##############ECHO OF PROBLEM################# ##############temp/h3sinpostode.ode################# diff ( y , x , 3 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(1.5) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $array_y_init[0 + 1] = exact_soln_y(x_start) $array_y_init[1 + 1] = exact_soln_yp(x_start) $array_y_init[2 + 1] = exact_soln_ypp(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $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 def exact_soln_y (x) x = c(x) return(c(1.0) + cos(c(x))) end def exact_soln_yp (x) x = c(x) return(neg(sin(c(x)))) end def exact_soln_ypp (x) x = c(x) return(neg(cos(c(x)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 1.9950041652780257 y[1] (numeric) 1.9950041652780257 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y[1] (closed_form) 1.9939560979566968 y[1] (numeric) 1.993956097956697 absolute error 2.220446049250313e-16 relative error 1.1135882337257633e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y[1] (closed_form) 1.9928086358538661 y[1] (numeric) 1.9928086358538664 absolute error 2.220446049250313e-16 relative error 1.1142294394458554e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y[1] (closed_form) 1.991561893714788 y[1] (numeric) 1.9915618937147883 absolute error 2.220446049250313e-16 relative error 1.1149269607225692e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (closed_form) 1.9902159962126371 y[1] (numeric) 1.9902159962126371 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y[1] (closed_form) 1.9887710779360424 y[1] (numeric) 1.9887710779360424 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y[1] (closed_form) 1.9872272833756268 y[1] (numeric) 1.9872272833756266 absolute error 2.220446049250313e-16 relative error 1.1173588787884023e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (closed_form) 1.9855847669095605 y[1] (numeric) 1.9855847669095605 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y[1] (closed_form) 1.9838436927881213 y[1] (numeric) 1.9838436927881213 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y[1] (closed_form) 1.9820042351172704 y[1] (numeric) 1.98200423511727 absolute error 4.440892098500626e-16 relative error 2.240606765523823e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y[1] (closed_form) 1.9800665778412416 y[1] (numeric) 1.980066577841241 absolute error 6.661338147750939e-16 relative error 3.364199074060142e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y[1] (closed_form) 1.9780309147241484 y[1] (numeric) 1.9780309147241475 absolute error 8.881784197001252e-16 relative error 4.49021505725045e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y[1] (closed_form) 1.9758974493306054 y[1] (numeric) 1.9758974493306043 absolute error 1.1102230246251565e-15 relative error 5.6188291806403105e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y[1] (closed_form) 1.9736663950053748 y[1] (numeric) 1.9736663950053734 absolute error 1.3322676295501878e-15 relative error 6.750216920760612e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y[1] (closed_form) 1.9713379748520294 y[1] (numeric) 1.9713379748520279 absolute error 1.5543122344752192e-15 relative error 7.884554826738359e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (closed_form) 1.9689124217106446 y[1] (numeric) 1.9689124217106433 absolute error 1.3322676295501878e-15 relative error 6.766515436947051e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (closed_form) 1.9663899781345133 y[1] (numeric) 1.966389978134512 absolute error 1.3322676295501878e-15 relative error 6.775195380186445e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (closed_form) 1.9637708963658906 y[1] (numeric) 1.9637708963658895 absolute error 1.1102230246251565e-15 relative error 5.653526216727775e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (closed_form) 1.9610554383107708 y[1] (numeric) 1.9610554383107697 absolute error 1.1102230246251565e-15 relative error 5.661354610053702e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (closed_form) 1.958243875512697 y[1] (numeric) 1.9582438755126956 absolute error 1.3322676295501878e-15 relative error 6.80337952902511e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (closed_form) 1.955336489125606 y[1] (numeric) 1.9553364891256044 absolute error 1.5543122344752192e-15 relative error 7.94907803909639e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (closed_form) 1.9523335698857134 y[1] (numeric) 1.952333569885712 absolute error 1.3322676295501878e-15 relative error 6.823975421516604e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (closed_form) 1.949235418082441 y[1] (numeric) 1.9492354180824398 absolute error 1.1102230246251565e-15 