560168 absolute error = 1.81e-31 relative error = 5.0367191920915383100947181183611e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=1180.9MB, alloc=52.3MB, time=13.17 x[1] = 3.52 y[1] (closed_form) = -0.035637719942141968585720903201987 y[1] (numeric) = -0.035637719942141968585720903202168 absolute error = 1.81e-31 relative error = 5.0788883321900076849322861710203e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (closed_form) = -0.035341728535651148450001280697606 y[1] (numeric) = -0.035341728535651148450001280697786 absolute error = 1.80e-31 relative error = 5.0931294947394574746949228795767e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (closed_form) = -0.03504809911529404215570242667988 y[1] (numeric) = -0.035048099115294042155702426680059 absolute error = 1.79e-31 relative error = 5.1072669993075100387445293732855e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (closed_form) = -0.034756813981629709236059742249032 y[1] (numeric) = -0.03475681398162970923605974224921 absolute error = 1.78e-31 relative error = 5.1212979444571568708353860051972e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (closed_form) = -0.034467855553591622389892062091893 y[1] (numeric) = -0.034467855553591622389892062092072 absolute error = 1.79e-31 relative error = 5.1932444628499038406537975090292e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (closed_form) = -0.034181206367884324758795914620488 y[1] (numeric) = -0.034181206367884324758795914620668 absolute error = 1.80e-31 relative error = 5.2660517028773684913882769181144e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (closed_form) = -0.033896849078380374170664469168011 y[1] (numeric) = -0.033896849078380374170664469168191 absolute error = 1.80e-31 relative error = 5.3102280859138952914029707545807e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (closed_form) = -0.033614766455517628373239917409908 y[1] (numeric) = -0.033614766455517628373239917410087 absolute error = 1.79e-31 relative error = 5.3250407149747846682539527850530e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (closed_form) = -0.033334941385696924177906936171374 y[1] (numeric) = -0.033334941385696924177906936171552 absolute error = 1.78e-31 relative error = 5.3397424024382637868539904344712e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (closed_form) = -0.033057356870680202347045156623923 y[1] (numeric) = -0.033057356870680202347045156624101 absolute error = 1.78e-31 relative error = 5.3845805245813470170921782800362e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1224.7MB, alloc=52.3MB, time=13.66 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (closed_form) = -0.032781996026989128987758901638798 y[1] (numeric) = -0.032781996026989128987758901638975 absolute error = 1.77e-31 relative error = 5.3993051507381508082197627029127e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (closed_form) = -0.032508842085304263160474289527232 y[1] (numeric) = -0.032508842085304263160474289527408 absolute error = 1.76e-31 relative error = 5.4139116840326165102317440152047e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (closed_form) = -0.032237878389864819372521306020379 y[1] (numeric) = -0.032237878389864819372521306020554 absolute error = 1.75e-31 relative error = 5.4283969274795013612823574353040e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (closed_form) = -0.031969088397869072604188478655587 y[1] (numeric) = -0.031969088397869072604188478655763 absolute error = 1.76e-31 relative error = 5.5053180688045966645539975126423e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (closed_form) = -0.031702455678875452507639872093658 y[1] (numeric) = -0.031702455678875452507639872093832 absolute error = 1.74e-31 relative error = 5.4885338146200072832327888712919e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (closed_form) = -0.031437963914204372427310412600276 y[1] (numeric) = -0.031437963914204372427310412600449 absolute error = 1.73e-31 relative error = 5.5029009026196746204867138986314e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (closed_form) = -0.031175596896340837913740796745567 y[1] (numeric) = -0.031175596896340837913740796745741 absolute error = 1.74e-31 relative error = 5.5812884859446857686386054791872e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (closed_form) = -0.03091533852833787844107476239294 y[1] (numeric) = -0.030915338528337878441074762393113 absolute error = 1.73e-31 relative error = 5.5959277250489520068661956364327e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (closed_form) = -0.030657172823220845091419154899419 