##############ECHO OF PROBLEM################# ##############temp/sub_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 - 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(5.0) $array_y_init[0 + 1] = exact_soln_y(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 # ELIMINATED in preodein.rb #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(2.0) + cos(c(x)) + c(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 3.095004165278026 y[1] (numeric) 3.095004165278026 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) 3.1039560979566967 y[1] (numeric) 3.1039560979566967 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] 0.12000000000000002 y[1] (closed_form) 3.1128086358538662 y[1] (numeric) 3.1128086358538662 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] 0.13000000000000003 y[1] (closed_form) 3.121561893714788 y[1] (numeric) 3.121561893714788 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] 0.14000000000000004 y[1] (closed_form) 3.130215996212637 y[1] (numeric) 3.130215996212637 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) 3.1387710779360423 y[1] (numeric) 3.1387710779360427 absolute error 4.440892098500626e-16 relative error 1.4148505858607623e-14% 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) 3.147227283375627 y[1] (numeric) 3.1472272833756265 absolute error 4.440892098500626e-16 relative error 1.4110490595828374e-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) 3.1555847669095605 y[1] (numeric) 3.155584766909561 absolute error 4.440892098500626e-16 relative error 1.4073119331380974e-14% 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) 3.1638436927881215 y[1] (numeric) 3.1638436927881224 absolute error 8.881784197001252e-16 relative error 2.8072765469567887e-14% 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) 3.1720042351172704 y[1] (numeric) 3.1720042351172717 absolute error 1.3322676295501878e-15 relative error 4.20008149674155e-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) 3.1800665778412416 y[1] (numeric) 3.180066577841243 absolute error 1.3322676295501878e-15 relative error 4.189433135876624e-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) 3.1880309147241483 y[1] (numeric) 3.1880309147241492 absolute error 8.881784197001252e-16 relative error 2.7859780643845384e-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) 3.1958974493306056 y[1] (numeric) 3.195897449330606 absolute error 4.440892098500626e-16 relative error 1.3895602624642384e-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) 3.2036663950053748 y[1] (numeric) 3.2036663950053756 absolute error 8.881784197001252e-16 relative error 2.7723811102330307e-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) 3.2113379748520297 y[1] (numeric) 3.2113379748520297 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] 0.2500000000000001 y[1] (closed_form) 3.2189124217106446 y[1] (numeric) 3.218912421710645 absolute error 4.440892098500626e-16 relative error 1.3796250151287366e-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) 3.2263899781345136 y[1] (numeric) 3.2263899781345136 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] 0.27000000000000013 y[1] (closed_form) 3.2337708963658907 y[1] (numeric) 3.233770896365891 absolute error 4.440892098500626e-16 relative error 1.3732859379405317e-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) 3.241055438310771 y[1] (numeric) 3.241055438310771 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] 0.29000000000000015 y[1] (closed_form) 3.248243875512697 y[1] (numeric) 3.2482438755126966 absolute error 4.440892098500626e-16 relative error 1.3671670812585412e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (closed_form) 3.255336489125606 y[1] (numeric) 3.2553364891256056 absolute error 4.440892098500626e-16 relative error 1.3641883453017369e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (closed_form) 3.262333569885713 y[1] (numeric) 3.262333569885713 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] 0.3200000000000002 y[1] (closed_form) 3.2692354180824412 y[1] (numeric) 3.2692354180824412 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] 0.3300000000000002 y[1] (closed_form) 3.276042343528387 y[1] (numeric) 3.2760423435283874 absolute error 4.440892098500626e-16 relative error 1.3555661474502385e-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) 3.2827546655283464 y[1] (numeric) 3.2827546655283464 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] 0.3500000000000002 y[1] (closed_form) 3.289372712847379 y[1] (numeric) 3.2893727128473786 absolute error 4.440892098500626e-16 relative error 1.350072638821296e-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) 3.295896823677935 y[1] (numeric) 3.295896823677935 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] 0.3700000000000002 y[1] (closed_form) 3.3023273456060345 y[1] (numeric) 3.3023273456060345 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] 0.3800000000000002 y[1] (closed_form) 3.3086646355765104 y[1] (numeric) 3.3086646355765104 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] 0.39000000000000024 y[1] (closed_form) 3.314909059857313 y[1] (numeric) 3.3149090598573134 absolute error 4.440892098500626e-16 relative error 1.339672376620727e-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) 3.3210609940028855 y[1] (numeric) 3.3210609940028855 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] 0.41000000000000025 