relative error 5.695684648072616e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (closed_form) 1.946042343528387 y[1] (numeric) 1.946042343528386 absolute error 8.881784197001252e-16 relative error 4.5640241213341786e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (closed_form) 1.942754665528346 y[1] (numeric) 1.942754665528345 absolute error 1.1102230246251565e-15 relative error 5.714684639932255e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (closed_form) 1.939372712847379 y[1] (numeric) 1.9393727128473779 absolute error 1.1102230246251565e-15 relative error 5.724650126664573e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (closed_form) 1.9358968236779348 y[1] (numeric) 1.935896823677934 absolute error 8.881784197001252e-16 relative error 4.5879429566535975e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (closed_form) 1.9323273456060344 y[1] (numeric) 1.932327345606034 absolute error 4.440892098500626e-16 relative error 2.2982090009743315e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (closed_form) 1.92866463557651 y[1] (numeric) 1.9286646355765096 absolute error 4.440892098500626e-16 relative error 2.3025735094547266e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (closed_form) 1.9249090598573129 y[1] (numeric) 1.9249090598573122 absolute error 6.661338147750939e-16 relative error 3.460598885770075e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (closed_form) 1.921060994002885 y[1] (numeric) 1.9210609940028847 absolute error 4.440892098500626e-16 relative error 2.311687193880923e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (closed_form) 1.917120822816605 y[1] (numeric) 1.9171208228166048 absolute error 2.220446049250313e-16 relative error 1.1582191496872207e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (closed_form) 1.9130889403123081 y[1] (numeric) 1.913088940312308 absolute error 2.220446049250313e-16 relative error 1.1606601253404505e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (closed_form) 1.908965749674885 y[1] (numeric) 1.9089657496748849 absolute error 2.220446049250313e-16 relative error 1.1631670445781838e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (closed_form) 1.9047516632199633 y[1] (numeric) 1.904751663219963 absolute error 2.220446049250313e-16 relative error 1.1657404438207297e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (closed_form) 1.9004471023526768 y[1] (numeric) 1.9004471023526766 absolute error 2.220446049250313e-16 relative error 1.1683808754800333e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (closed_form) 1.896052497525525 y[1] (numeric) 1.8960524975255244 absolute error 6.661338147750939e-16 relative error 3.5132667246526294e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (closed_form) 1.8915682881953289 y[1] (numeric) 1.8915682881953282 absolute error 6.661338147750939e-16 relative error 3.5215953816323813e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (closed_form) 1.8869949227792842 y[1] (numeric) 1.8869949227792835 absolute error 6.661338147750939e-16 relative error 3.530130403286779e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (closed_form) 1.8823328586101213 y[1] (numeric) 1.8823328586101207 absolute error 6.661338147750939e-16 relative error 3.538873646752118e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y[1] (closed_form) 1.8775825618903725 y[1] (numeric) 1.8775825618903719 absolute error 6.661338147750939e-16 relative error 3.547827021275818e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (closed_form) 1.8727445076457512 y[1] (numeric) 1.8727445076457503 absolute error 8.881784197001252e-16 relative error 4.74265665217016e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (closed_form) 1.8678191796776498 y[1] (numeric) 1.867819179677649 absolute error 6.661338147750939e-16 relative error 3.566372066540488e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (closed_form) 1.8628070705147608 y[1] (numeric) 1.8628070705147597 absolute error 1.1102230246251565e-15 relative error 5.959946374470019e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y[1] (closed_form) 1.857708681363824 y[1] (numeric) 1.857708681363823 absolute error 8.881784197001252e-16 relative error 4.781042520876175e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (closed_form) 1.8525245220595057 y[1] (numeric) 1.8525245220595048 absolute error 8.881784197001252e-16 relative error 4.794421931390745e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y[1] (closed_form) 1.8472551110134159 y[1] (numeric) 1.8472551110134154 absolute error 4.440892098500626e-16 relative error 2.40404916030484e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (closed_form) 