y[1] (numeric) = -0.030657172823220845091419154899593 absolute error = 1.74e-31 relative error = 5.6756701279449402838932168770910e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1268.3MB, alloc=52.3MB, time=14.14 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (closed_form) = -0.030401083903392616036763369913487 y[1] (numeric) = -0.030401083903392616036763369913661 absolute error = 1.74e-31 relative error = 5.7234801414624045521606538931590e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (closed_form) = -0.030147056000039750730974234095278 y[1] (numeric) = -0.030147056000039750730974234095452 absolute error = 1.74e-31 relative error = 5.7717078576352719281673562846141e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (closed_form) = -0.029895073452539632820332480736991 y[1] (numeric) = -0.029895073452539632820332480737167 absolute error = 1.76e-31 relative error = 5.8872576539880863627775516377078e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (closed_form) = -0.029645120707868640890967389881705 y[1] (numeric) = -0.029645120707868640890967389881882 absolute error = 1.77e-31 relative error = 5.9706284128240796511946979850214e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (closed_form) = -0.029397182320011385295188981375541 y[1] (numeric) = -0.029397182320011385295188981375718 absolute error = 1.77e-31 relative error = 6.0209852112088900806613732432191e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (closed_form) = -0.029151242949371048435926822903941 y[1] (numeric) = -0.029151242949371048435926822904118 absolute error = 1.77e-31 relative error = 6.0717822669656992088400764896357e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (closed_form) = -0.028907287362180865039077822987969 y[1] (numeric) = -0.028907287362180865039077822988145 absolute error = 1.76e-31 relative error = 6.0884301524002269972163546230305e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (closed_form) = -0.028665300429916778107361403631793 y[1] (numeric) = -0.028665300429916778107361403631971 absolute error = 1.78e-31 relative error = 6.2095982714428077780545636143277e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (closed_form) = -0.028425267128711305426100546560153 y[1] (numeric) = -0.028425267128711305426100546560331 absolute error = 1.78e-31 relative error = 6.2620343792726865299344873098167e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=1312.0MB, alloc=52.3MB, time=14.62 x[1] = 3.8 y[1] (closed_form) = -0.028187172538768650681014986401437 y[1] (numeric) = -0.028187172538768650681014986401613 absolute error = 1.76e-31 relative error = 6.2439749768420197258810935367582e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (closed_form) = -0.027951001843781092450454110242328 y[1] (numeric) = -0.027951001843781092450454110242504 absolute error = 1.76e-31 relative error = 6.2967331540983315898388099011188e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (closed_form) = -0.027716740330346683549339936304052 y[1] (numeric) = -0.027716740330346683549339936304228 absolute error = 1.76e-31 relative error = 6.3499530573333684558837041200644e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (closed_form) = -0.027484373387388292429265073364723 y[1] (numeric) = -0.0274843733873882924292650733649 absolute error = 1.77e-31 relative error = 6.4400231180536823995290929392545e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (closed_form) = -0.027253886505574017578529136859446 y[1] (numeric) = -0.027253886505574017578529136859623 absolute error = 1.77e-31 relative error = 6.4944865740084306021071724091232e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (closed_form) = -0.027025265276739005117234162991433 y[1] (numeric) = -0.02702526527673900511723416299161 absolute error = 1.77e-31 relative error = 6.5494269228264037110826726729808e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (closed_form) = -0.026798495393308699045731654620683 y[1] (numeric) = -0.026798495393308699045731654620862 absolute error = 1.79e-31 relative error = 6.6794794772207400643822326948752e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (closed_form) = -0.026573562647723552879559613167534 y[1] (numeric) = -0.026573562647723552879559613167712 absolute error = 1.78e-31 relative error = 6.6983867522651699558165973257896e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (closed_form) = -0.026350452931865230690367900440014 y[1] (numeric) = -0.026350452931865230690367900440192 absolute error = 1.78e-31 relative error = 6.7551021024290293382057871858996e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (closed_form) = -0.026129152236484324870047189866362 