y[1] (closed_form) 3.327120822816605 y[1] (numeric) 3.327120822816606 absolute error 8.881784197001252e-16 relative error 2.6695105678435493e-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) 3.3330889403123085 y[1] (numeric) 3.333088940312309 absolute error 4.440892098500626e-16 relative error 1.3323653157855779e-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) 3.3389657496748852 y[1] (numeric) 3.3389657496748866 absolute error 1.3322676295501878e-15 relative error 3.990060783582194e-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) 3.344751663219964 y[1] (numeric) 3.3447516632199648 absolute error 8.881784197001252e-16 relative error 2.655439055361986e-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) 3.350447102352677 y[1] (numeric) 3.3504471023526787 absolute error 1.7763568394002505e-15 relative error 5.3018501266678597e-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) 3.3560524975255253 y[1] (numeric) 3.356052497525526 absolute error 8.881784197001252e-16 relative error 2.6464973964352296e-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) 3.361568288195329 y[1] (numeric) 3.3615682881953295 absolute error 4.440892098500626e-16 relative error 1.3210774608076567e-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) 3.3669949227792846 y[1] (numeric) 3.3669949227792846 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] 0.4900000000000003 y[1] (closed_form) 3.3723328586101218 y[1] (numeric) 3.3723328586101213 absolute error 4.440892098500626e-16 relative error 1.316860548673983e-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) 3.377582561890373 y[1] (numeric) 3.3775825618903723 absolute error 8.881784197001252e-16 relative error 2.6296275617997846e-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) 3.3827445076457514 y[1] (numeric) 3.3827445076457505 absolute error 8.881784197001252e-16 relative error 2.62561484526143e-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) 3.38781917967765 y[1] (numeric) 3.387819179677649 absolute error 8.881784197001252e-16 relative error 2.621681892079716e-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) 3.392807070514761 y[1] (numeric) 3.392807070514759 absolute error 2.220446049250313e-15 relative error 6.544569152036765e-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) 3.397708681363824 y[1] (numeric) 3.397708681363822 absolute error 2.220446049250313e-15 relative error 6.5351278096009e-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) 3.402524522059506 y[1] (numeric) 3.4025245220595037 absolute error 2.220446049250313e-15 relative error 6.525878167385858e-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) 3.4072551110134164 y[1] (numeric) 3.4072551110134146 absolute error 1.7763568394002505e-15 relative error 5.2134541779934714e-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) 3.411900975162269 y[1] (numeric) 3.411900975162267 absolute error 1.7763568394002505e-15 relative error 5.206355202954762e-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) 3.416462649915187 y[1] (numeric) 3.416462649915186 absolute error 1.3322676295501878e-15 relative error 3.8995527423174406e-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) 3.4209406791001635 y[1] (numeric) 3.420940679100162 absolute error 1.3322676295501878e-15 relative error 3.894448207446335e-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) 3.4253356149096787 y[1] (numeric) 3.4253356149096774 absolute error 1.3322676295501878e-15 relative error 3.8894513686517045e-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) 3.4296480178454796 y[1] (numeric) 3.429648017845479 absolute error 4.440892098500626e-16 relative error 1.2948536046245396e-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) 3.433878456662534 y[1] (numeric) 3.4338784566625336 absolute error 4.440892098500626e-16 relative error 1.2932583824812577e-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) 3.438027508312152 y[1] (numeric) 3.4380275083121523 absolute error 4.440892098500626e-16 relative error 1.2916976631989823e-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) 3.442095757884293 y[1] (numeric) 3.4420957578842937 absolute error 8.881784197001252e-16 relative error 2.5803419839953843e-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) 3.446083798549056 y[1] (numeric) 3.4460837985490564 absolute error 4.440892098500626e-16 relative error 1.2886779190832288e-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) 3.4499922314973652 y[1] (numeric) 3.4499922314973657 absolute error 4.440892098500626e-16 relative error 1.2872179994947961e-14% 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) 3.453821665880849 y[1] (numeric) 3.4538216658808496 absolute error 4.440892098500626e-16 relative error 1.2857907929557325e-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) 3.457572718750928 y[1] (numeric) 3.4575727187509284 absolute error 4.440892098500626e-16 relative error 1.2843958637274674e-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) 3.4612460149971067 y[1] (numeric) 3.4612460149971076 absolute error 8.881784197001252e-16 relative error 2.5660655609331707e-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) 3.464842187284489 y[1] (numeric) 3.464842187284489 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] 0.7100000000000005 y[1] (closed_form) 3.4683618759905084 y[1] (numeric) 3.468361875990509 absolute error 4.440892098500626e-16 relative error 