1.8419009751622686 y[1] (numeric) 1.841900975162268 absolute error 6.661338147750939e-16 relative error 3.616556067659438e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (closed_form) 1.8364626499151866 y[1] (numeric) 1.8364626499151862 absolute error 4.440892098500626e-16 relative error 2.418177194458989e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (closed_form) 1.8309406791001632 y[1] (numeric) 1.8309406791001626 absolute error 6.661338147750939e-16 relative error 3.638205335535355e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (closed_form) 1.8253356149096782 y[1] (numeric) 1.8253356149096773 absolute error 8.881784197001252e-16 relative error 4.865836246470622e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (closed_form) 1.8196480178454792 y[1] (numeric) 1.8196480178454786 absolute error 6.661338147750939e-16 relative error 3.6607838892041185e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (closed_form) 1.8138784566625337 y[1] (numeric) 1.813878456662533 absolute error 6.661338147750939e-16 relative error 3.6724280633486015e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (closed_form) 1.8080275083121515 y[1] (numeric) 1.808027508312151 absolute error 4.440892098500626e-16 relative error 2.4562082590470837e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (closed_form) 1.8020957578842922 y[1] (numeric) 1.802095757884292 absolute error 2.220446049250313e-16 relative error 1.2321465380159237e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (closed_form) 1.7960837985490556 y[1] (numeric) 1.7960837985490554 absolute error 2.220446049250313e-16 relative error 1.2362708527542386e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (closed_form) 1.7899922314973646 y[1] (numeric) 1.7899922314973646 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (closed_form) 1.783821665880849 y[1] (numeric) 1.7838216658808488 absolute error 2.220446049250313e-16 relative error 1.2447690773807591e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (closed_form) 1.7775727187509276 y[1] (numeric) 1.7775727187509278 absolute error 2.220446049250313e-16 relative error 1.2491449862093888e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (closed_form) 1.7712460149971063 y[1] (numeric) 1.7712460149971068 absolute error 4.440892098500626e-16 relative error 2.5072136004257326e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (closed_form) 1.7648421872844882 y[1] (numeric) 1.7648421872844886 absolute error 4.440892098500626e-16 relative error 2.516311163965147e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (closed_form) 1.758361875990508 y[1] (numeric) 1.7583618759905084 absolute error 4.440892098500626e-16 relative error 2.525584840719442e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (closed_form) 1.7518057291408946 y[1] (numeric) 1.7518057291408953 absolute error 6.661338147750939e-16 relative error 3.8025552930562313e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (closed_form) 1.7451744023448699 y[1] (numeric) 1.7451744023448705 absolute error 6.661338147750939e-16 relative error 3.817004271206683e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (closed_form) 1.7384685587295876 y[1] (numeric) 1.7384685587295876 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y[1] (closed_form) 1.7316888688738206 y[1] (numeric) 1.7316888688738206 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (closed_form) 1.7248360107409049 y[1] (numeric) 1.7248360107409049 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (closed_form) 1.717910669610943 y[1] (numeric) 1.7179106696109432 absolute error 2.220446049250313e-16 relative error 1.2925270728734573e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (closed_form) 1.710913538012277 y[1] (numeric) 1.710913538012277 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y[1] (closed_form) 1.7038453156522357 y[1] (numeric) 1.703845315652236 absolute error 2.220446049250313e-16 relative error 1.3031969679714272e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (closed_form) 1.6967067093471648 y[1] (numeric) 1.696706709347165 absolute error 2.220446049250313e-16 relative error 1.3086799486427831e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (closed_form) 1.6894984329517466 y[1] (numeric) 1.6894984329517468 absolute error 2.220446049250313e-16 relative error 1.3142634559127353e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (closed_form) 1.682221207287613 y[1] (numeric) 1.6822212072876137 absolute error 6.661338147750939e-16 relative error 3.959846730556664e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (closed_form) 1.6748757600712665 y[1] (numeric) 1.6748757600712676 absolute