y[1] (numeric) = -0.02612915223648432487004718986654 absolute error = 1.78e-31 relative error = 6.8123143984540496637277942028047e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1355.9MB, alloc=52.3MB, time=15.13 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (closed_form) = -0.025909646650629617244195255991877 y[1] (numeric) = -0.025909646650629617244195255992053 absolute error = 1.76e-31 relative error = 6.7928367520103989084672043994177e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (closed_form) = -0.025691922361078909481021029343645 y[1] (numeric) = -0.025691922361078909481021029343822 absolute error = 1.77e-31 relative error = 6.8893248824439870394539482000543e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (closed_form) = -0.025475965651771448072650269329411 y[1] (numeric) = -0.025475965651771448072650269329587 absolute error = 1.76e-31 relative error = 6.9084721814170761479759931556167e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (closed_form) = -0.025261762903241968507407359071699 y[1] (numeric) = -0.025261762903241968507407359071875 absolute error = 1.76e-31 relative error = 6.9670513761893093711565615940266e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (closed_form) = -0.025049300592056382603857978028571 y[1] (numeric) = -0.025049300592056382603857978028748 absolute error = 1.77e-31 relative error = 7.0660655513922860279907228975491e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (closed_form) = -0.024838565290249132340061509709132 y[1] (numeric) = -0.024838565290249132340061509709308 absolute error = 1.76e-31 relative error = 7.0857554751397925510928239646476e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (closed_form) = -0.024629543664762232884456092621648 y[1] (numeric) = -0.024629543664762232884456092621825 absolute error = 1.77e-31 relative error = 7.1864912484446841372293945990528e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (closed_form) = -0.024422222476886026917941151330309 y[1] (numeric) = -0.024422222476886026917941151330486 absolute error = 1.77e-31 relative error = 7.2474976496311285996128599383615e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (closed_form) = -0.024216588581701671729891786202869 y[1] (numeric) = -0.024216588581701671729891786203045 absolute error = 1.76e-31 relative error = 7.2677453889185527523062009188250e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1399.7MB, alloc=52.3MB, time=15.61 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (closed_form) = -0.024012628927525379973898074805517 y[1] (numeric) = -0.024012628927525379973898074805694 absolute error = 1.77e-31 relative error = 7.3711212768172620208993496951982e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4 y[1] (closed_form) = -0.023810330555354434381833427655214 y[1] (numeric) = -0.023810330555354434381833427655389 absolute error = 1.75e-31 relative error = 7.3497509660001860297456120850004e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (closed_form) = -0.023609680598314996157284670523026 y[1] (numeric) = -0.023609680598314996157284670523202 absolute error = 1.76e-31 relative error = 7.4545692927570133203785596053569e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (closed_form) = -0.023410666281111726201289239559235 y[1] (numeric) = -0.02341066628111172620128923955941 absolute error = 1.75e-31 relative error = 7.4752250917862213191536083465106e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (closed_form) = -0.023213274919479237764590218685376 y[1] (numeric) = -0.02321327491947923776459021868555 absolute error = 1.74e-31 relative error = 7.4957109931089155951269400116398e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (closed_form) = -0.023017493919635398571108044482309 y[1] (numeric) = -0.023017493919635398571108044482483 absolute error = 1.74e-31 relative error = 7.5594676209110167409678902272071e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (closed_form) = -0.02282331077773649991691033432962 y[1] (numeric) = -0.022823310777736499916910334329794 absolute error = 1.74e-31 relative error = 7.6237843709218613443005190360813e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (closed_form) = -0.022630713079334309717511879425232 y[1] (numeric) = -0.022630713079334309717511879425408 absolute error = 1.76e-31 relative error = 7.7770417301042951098311140879158e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (closed_form) = -0.022439688498835025953730424700265 y[1] (numeric) = -0.022439688498835025953730424700443 absolute error = 1.78e-31 relative