1.2804004476125718e-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) 3.471805729140895 y[1] (numeric) 3.471805729140896 absolute error 8.881784197001252e-16 relative error 2.5582607121277684e-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) 3.4751744023448703 y[1] (numeric) 3.4751744023448707 absolute error 4.440892098500626e-16 relative error 1.277890426306127e-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) 3.4784685587295883 y[1] (numeric) 3.4784685587295874 absolute error 8.881784197001252e-16 relative error 2.553360493862009e-14% 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) 3.481688868873821 y[1] (numeric) 3.481688868873821 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) 3.4848360107409055 y[1] (numeric) 3.484836010740905 absolute error 4.440892098500626e-16 relative error 1.2743475115652444e-14% 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) 3.4879106696109434 y[1] (numeric) 3.4879106696109434 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] 0.7800000000000006 y[1] (closed_form) 3.4909135380122778 y[1] (numeric) 3.490913538012277 absolute error 8.881784197001252e-16 relative error 2.5442578569443832e-14% 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) 3.493845315652236 y[1] (numeric) 3.493845315652236 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] 0.8000000000000006 y[1] (closed_form) 3.4967067093471655 y[1] (numeric) 3.496706709347165 absolute error 4.440892098500626e-16 relative error 1.2700213279625444e-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) 3.4994984329517473 y[1] (numeric) 3.499498432951747 absolute error 4.440892098500626e-16 relative error 1.2690081689091756e-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) 3.5022212072876138 y[1] (numeric) 3.5022212072876133 absolute error 4.440892098500626e-16 relative error 1.2680215884878358e-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) 3.504875760071267 y[1] (numeric) 3.5048757600712674 absolute error 4.440892098500626e-16 relative error 1.2670612034505686e-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) 3.5074628258413085 y[1] (numeric) 3.507462825841309 absolute error 4.440892098500626e-16 relative error 1.2661266331270163e-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) 3.5099831458849824 y[1] (numeric) 3.5099831458849833 absolute error 8.881784197001252e-16 relative error 2.530434998644947e-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) 3.5124374681640522 y[1] (numeric) 3.512437468164053 absolute error 8.881784197001252e-16 relative error 2.5286668524361668e-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) 3.514826547240001 y[1] (numeric) 3.514826547240003 absolute error 1.7763568394002505e-15 relative error 5.053896161092573e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (closed_form) 3.5171511441985803 y[1] (numeric) 3.517151144198582 absolute error 1.7763568394002505e-15 relative error 5.0505558805179297e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (closed_form) 3.519412026573697 y[1] (numeric) 3.5194120265736983 absolute error 1.3322676295501878e-15 relative error 3.7854835395536484e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (closed_form) 3.5216099682706647 y[1] (numeric) 3.521609968270665 absolute error 4.440892098500626e-16 relative error 1.2610403021665081e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (closed_form) 3.523745749488812 y[1] (numeric) 3.5237457494888127 absolute error 8.881784197001252e-16 relative error 2.520551943422629e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (closed_form) 3.525820156643463 y[1] (numeric) 3.525820156643464 absolute error 8.881784197001252e-16 relative error 2.51906898321683e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (closed_form) 3.5278339822872984 y[1] (numeric) 3.527833982287299 absolute error 4.440892098500626e-16 relative error 1.2588155000483724e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (closed_form) 3.5297880250310985 y[1] (numeric) 3.5297880250310993 absolute error 8.881784197001252e-16 relative error 2.5162372737447886e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (closed_form) 3.5316830894638835 y[1] (numeric) 3.531683089463885 absolute error 1.3322676295501878e-15 relative error 3.772330630471232e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (closed_form) 3.5335199860724567 y[1] (numeric) 3.533519986072458 absolute error 1.3322676295501878e-15 relative error 3.770369588403027e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (closed_form) 3.535299531160354 y[1] (numeric) 3.535299531160356 absolute error 1.7763568394002505e-15 relative error 5.0246289564528516e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (closed_form) 3.5370225467662175 y[1] (numeric) 3.5370225467662184 absolute error 8.881784197001252e-16 relative error 2.511090636140155e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (closed_form) 3.5386898605815875 y[1] (numeric) 3.5386898605815893 absolute error 1.7763568394002505e-15 relative error 5.019814986296381e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y[1] (closed_form) 3.54030230586814 y[1] (numeric) 3.5403023058681415 absolute error 1.3322676295501878e-15 relative error 3.763146518143156e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0099999999999996 y[1] (closed_form) 3.5418607213743556 y[1] (numeric) 3.541860721374357 absolute error 1.3322676295501878e-15 relative error 