error 1.1102230246251565e-15 relative error 6.62868883228638e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (closed_form) 1.6674628258413078 y[1] (numeric) 1.6674628258413087 absolute error 8.881784197001252e-16 relative error 5.326526060645463e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (closed_form) 1.6599831458849816 y[1] (numeric) 1.6599831458849832 absolute error 1.5543122344752192e-15 relative error 9.363421781289071e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (closed_form) 1.6524374681640515 y[1] (numeric) 1.652437468164053 absolute error 1.5543122344752192e-15 relative error 9.406178838356559e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (closed_form) 1.6448265472400005 y[1] (numeric) 1.6448265472400023 absolute error 1.7763568394002505e-15 relative error 1.0799660562269962e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (closed_form) 1.6371511441985795 y[1] (numeric) 1.6371511441985818 absolute error 2.220446049250313e-15 relative error 1.356286532931734e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (closed_form) 1.6294120265736964 y[1] (numeric) 1.6294120265736987 absolute error 2.220446049250313e-15 relative error 1.362728403275281e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (closed_form) 1.621609968270664 y[1] (numeric) 1.6216099682706662 absolute error 2.220446049250313e-15 relative error 1.369284903704845e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (closed_form) 1.613745749488811 y[1] (numeric) 1.6137457494888132 absolute error 2.220446049250313e-15 relative error 1.3759577987757287e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (closed_form) 1.6058201566434622 y[1] (numeric) 1.605820156643465 absolute error 2.6645352591003757e-15 relative error 1.6592986755564672e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (closed_form) 1.5978339822872978 y[1] (numeric) 1.5978339822873 absolute error 2.220446049250313e-15 relative error 1.3896600484561898e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (closed_form) 1.5897880250310976 y[1] (numeric) 1.5897880250311003 absolute error 2.6645352591003757e-15 relative error 1.6760317835758356e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (closed_form) 1.581683089463883 y[1] (numeric) 1.5816830894638854 absolute error 2.4424906541753444e-15 relative error 1.544235169766679e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (closed_form) 1.573519986072456 y[1] (numeric) 1.5735199860724585 absolute error 2.4424906541753444e-15 relative error 1.5522463494549314e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (closed_form) 1.5652995311603537 y[1] (numeric) 1.5652995311603566 absolute error 2.886579864025407e-15 relative error 1.844107026522643e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (closed_form) 1.5570225467662167 y[1] (numeric) 1.5570225467662195 absolute error 2.886579864025407e-15 relative error 1.8539101248216032e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (closed_form) 1.5486898605815869 y[1] (numeric) 1.54868986058159 absolute error 3.1086244689504383e-15 relative error 2.00726081320313e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y[1] (closed_form) 1.5403023058681393 y[1] (numeric) 1.540302305868142 absolute error 2.6645352591003757e-15 relative error 1.7298781212942486e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0099999999999996 y[1] (closed_form) 1.5318607213743558 y[1] (numeric) 1.5318607213743576 absolute error 1.7763568394002505e-15 relative error 1.1596072767023737e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0199999999999985 y[1] (closed_form) 1.5233659512516509 y[1] (numeric) 1.523365951251652 absolute error 1.1102230246251565e-15 relative error 7.287960084134468e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0299999999999974 y[1] (closed_form) 1.5148188449699576 y[1] (numeric) 1.5148188449699578 absolute error 2.220446049250313e-16 relative error 1.4658162305172205e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0399999999999963 y[1] (closed_form) 1.5062202572327816 y[1] (numeric) 1.506220257232781 absolute error 6.661338147750939e-16 relative error 4.422552489095524e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0499999999999952 y[1] (closed_form) 1.4975710478917312 y[1] (numeric) 1.4975710478917297 absolute error 1.5543122344752192e-15 relative error 1.0378888111274371e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.059999999999994 y[1] (closed_form) 1.4888720818605328 y[1] (numeric) 1.4888720818605303 absolute error 2.4424906541753444e-15 relative error 1.6404973160106175e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.069999999999993 y[1] (closed_form) 