error = 7.9323739279732430221299316869963e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (closed_form) = -0.022250224798960146452437070590735 y[1] (numeric) = -0.022250224798960146452437070590912 absolute error = 1.77e-31 relative error = 7.9549758080768698487399558405013e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1443.7MB, alloc=52.3MB, time=16.09 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (closed_form) = -0.022062309830209270433251194618407 y[1] (numeric) = -0.022062309830209270433251194618584 absolute error = 1.77e-31 relative error = 8.0227320422106989959567767356460e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (closed_form) = -0.021875931530324846755418481470155 y[1] (numeric) = -0.021875931530324846755418481470333 absolute error = 1.78e-31 relative error = 8.1367963578260837655702462939745e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (closed_form) = -0.021691077923758883310658287677234 y[1] (numeric) = -0.021691077923758883310658287677412 absolute error = 1.78e-31 relative error = 8.2061389768477712035707092350010e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (closed_form) = -0.021507737121141631527555992470023 y[1] (numeric) = -0.021507737121141631527555992470201 absolute error = 1.78e-31 relative error = 8.2760914826799665216679443598280e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (closed_form) = -0.021325897318752259480991545218319 y[1] (numeric) = -0.021325897318752259480991545218496 absolute error = 1.77e-31 relative error = 8.2997679935540436534337999808522e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (closed_form) = -0.021145546797991526636022942942347 y[1] (numeric) = -0.021145546797991526636022942942524 absolute error = 1.77e-31 relative error = 8.3705567744794398186572155532968e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (closed_form) = -0.020966673924856472799470157044775 y[1] (numeric) = -0.020966673924856472799470157044954 absolute error = 1.79e-31 relative error = 8.5373579348602066402533479953720e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (closed_form) = -0.02078926714941713340405982458783 y[1] (numeric) = -0.02078926714941713340405982458801 absolute error = 1.80e-31 relative error = 8.6583138648563011962155874383057e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (closed_form) = -0.020613315005295292809284005921241 y[1] (numeric) = -0.020613315005295292809284005921422 absolute error = 1.81e-31 relative error = 8.7807322574512373005928617740558e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1487.6MB, alloc=52.3MB, time=16.58 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (closed_form) = -0.020438806109145286869989081455812 y[1] (numeric) = -0.020438806109145286869989081455992 absolute error = 1.80e-31 relative error = 8.8067766306300787947184477547048e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (closed_form) = -0.020265729160136865598036407199233 y[1] (numeric) = -0.020265729160136865598036407199414 absolute error = 1.81e-31 relative error = 8.9313342031645708425633012187886e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = -0.020094072939440126324059042706496 y[1] (numeric) = -0.020094072939440126324059042706679 absolute error = 1.83e-31 relative error = 9.1071631197681350157007294340902e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (closed_form) = -0.019923826309712527355274440914421 y[1] (numeric) = -0.019923826309712527355274440914602 absolute error = 1.81e-31 relative error = 9.0846003767742931150149198713441e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (closed_form) = -0.019754978214587991721398528012411 y[1] (numeric) = -0.019754978214587991721398528012593 absolute error = 1.82e-31 relative error = 9.2128676641922471361888571856827e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (closed_form) = -0.01958751767816811020384051417679 y[1] (numeric) = -0.019587517678168110203840514176973 absolute error = 1.83e-31 relative error = 9.3426846120459899240046681285674e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (closed_form) = -0.019421433804515452453439787555739 y[1] (numeric) = -0.019421433804515452453439787555921 absolute error = 1.82e-31 relative error = 9.3710897883185787047263387098462e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (closed_form) = -0.019256715777148994618937376905602 y[1] (numeric) = -0.019256715777148994618937376905785 absolute error = 1.83e-31 relative error = 9.5031781181065763204569881771128e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (closed_form) = -0.019093352858541671532057027098704 