3.761490737086989e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0199999999999985 y[1] (closed_form) 3.5433659512516495 y[1] (numeric) 3.5433659512516518 absolute error 2.220446049250313e-15 relative error 6.26648807884483e-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) 3.5448188449699547 y[1] (numeric) 3.544818844969958 absolute error 3.1086244689504383e-15 relative error 8.769487539148948e-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) 3.546220257232778 y[1] (numeric) 3.5462202572327812 absolute error 3.1086244689504383e-15 relative error 8.76602197116823e-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) 3.5475710478917266 y[1] (numeric) 3.5475710478917297 absolute error 3.1086244689504383e-15 relative error 8.762684177383429e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.059999999999994 y[1] (closed_form) 3.5488720818605266 y[1] (numeric) 3.5488720818605297 absolute error 3.1086244689504383e-15 relative error 8.759471734243842e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.069999999999993 y[1] (closed_form) 3.5501242290285333 y[1] (numeric) 3.5501242290285364 absolute error 3.1086244689504383e-15 relative error 8.756382223280935e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y[1] (closed_form) 3.551328364173739 y[1] (numeric) 3.551328364173742 absolute error 3.1086244689504383e-15 relative error 8.753413230695999e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y[1] (closed_form) 3.5524853668753 y[1] (numeric) 3.5524853668753034 absolute error 3.552713678800501e-15 relative error 1.0000642682239679e-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) 3.553596121425576 y[1] (numeric) 3.5535961214255796 absolute error 3.552713678800501e-15 relative error 9.997516761627033e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y[1] (closed_form) 3.5546615167417057 y[1] (numeric) 3.554661516741709 absolute error 3.1086244689504383e-15 relative error 8.745205286943562e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y[1] (closed_form) 3.5556824462767107 y[1] (numeric) 3.5556824462767147 absolute error 3.9968028886505635e-15 relative error 1.1240606969375926e-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) 3.5566598079301563 y[1] (numeric) 3.5566598079301595 absolute error 3.1086244689504383e-15 relative error 8.740291837918403e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y[1] (closed_form) 3.5575945039583567 y[1] (numeric) 3.55759450395836 absolute error 3.1086244689504383e-15 relative error 8.73799547838189e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y[1] (closed_form) 3.5584874408841562 y[1] (numeric) 3.558487440884159 absolute error 2.6645352591003757e-15 relative error 7.487831005069767e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.159999999999983 y[1] (closed_form) 3.559339529406272 y[1] (numeric) 3.5593395294062757 absolute error 3.552713678800501e-15 relative error 9.98138460646693e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.169999999999982 y[1] (closed_form) 3.560151684308229 y[1] (numeric) 3.5601516843082335 absolute error 4.440892098500626e-15 relative error 1.2473884520354455e-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) 3.5609248243668805 y[1] (numeric) 3.5609248243668863 absolute error 5.773159728050814e-15 relative error 1.6212529083865905e-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) 3.561659872260532 y[1] (numeric) 3.5616598722605377 absolute error 5.773159728050814e-15 relative error 1.6209183176120286e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1999999999999786 y[1] (closed_form) 3.562357754476672 y[1] (numeric) 3.562357754476679 absolute error 7.105427357601002e-15 relative error 1.9945855658859353e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2099999999999775 y[1] (closed_form) 3.5630194012193286 y[1] (numeric) 3.5630194012193357 absolute error 7.105427357601002e-15 relative error 1.9942151746828542e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2199999999999764 y[1] (closed_form) 3.5636457463160456 y[1] (numeric) 3.5636457463160527 absolute error 7.105427357601002e-15 relative error 1.9938646721398468e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2299999999999753 y[1] (closed_form) 3.5642377271245014 y[1] (numeric) 3.564237727124509 absolute error 7.549516567451064e-15 relative error 2.1181293576457771e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2399999999999742 y[1] (closed_form) 3.564796284438775 y[1] (numeric) 3.564796284438783 absolute error 7.993605777301127e-15 relative error 2.242373796279807e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2499999999999731 y[1] (closed_form) 3.5653223623952677 y[1] (numeric) 3.5653223623952757 absolute error 7.993605777301127e-15 relative error 2.2420429248172762e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.259999999999972 y[1] (closed_form) 3.565816908378288 y[1] (numeric) 3.5658169083782965 absolute error 8.43769498715119e-15 relative error 2.366272639328698e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.269999999999971 y[1] (closed_form) 3.5662808729253177 y[1] (numeric) 3.566280872925326 absolute error 8.43769498715119e-15 relative error 2.3659647929609065e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2799999999999698 y[1] (closed_form) 3.566715209631954 y[1] (numeric) 3.5667152096319628 absolute error 8.881784197001252e-15 relative error 2.490185976445749e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2899999999999687 