1.4801242290285404 y[1] (numeric) 1.480124229028537 absolute error 3.3306690738754696e-15 relative error 2.2502631931520435e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y[1] (closed_form) 1.4713283641737471 y[1] (numeric) 1.471328364173743 absolute error 4.218847493575595e-15 relative error 2.8673731821548685e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y[1] (closed_form) 1.462485366875309 y[1] (numeric) 1.4624853668753037 absolute error 5.329070518200751e-15 relative error 3.643845360030263e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0999999999999897 y[1] (closed_form) 1.4535961214255866 y[1] (numeric) 1.4535961214255801 absolute error 6.439293542825908e-15 relative error 4.429905561739319e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y[1] (closed_form) 1.4446615167417172 y[1] (numeric) 1.4446615167417098 absolute error 7.327471962526033e-15 relative error 5.072102965026977e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y[1] (closed_form) 1.4356824462767235 y[1] (numeric) 1.4356824462767153 absolute error 8.215650382226158e-15 relative error 5.7224704554496e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1299999999999863 y[1] (closed_form) 1.4266598079301698 y[1] (numeric) 1.4266598079301607 absolute error 9.103828801926284e-15 relative error 6.381219090439173e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y[1] (closed_form) 1.4175945039583715 y[1] (numeric) 1.4175945039583615 absolute error 9.992007221626409e-15 relative error 7.048565152958458e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y[1] (closed_form) 1.4084874408841719 y[1] (numeric) 1.4084874408841608 absolute error 1.1102230246251565e-14 relative error 7.882377878557575e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.159999999999983 y[1] (closed_form) 1.3993395294062887 y[1] (numeric) 1.3993395294062767 absolute error 1.199040866595169e-14 relative error 8.568619991060337e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.169999999999982 y[1] (closed_form) 1.3901516843082469 y[1] (numeric) 1.390151684308234 absolute error 1.2878587085651816e-14 relative error 9.264159610079044e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1799999999999808 y[1] (closed_form) 1.3809248243668995 y[1] (numeric) 1.3809248243668857 absolute error 1.3766765505351941e-14 relative error 9.969236023882379e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1899999999999797 y[1] (closed_form) 1.3716598722605517 y[1] (numeric) 1.3716598722605367 absolute error 1.509903313490213e-14 relative error 1.1007855110624694e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1999999999999786 y[1] (closed_form) 1.3623577544766934 y[1] (numeric) 1.3623577544766776 absolute error 1.5765166949677223e-14 relative error 1.1571972852118359e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2099999999999775 y[1] (closed_form) 1.3530194012193513 y[1] (numeric) 1.3530194012193344 absolute error 1.687538997430238e-14 relative error 1.2472393196353394e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2199999999999764 y[1] (closed_form) 1.3436457463160691 y[1] (numeric) 1.3436457463160512 absolute error 1.7985612998927536e-14 relative error 1.3385680748247414e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2299999999999753 y[1] (closed_form) 1.3342377271245258 y[1] (numeric) 1.3342377271245065 absolute error 1.9317880628477724e-14 relative error 1.4478589711378148e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2399999999999742 y[1] (closed_form) 1.3247962844388006 y[1] (numeric) 1.3247962844387804 absolute error 2.020605904817785e-14 relative error 1.5252200874595127e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2499999999999731 y[1] (closed_form) 1.315322362395294 y[1] (numeric) 1.3153223623952728 absolute error 2.1316282072803006e-14 relative error 1.620612762485431e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.259999999999972 y[1] (closed_form) 1.305816908378316 y[1] (numeric) 1.3058169083782936 absolute error 2.2426505097428162e-14 relative error 1.7174310543489183e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.269999999999971 y[1] (closed_form) 1.2962808729253466 y[1] (numeric) 1.296280872925323 absolute error 2.353672812205332e-14 relative error 1.8157120585245887e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2799999999999698 y[1] (closed_form) 1.2867152096319845 y[1] (numeric) 1.28671520963196 absolute error 2.4424906541753444e-14 relative error 1.8982371824717336e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2899999999999687 y[1] (closed_form) 1.2771208750565877 y[1] (numeric) 1.2771208750565624 absolute error 2.531308496145357e-14 relative