y[1] (numeric) = -0.019093352858541671532057027098887 absolute error = 1.83e-31 relative error = 9.5844874054235297275059114729716e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=1531.5MB, alloc=52.3MB, time=17.06 x[1] = 4.27 y[1] (closed_form) = -0.018931334389620061125408486772067 y[1] (numeric) = -0.01893133438962006112540848677225 absolute error = 1.83e-31 relative error = 9.6665135290377533852988078219202e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (closed_form) = -0.018770649789266208396322979640463 y[1] (numeric) = -0.018770649789266208396322979640647 absolute error = 1.84e-31 relative error = 9.8025375821149460469734962706523e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (closed_form) = -0.018611288553821595873094076641628 y[1] (numeric) = -0.018611288553821595873094076641811 absolute error = 1.83e-31 relative error = 9.8327420732200314777121561812335e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = -0.018453240256593267189833581355044 y[1] (numeric) = -0.018453240256593267189833581355226 absolute error = 1.82e-31 relative error = 9.8627665097988492926034375831313e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (closed_form) = -0.018296494547362110032170067351987 y[1] (numeric) = -0.018296494547362110032170067352168 absolute error = 1.81e-31 relative error = 9.8926053584453205781291884697131e-28 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (closed_form) = -0.018141041151893304378227034880409 y[1] (numeric) = -0.018141041151893304378227034880591 absolute error = 1.82e-31 relative error = 1.0032500255973755031188000003546e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (closed_form) = -0.017986869871448941627629132798142 y[1] (numeric) = -0.017986869871448941627629132798325 absolute error = 1.83e-31 relative error = 1.0174088171421142333825020471158e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (closed_form) = -0.01783397058230281988561052837111 y[1] (numeric) = -0.017833970582302819885610528371292 absolute error = 1.82e-31 relative error = 1.0205242806703069257123355115269e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (closed_form) = -0.017682333235257420349552457792092 y[1] (numeric) = -0.017682333235257420349552457792275 absolute error = 1.83e-31 relative error = 1.0349312930892509347491769447518e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (closed_form) = -0.017531947855163069431371542193595 y[1] (numeric) = -0.017531947855163069431371542193779 absolute error = 1.84e-31 relative error = 1.0495125899305760043707788241991e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1575.4MB, alloc=52.3MB, time=17.55 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (closed_form) = -0.017382804540439290941032014524905 y[1] (numeric) = -0.017382804540439290941032014525089 absolute error = 1.84e-31 relative error = 1.0585173386258994845843399812368e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (closed_form) = -0.017234893462598352353980084014123 y[1] (numeric) = -0.017234893462598352353980084014307 absolute error = 1.84e-31 relative error = 1.0676016094865952739621738733412e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (closed_form) = -0.017088204865771008888414870576956 y[1] (numeric) = -0.01708820486577100888841487057714 absolute error = 1.84e-31 relative error = 1.0767661170107234521992468895201e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = -0.016942729066234448826936353006427 y[1] (numeric) = -0.016942729066234448826936353006611 absolute error = 1.84e-31 relative error = 1.0860115821995748992586774896824e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (closed_form) = -0.016798456451942443231166338333738 y[1] (numeric) = -0.016798456451942443231166338333921 absolute error = 1.83e-31 relative error = 1.0893858047227862960877890246963e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (closed_form) = -0.016655377482057702917344373215563 y[1] (numeric) = -0.016655377482057702917344373215745 absolute error = 1.82e-31 relative error = 1.0927401687296651631882188576848e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (closed_form) = -0.016513482686486445285578617995082 y[1] (numeric) = -0.016513482686486445285578617995265 absolute error = 1.83e-31 relative error = 1.1081853747892637872165077439042e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (closed_form) = -0.016372762665415173325304852386465 y[1] (numeric) = -0.016372762665415173325304852386648 absolute error = 1.83e-31 relative error = 1.1177099658725161540562974007864e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (closed_form) = -0.01623320808884966885449885381994 