y[1] (closed_form) 3.567120875056556 y[1] (numeric) 3.567120875056565 absolute error 8.881784197001252e-15 relative error 2.4899027838131314e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2999999999999676 y[1] (closed_form) 3.5674988286245863 y[1] (numeric) 3.567498828624595 absolute error 8.881784197001252e-15 relative error 2.4896389946189656e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3099999999999665 y[1] (closed_form) 3.567850032532669 y[1] (numeric) 3.567850032532678 absolute error 8.881784197001252e-15 relative error 2.4893939251971424e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3199999999999654 y[1] (closed_form) 3.5681754516523716 y[1] (numeric) 3.568175451652381 absolute error 9.325873406851315e-15 relative error 2.613625235982338e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3299999999999643 y[1] (closed_form) 3.568476053433722 y[1] (numeric) 3.568476053433731 absolute error 9.325873406851315e-15 relative error 2.61340506905675e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3399999999999632 y[1] (closed_form) 3.5687528078084583 y[1] (numeric) 3.568752807808468 absolute error 9.769962616701378e-15 relative error 2.737640610838785e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3499999999999621 y[1] (closed_form) 3.569006687093041 y[1] (numeric) 3.56900668709305 absolute error 8.881784197001252e-15 relative error 2.4885871548297583e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.359999999999961 y[1] (closed_form) 3.569238665891419 y[1] (numeric) 3.5692386658914277 absolute error 8.881784197001252e-15 relative error 2.4884254118050195e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.36999999999996 y[1] (closed_form) 3.5694497209975724 y[1] (numeric) 3.5694497209975817 absolute error 9.325873406851315e-15 relative error 2.612692189496639e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3799999999999588 y[1] (closed_form) 3.569640831297834 y[1] (numeric) 3.5696408312978436 absolute error 9.769962616701378e-15 relative error 2.7369595649625226e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3899999999999577 y[1] (closed_form) 3.569812977672999 y[1] (numeric) 3.5698129776730085 absolute error 9.325873406851315e-15 relative error 2.612426327423582e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3999999999999566 y[1] (closed_form) 3.56996714290024 y[1] (numeric) 3.5699671429002495 absolute error 9.325873406851315e-15 relative error 2.612313512576191e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4099999999999555 y[1] (closed_form) 3.5701043115548305 y[1] (numeric) 3.5701043115548403 absolute error 9.769962616701378e-15 relative error 2.736604245730406e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4199999999999544 y[1] (closed_form) 3.5702254699116853 y[1] (numeric) 3.570225469911695 absolute error 9.769962616701378e-15 relative error 2.7365113769531903e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4299999999999533 y[1] (closed_form) 3.570331605846736 y[1] (numeric) 3.570331605846746 absolute error 1.021405182655144e-14 relative error 2.860813211250468e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4399999999999522 y[1] (closed_form) 3.5704237087381454 y[1] (numeric) 3.570423708738155 absolute error 9.769962616701378e-15 relative error 2.736359439018588e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.449999999999951 y[1] (closed_form) 3.5705027693673665 y[1] (numeric) 3.5705027693673763 absolute error 9.769962616701378e-15 relative error 2.7362988485883326e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.45999999999995 y[1] (closed_form) 3.570569779820069 y[1] (numeric) 3.57056977982008 absolute error 1.1102230246251565e-14 relative error 3.109372153710167e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.469999999999949 y[1] (closed_form) 3.5706257333869313 y[1] (numeric) 3.5706257333869424 absolute error 1.1102230246251565e-14 relative error 3.1093234282273827e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4799999999999478 y[1] (closed_form) 3.5706716244643095 y[1] (numeric) 3.57067162446432 absolute error 1.0658141036401503e-14 relative error 2.9849121278410727e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4899999999999467 y[1] (closed_form) 3.5707084484548 y[1] (numeric) 3.5707084484548117 absolute error 1.1546319456101628e-14 relative error 3.2336214571363895e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4999999999999456 y[1] (closed_form) 3.5707372016677024 y[1] (numeric) 3.5707372016677144 absolute error 1.199040866595169e-14 relative error 3.357964473093009e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5099999999999445 y[1] (closed_form) 3.570758881219386 y[1] (numeric) 3.570758881219397 absolute error 1.1102230246251565e-14 relative error 3.1092074865778226e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5199999999999434 y[1] (closed_form) 3.5707744849335787 y[1] (numeric) 3.5707744849335903 absolute error 1.1546319456101628e-14 relative error 3.2335616558312015e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5299999999999423 y[1] (closed_form) 3.5707850112415906 y[1] (numeric) 3.570785011241602 absolute error 1.1546319456101628e-14 relative error 3.2335521236230574e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5399999999999412 y[1] (closed_form) 3.570791459082466 y[1] (numeric) 3.570791459082477 absolute error 1.1102230246251565e-14 