error 1.982043004373566e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2999999999999676 y[1] (closed_form) 1.2674988286246185 y[1] (numeric) 1.2674988286245923 absolute error 2.6201263381153694e-14 relative error 2.0671627294192506e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3099999999999665 y[1] (closed_form) 1.257850032532702 y[1] (numeric) 1.2578500325326747 absolute error 2.731148640577885e-14 relative error 2.1712831974720163e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3199999999999654 y[1] (closed_form) 1.2481754516524064 y[1] (numeric) 1.2481754516523778 absolute error 2.864375403532904e-14 relative error 2.2948499746096427e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3299999999999643 y[1] (closed_form) 1.2384760534337578 y[1] (numeric) 1.2384760534337278 absolute error 2.9976021664879227e-14 relative error 2.420395742151711e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3399999999999632 y[1] (closed_form) 1.2287528078084953 y[1] (numeric) 1.228752807808464 absolute error 3.1308289294429414e-14 relative error 2.5479729605068705e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3499999999999621 y[1] (closed_form) 1.2190066870930785 y[1] (numeric) 1.219006687093046 absolute error 3.241851231905457e-14 relative error 2.659420384014614e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.359999999999961 y[1] (closed_form) 1.2092386658914576 y[1] (numeric) 1.209238665891424 absolute error 3.352873534367973e-14 relative error 2.77271445988391e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.36999999999996 y[1] (closed_form) 1.1994497209976123 y[1] (numeric) 1.1994497209975779 absolute error 3.441691376337985e-14 relative error 2.8693919520656894e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3799999999999588 y[1] (closed_form) 1.1896408312978748 y[1] (numeric) 1.1896408312978395 absolute error 3.530509218307998e-14 relative error 2.9677101906936747e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3899999999999577 y[1] (closed_form) 1.179812977673041 y[1] (numeric) 1.1798129776730049 absolute error 3.6193270602780103e-14 relative error 3.067712534758222e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3999999999999566 y[1] (closed_form) 1.1699671429002838 y[1] (numeric) 1.1699671429002463 absolute error 3.752553823233029e-14 relative error 3.2074010334432603e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4099999999999555 y[1] (closed_form) 1.160104311554875 y[1] (numeric) 1.1601043115548366 absolute error 3.8413716652030416e-14 relative error 3.3112295393976197e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4199999999999544 y[1] (closed_form) 1.150225469911731 y[1] (numeric) 1.1502254699116912 absolute error 3.9745984281580604e-14 relative error 3.4554950591235594e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4299999999999533 y[1] (closed_form) 1.140331605846783 y[1] (numeric) 1.1403316058467423 absolute error 4.063416270128073e-14 relative error 3.5633637174431182e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4399999999999522 y[1] (closed_form) 1.130423708738193 y[1] (numeric) 1.130423708738151 absolute error 4.196643033083092e-14 relative error 3.712451358409219e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.449999999999951 y[1] (closed_form) 1.1205027693674152 y[1] (numeric) 1.1205027693673721 absolute error 4.3076653355456074e-14 relative error 3.8444040062279534e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.45999999999995 y[1] (closed_form) 1.1105697798201193 y[1] (numeric) 1.1105697798200753 absolute error 4.39648317751562e-14 relative error 3.958763562094878e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.469999999999949 y[1] (closed_form) 1.1006257333869824 y[1] (numeric) 1.1006257333869376 absolute error 4.4853010194856324e-14 relative error 4.075228193768381e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4799999999999478 y[1] (closed_form) 1.0906716244643617 y[1] (numeric) 1.0906716244643153 absolute error 4.6407322429331543e-14 relative error 4.254930759028647e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4899999999999467 y[1] (closed_form) 1.0807084484548537 y[1] (numeric) 1.0807084484548062 absolute error 4.75175454539567e-14 relative error 4.3968884967906986e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4999999999999456 y[1] (closed_form) 1.0707372016677572 y[1] (numeric) 1.0707372016677088 absolute error 4.8405723873656825e-14 relative error 4.520784726472669e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Finished! diff ( y , x , 3 ) = sin ( x ) ; Iterations 1401 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.14285714285325%