y[1] (numeric) = -0.016233208088849668854498853820123 absolute error = 1.83e-31 relative error = 1.1273187591656622372279321268714e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1619.3MB, alloc=52.3MB, time=18.03 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (closed_form) = -0.016094809696156201790223261198965 y[1] (numeric) = -0.016094809696156201790223261199148 absolute error = 1.83e-31 relative error = 1.1370125118267441619675312012711e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (closed_form) = -0.015957558295604956993095572196783 y[1] (numeric) = -0.015957558295604956993095572196964 absolute error = 1.81e-31 relative error = 1.1342587421400876820022650320785e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (closed_form) = -0.015821444763915679978165961256329 y[1] (numeric) = -0.015821444763915679978165961256511 absolute error = 1.82e-31 relative error = 1.1503374231352843142053318891456e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (closed_form) = -0.01568646004580554253941995203708 y[1] (numeric) = -0.015686460045805542539419952037263 absolute error = 1.83e-31 relative error = 1.1666112014159179946641466916794e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = -0.015552595153539229094600388001703 y[1] (numeric) = -0.015552595153539229094600388001886 absolute error = 1.83e-31 relative error = 1.1766525019996779914050806131743e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (closed_form) = -0.015419841166481244321205314129138 y[1] (numeric) = -0.015419841166481244321205314129321 absolute error = 1.83e-31 relative error = 1.1867826524555569204882420304664e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (closed_form) = -0.015288189230650442423293935846499 y[1] (numeric) = -0.015288189230650442423293935846682 absolute error = 1.83e-31 relative error = 1.1970024522793939033583382214230e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (closed_form) = -0.015157630558276778142053299633143 y[1] (numeric) = -0.015157630558276778142053299633326 absolute error = 1.83e-31 relative error = 1.2073127082522367300814515950459e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (closed_form) = -0.015028156427360279400876190406069 y[1] (numeric) = -0.015028156427360279400876190406252 absolute error = 1.83e-31 relative error = 1.2177142345073676710906701523830e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (closed_form) = -0.014899758181232241257909305138172 y[1] (numeric) = -0.014899758181232241257909305138356 absolute error = 1.84e-31 relative error = 1.2349193709181581765082875321706e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1663.2MB, alloc=52.3MB, time=18.52 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (closed_form) = -0.014772427228118640625584264824498 y[1] (numeric) = -0.014772427228118640625584264824683 absolute error = 1.85e-31 relative error = 1.2523331280851460095778973113323e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (closed_form) = -0.014646155040705771007477564796187 y[1] (numeric) = -0.014646155040705771007477564796372 absolute error = 1.85e-31 relative error = 1.2631301490789434769024039668781e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (closed_form) = -0.014520933155708096297895094806434 y[1] (numeric) = -0.01452093315570809629789509480662 absolute error = 1.86e-31 relative error = 1.2809094154316415751721628649508e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (closed_form) = -0.01439675317343832248877919429881 y[1] (numeric) = -0.014396753173438322488779194298996 absolute error = 1.86e-31 relative error = 1.2919579696842042793928995230178e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = -0.014273606757379685931828993950801 y[1] (numeric) = -0.014273606757379685931828993950988 absolute error = 1.87e-31 relative error = 1.3101103538761705798260498593081e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (closed_form) = -0.014151485633760456611046510750785 y[1] (numeric) = -0.014151485633760456611046510750972 absolute error = 1.87e-31 relative error = 1.3214160324897897200267954768474e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (closed_form) = -0.014030381591130654692210908615478 y[1] (numeric) = -0.014030381591130654692210908615665 absolute error = 1.87e-31 relative error = 1.3328219106899599765480710757605e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (closed_form) = -0.013910286479940978430981617088102 y[1] (numeric) = -0.013910286479940978430981617088287 absolute error = 1.85e-31 relative error = 1.3299510421066824640424493857907e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (closed_form) = -0.013791192212123941340378523185078 