relative error 3.1091791199434375e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.54999999999994 y[1] (closed_form) 3.570794827803092 y[1] (numeric) 3.570794827803103 absolute error 1.1102230246251565e-14 relative error 3.1091761867153087e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.559999999999939 y[1] (closed_form) 3.5707961170582676 y[1] (numeric) 3.570796117058278 absolute error 1.021405182655144e-14 relative error 2.860441059000056e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.569999999999938 y[1] (closed_form) 3.5707963267107337 y[1] (numeric) 3.5707963267107434 absolute error 9.769962616701378e-15 relative error 2.7360738957914895e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5799999999999368 y[1] (closed_form) 3.570796456731192 y[1] (numeric) 3.5707964567312023 absolute error 1.021405182655144e-14 relative error 2.86044078689987e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5899999999999357 y[1] (closed_form) 3.570797507098307 y[1] (numeric) 3.5707975070983182 absolute error 1.1102230246251565e-14 relative error 3.1091738537908393e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5999999999999346 y[1] (closed_form) 3.570800477698711 y[1] (numeric) 3.5708004776987226 absolute error 1.1546319456101628e-14 relative error 3.2335381179132514e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6099999999999335 y[1] (closed_form) 3.5708063682270126 y[1] (numeric) 3.5708063682270237 absolute error 1.1102230246251565e-14 relative error 3.1091661382255453e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6199999999999324 y[1] (closed_form) 3.5708161780858294 y[1] (numeric) 3.57081617808584 absolute error 1.0658141036401503e-14 relative error 2.984791292761226e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6299999999999313 y[1] (closed_form) 3.5708309062858516 y[1] (numeric) 3.5708309062858623 absolute error 1.0658141036401503e-14 relative error 2.9847789817321297e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6399999999999302 y[1] (closed_form) 3.570851551345938 y[1] (numeric) 3.5708515513459487 absolute error 1.0658141036401503e-14 relative error 2.98476172508045e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.649999999999929 y[1] (closed_form) 3.570879111193266 y[1] (numeric) 3.570879111193278 absolute error 1.199040866595169e-14 relative error 3.357831024961499e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.659999999999928 y[1] (closed_form) 3.5709145830635407 y[1] (numeric) 3.5709145830635523 absolute error 1.1546319456101628e-14 relative error 3.233434793110024e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6699999999999269 y[1] (closed_form) 3.5709589634012717 y[1] (numeric) 3.5709589634012833 absolute error 1.1546319456101628e-14 relative error 3.233394607566135e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6799999999999258 y[1] (closed_form) 3.5710132477601286 y[1] (numeric) 3.57101324776014 absolute error 1.1546319456101628e-14 relative error 3.2333454554793113e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6899999999999247 y[1] (closed_form) 3.571078430703387 y[1] (numeric) 3.5710784307033987 absolute error 1.1546319456101628e-14 relative error 3.2332864371806516e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6999999999999236 y[1] (closed_form) 3.571155505704475 y[1] (numeric) 3.571155505704486 absolute error 1.1102230246251565e-14 relative error 3.1088621675861325e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7099999999999225 y[1] (closed_form) 3.571245465047622 y[1] (numeric) 3.571245465047634 absolute error 1.199040866595169e-14 relative error 3.3574865640863474e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7199999999999214 y[1] (closed_form) 3.5713492997286354 y[1] (numeric) 3.571349299728648 absolute error 1.2434497875801753e-14 relative error 3.4817366861165255e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7299999999999203 y[1] (closed_form) 3.571467999355801 y[1] (numeric) 3.5714679993558143 absolute error 1.3322676295501878e-14 relative error 3.730308180811067e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7399999999999192 y[1] (closed_form) 3.571602552050922 y[1] (numeric) 3.571602552050935 absolute error 1.3322676295501878e-14 relative error 3.730167649211583e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.749999999999918 y[1] (closed_form) 3.5717539443505064 y[1] (numeric) 3.5717539443505197 absolute error 1.3322676295501878e-14 relative error 3.730009542391503e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.759999999999917 y[1] (closed_form) 3.5719231611071187 y[1] (numeric) 3.571923161107131 absolute error 1.2434497875801753e-14 relative error 3.4811773140012554e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7699999999999159 y[1] (closed_form) 3.5721111853908893 y[1] (numeric) 3.5721111853909027 absolute error 1.3322676295501878e-14 relative error 3.729636510192782e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7799999999999148 y[1] (closed_form) 3.5723189983912143 y[1] (numeric) 3.5723189983912276 absolute error 1.3322676295501878e-14 relative error 3.7294195455393865e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7899999999999137 y[1] (closed_form) 3.572547579318633 y[1] (numeric) 3.572547579318646 absolute error 1.2878587085651816e-14 relative error 3.604874896615949e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7999999999999126 y[1] (closed_form) 3.5727979053069108 y[1] (numeric) 3.5727979053069236 absolute error 1.2878587085651816e-14 relative error 3.604622323172102e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8099999999999115 y[1] (closed_form) 3.573070951315323 y[1] (numeric) 3.573070951315336 absolute error 1.2878587085651816e-14 relative error 3.604346866079146e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8199999999999104 y[1] (closed_form) 3.573367690031163 y[1] (numeric) 3.573367690031176 absolute error 1.2878587085651816e-14 relative error 3.604047554798231e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8299999999999093 y[1] (closed_form) 3.5736890917724744 y[1] (numeric) 3.5736890917724877 absolute error 1.3322676295501878e-14 relative error 3.727989747673912e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8399999999999082 y[1] (closed_form) 3.574036124391016 y[1] (numeric) 3.5740361243910295 absolute error 1.3322676295501878e-14 relative error 3.7276277664294574e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.849999999999907 y[1] (closed_form) 3.5744097531754835 y[1] (numeric) 3.574409753175496 absolute error 1.2434497875801753e-14 relative error 3.4787555804857074e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.859999999999906 y[1] (closed_form) 3.5748109407549755 y[1] (numeric) 3.574810940754987 absolute error 1.1546319456101628e-14 relative error 3.22991051763513e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8699999999999048 y[1] (closed_form) 3.575240647002735 y[1] (numeric) 3.5752406470027465 absolute error 1.1546319456101628e-14 relative error 3.229522316429626e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8799999999999037 y[1] (closed_form) 3.575699828940162 y[1] (numeric) 3.5756998289401736 absolute error 1.1546319456101628e-14 relative error 3.2291075896949547e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8899999999999026 y[1] (closed_form) 3.5761894406411128 y[1] (numeric) 3.5761894406411248 absolute error 1.199040866595169e-14 relative error 3.352844938718386e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8999999999999015 y[1] (closed_form) 3.5767104331364914 y[1] (numeric) 3.576710433136504 absolute error 1.2434497875801753e-14 relative error 3.476517908914892e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9099999999999004 y[1] (closed_form) 3.577263754319149 y[1] (numeric) 3.5772637543191617 absolute error 1.2878587085651816e-14 relative error 3.6001223197764916e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9199999999998993 y[1] (closed_form) 3.577850348849096 y[1] (numeric) 3.577850348849109 absolute error 1.2878587085651816e-14 relative error 3.5995320737197773e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9299999999998982 y[1] (closed_form) 3.578471158059034 y[1] (numeric) 3.5784711580590467 absolute error 1.2878587085651816e-14 relative error 3.5989076107678267e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9399999999998971 y[1] (closed_form) 3.579127119860226 y[1] (numeric) 3.579127119860239 absolute error 1.2878587085651816e-14 relative error 3.5982480237122053e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.949999999999896 y[1] (closed_form) 3.5798191686487058 y[1] (numeric) 3.579819168648719 absolute error 1.3322676295501878e-14 relative error 3.721605943724488e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.959999999999895 y[1] (closed_form) 3.580548235211838 y[1] (numeric) 3.5805482352118516 absolute error 1.3766765505351941e-14 relative error 3.8448764270138233e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9699999999998938 y[1] (closed_form) 3.5813152466352394 y[1] (numeric) 3.5813152466352536 absolute error 1.4210854715202004e-14 relative error 3.96805467727354e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9799999999998927 y[1] (closed_form) 3.582121126210075 y[1] (numeric) 3.5821211262100894 absolute error 1.4210854715202004e-14 relative error 3.9671619731734894e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9899999999998916 y[1] (closed_form) 3.5829667933407254 y[1] (numeric) 3.5829667933407396 absolute error 1.4210854715202004e-14 relative error 3.966225626655036e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9999999999998905 y[1] (closed_form) 3.5838531634528477 y[1] (numeric) 3.5838531634528623 absolute error 1.4654943925052066e-14 relative error 4.08915858342054e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0099999999998897 y[1] (closed_form) 3.584781147901837 y[1] (numeric) 3.584781147901852 absolute error 1.509903313490213e-14 relative error 4.211981851037002e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0199999999998886 y[1] (closed_form) 3.5857516538816885 y[1] (numeric) 3.5857516538817036 absolute error 1.509903313490213e-14 relative error 4.210841851960649e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0299999999998875 y[1] (closed_form) 3.5867655843342794 y[1] (numeric) 3.586765584334295 absolute error 1.554312234475219e-14 relative error 4.333464783045494e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0399999999998863 y[1] (closed_form) 3.5878238378590757 y[1] (numeric) 3.587823837859092 absolute error 1.6431300764452317e-14 relative error 4.579740117412564e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0499999999998852 y[1] (closed_form) 3.5889273086232745 y[1] (numeric) 3.5889273086232905 absolute error 1.5987211554602254e-14 relative error 