y[1] (numeric) = -0.013791192212123941340378523185264 absolute error = 1.86e-31 relative error = 1.3486868802864337846636032774125e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1706.9MB, alloc=52.3MB, time=19.00 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (closed_form) = -0.013673090760677216341225911229106 y[1] (numeric) = -0.013673090760677216341225911229294 absolute error = 1.88e-31 relative error = 1.3749634467480747041624918474411e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (closed_form) = -0.013555974159249184445718696953557 y[1] (numeric) = -0.013555974159249184445718696953742 absolute error = 1.85e-31 relative error = 1.3647119552361736696542189753736e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (closed_form) = -0.013439834501726685354518029175181 y[1] (numeric) = -0.013439834501726685354518029175367 absolute error = 1.86e-31 relative error = 1.3839456131405756059228775438903e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (closed_form) = -0.013324663941824967181652518632892 y[1] (numeric) = -0.013324663941824967181652518633077 absolute error = 1.85e-31 relative error = 1.3884027455229171471700488426442e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (closed_form) = -0.013210454692679832358935953237933 y[1] (numeric) = -0.013210454692679832358935953238118 absolute error = 1.85e-31 relative error = 1.4004059989132097533021668567833e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = -0.013097199026441976612557866979598 y[1] (numeric) = -0.013097199026441976612557866979784 absolute error = 1.86e-31 relative error = 1.4201509775065951938631623808819e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (closed_form) = -0.012984889273873517748905972756003 y[1] (numeric) = -0.012984889273873517748905972756189 absolute error = 1.86e-31 relative error = 1.4324342401151211778314562522403e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (closed_form) = -0.012873517823946710834486196633319 y[1] (numeric) = -0.012873517823946710834486196633506 absolute error = 1.87e-31 relative error = 1.4525944078171967693406904926531e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (closed_form) = -0.012763077123444846205964525113938 y[1] (numeric) = -0.012763077123444846205964525114126 absolute error = 1.88e-31 relative error = 1.4729990125551905260453178255876e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 memory used=1750.8MB, alloc=52.3MB, time=19.50 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (closed_form) = -0.012653559676565326600813465055423 y[1] (numeric) = -0.01265355967656532660081346505561 absolute error = 1.87e-31 relative error = 1.4778450078860271307233248333110e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (closed_form) = -0.012544958044524919556753680738013 y[1] (numeric) = -0.0125449580445249195567536807382 absolute error = 1.87e-31 relative error = 1.4906387039023511773067908934159e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (closed_form) = -0.01243726484516718108908806397543 y[1] (numeric) = -0.012437264845167181089088063975617 absolute error = 1.87e-31 relative error = 1.5035460153657792063892589769473e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (closed_form) = -0.012330472752572046519081539157613 y[1] (numeric) = -0.0123304727525720465190815391578 absolute error = 1.87e-31 relative error = 1.5165679674446640043370102697800e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (closed_form) = -0.012224574496667584193696403546793 y[1] (numeric) = -0.012224574496667584193696403546979 absolute error = 1.86e-31 relative error = 1.5215253508472098663928848688965e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (closed_form) = -0.012119562862843907707201713226515 y[1] (numeric) = -0.0121195628628439077072017132267 absolute error = 1.85e-31 relative error = 1.5264576956580837598461540923591e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = -0.012015430691569242108388559078469 y[1] (numeric) = -0.012015430691569242108388559078653 absolute error = 1.84e-31 relative error = 1.5313641659895354835134831095075e-27 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (closed_form) = -0.011912170878008139453294092111419 y[1] (numeric) = -0.011912170878008139453294092111603 absolute error = 1.84e-31 relative error = 1.5446386883157862206701133552756e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (closed_form) = -0.011809776371641838942419547171497 y[1] (numeric) = -0.011809776371641838942419547171682 absolute error = 1.85e-31 relative error = 1.5664987564390316510647529275860e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (closed_form) = -0.011708240175890766763375600986895 y[1] (numeric) = -0.011708240175890766763375600987081 absolute error = 1.86e-31 relative error = 1.5886247395488627207404935604624e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 memory used=1794.6MB, alloc=52.3MB, time=19.98 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (closed_form) = -0.011607555347739170644657127860712 y[1] (numeric) = -0.011607555347739170644657127860898 absolute error = 1.86e-31 relative error = 1.6024045927657595311368530047623e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (closed_form) = -0.011507714997361884013794340265994 y[1] (numeric) = -0.011507714997361884013794340266179 absolute error = 1.85e-31 relative error = 1.6076171511234924140958726657255e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (closed_form) = -0.01140871228775321454340458344703 y[1] (numeric) = -0.011408712287753214543404583447213 absolute error = 1.83e-31 relative error = 1.6040372952208024931040440592363e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (closed_form) = -0.011310540434357951761635451765616 y[1] (numeric) = -0.011310540434357951761635451765799 absolute error = 1.83e-31 relative error = 1.6179598230700112654826220848436e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (closed_form) = -0.011213192704704488299102758818536 y[1] (numeric) = -0.011213192704704488299102758818719 absolute error = 1.83e-31 relative error = 1.6320061985844803982273611131943e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (closed_form) = -0.011116662418040049242644154694593 y[1] (numeric) = -0.011116662418040049242644154694775 absolute error = 1.82e-31 relative error = 1.6371820350022643009638203940927e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (closed_form) = -0.01102094294496802396698934870179 y[1] (numeric) = -0.011020942944968023966989348701971 absolute error = 1.81e-31 relative error = 1.6423277110117109970304467315647e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (closed_form) = -0.010926027707087394718750038925556 y[1] (numeric) = -0.010926027707087394718750038925735 absolute error = 1.79e-31 relative error = 1.6382898231521775621719613155436e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (closed_form) = -0.010831910176634256132916406215345 y[1] (numeric) = -0.010831910176634256132916406215522 absolute error = 1.77e-31 relative error = 1.6340608176553242223676757029234e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 memory used=1838.5MB, alloc=52.3MB, time=20.47 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (closed_form) = -0.010738583876125419770272588360867 y[1] (numeric) = -0.010738583876125419770272588361045 absolute error = 1.78e-31 relative error = 1.6575742393346565149735099933718e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (closed_form) = -0.010646042378004097674771645595919 y[1] (numeric) = -0.010646042378004097674771645596097 absolute error = 1.78e-31 relative error = 1.6719828240376697059737475415866e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (closed_form) = -0.010554279304287658862902436070549 y[1] (numeric) = -0.010554279304287658862902436070727 absolute error = 1.78e-31 relative error = 1.6865197032230120011146821192432e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (closed_form) = -0.010463288326217452572398347251641 y[1] (numeric) = -0.010463288326217452572398347251819 absolute error = 1.78e-31 relative error = 1.7011860368407545228684189842783e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (closed_form) = -0.010373063163910692015243310046742 y[1] (numeric) = -0.010373063163910692015243310046918 absolute error = 1.76e-31 relative error = 1.6967022876360004648324955386400e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (closed_form) = -0.010283597586014392299786809817067 y[1] (numeric) = -0.010283597586014392299786809817243 absolute error = 1.76e-31 relative error = 1.7114633135718821297444871232758e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = -0.010194885409361356108850068090735 y[1] (numeric) = -0.01019488540936135610885006809091 absolute error = 1.75e-31 relative error = 1.7165470034543784300982996385788e-27 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 32 h = 0.001 Finished! diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; Iterations = 4000 Total Elapsed Time = 20 Seconds Elapsed Time(since restart) = 20 Seconds Time to Timeout = 2 Minutes 39 Seconds Percent Done = 100 % > quit memory used=1873.0MB, alloc=52.3MB, time=20.84