4.454593303182562e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.059999999999884 y[1] (closed_form) 3.590076886272384 y[1] (numeric) 3.5900768862724 absolute error 1.5987211554602254e-14 relative error 4.4531668989412506e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.069999999999883 y[1] (closed_form) 3.591273455841266 y[1] (numeric) 3.5912734558412813 absolute error 1.554312234475219e-14 relative error 4.3280252912712747e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.079999999999882 y[1] (closed_form) 3.592517897665626 y[1] (numeric) 3.5925178976656422 absolute error 1.6431300764452317e-14 relative error 4.573756132190511e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.089999999999881 y[1] (closed_form) 3.593811087293985 y[1] (numeric) 3.5938110872940014 absolute error 1.6431300764452317e-14 relative error 4.57211032114226e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0999999999998797 y[1] (closed_form) 3.5951538954001263 y[1] (numeric) 3.595153895400142 absolute error 1.554312234475219e-14 relative error 4.323353824891633e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1099999999998786 y[1] (closed_form) 3.5965471876960233 y[1] (numeric) 3.596547187696039 absolute error 1.554312234475219e-14 relative error 4.321678969742432e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1199999999998775 y[1] (closed_form) 3.5979918248452747 y[1] (numeric) 3.59799182484529 absolute error 1.509903313490213e-14 relative error 4.1965167987982953e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1299999999998764 y[1] (closed_form) 3.5994886623770364 y[1] (numeric) 3.5994886623770515 absolute error 1.509903313490213e-14 relative error 4.194771688746202e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1399999999998753 y[1] (closed_form) 3.601038550600469 y[1] (numeric) 3.601038550600484 absolute error 1.4654943925052066e-14 relative error 4.0696437205895425e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1499999999998742 y[1] (closed_form) 3.6026423345197083 y[1] (numeric) 3.6026423345197225 absolute error 1.4210854715202004e-14 relative error 3.9445644045862647e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.159999999999873 y[1] (closed_form) 3.604300853749366 y[1] (numeric) 3.6043008537493804 absolute error 1.4210854715202004e-14 relative error 3.942749313065582e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.169999999999872 y[1] (closed_form) 3.6060149424305674 y[1] (numeric) 3.606014942430582 absolute error 1.4654943925052066e-14 relative error 4.064027509318687e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.179999999999871 y[1] (closed_form) 3.60778542914754 y[1] (numeric) 3.6077854291475537 absolute error 1.3766765505351941e-14 relative error 3.8158493002741574e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.18999999999987 y[1] (closed_form) 3.6096131368447537 y[1] (numeric) 3.609613136844768 absolute error 1.4210854715202004e-14 relative error 3.9369467520344966e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1999999999998687 y[1] (closed_form) 3.611498882744629 y[1] (numeric) 3.6114988827446433 absolute error 1.4210854715202004e-14 relative error 3.934891073371228e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2099999999998676 y[1] (closed_form) 3.613443478265814 y[1] (numeric) 3.6134434782658276 absolute error 1.3766765505351941e-14 relative error 3.809874317436113e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2199999999998665 y[1] (closed_form) 3.6154477289420432 y[1] (numeric) 3.6154477289420575 absolute error 1.4210854715202004e-14 relative error 3.9305933263652526e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2299999999998654 y[1] (closed_form) 3.6175124343415868 y[1] (numeric) 3.617512434341601 absolute error 1.4210854715202004e-14 relative error 3.928349929165753e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2399999999998643 y[1] (closed_form) 3.6196383879872913 y[1] (numeric) 3.6196383879873055 absolute error 1.4210854715202004e-14 relative error 3.926042657289858e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.249999999999863 y[1] (closed_form) 3.6218263772772303 y[1] (numeric) 3.6218263772772454 absolute error 1.509903313490213e-14 relative error 4.1689003177046505e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.259999999999862 y[1] (closed_form) 3.6240771834059657 y[1] (numeric) 3.6240771834059813 absolute error 1.554312234475219e-14 relative error 4.2888497010829436e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.269999999999861 y[1] (closed_form) 3.626391581286427 y[1] (numeric) 3.6263915812864425 absolute error 1.554312234475219e-14 relative error 4.286112516078151e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.27999999999986 y[1] (closed_form) 3.6287703394724207 y[1] (numeric) 3.6287703394724367 absolute error 1.5987211554602254e-14 relative error 4.405682933609571e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.289999999999859 y[1] (closed_form) 3.631214220081777 y[1] (numeric) 3.6312142200817936 absolute error 1.6431300764452317e-14 relative error 4.5250155371120663e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2999999999998577 y[1] (closed_form) 3.6337239787201394 y[1] (numeric) 3.6337239787201567 absolute error 1.7319479184152442e-14 relative error 4.766316672807015e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3099999999998566 y[1] (closed_form) 3.6363003644054017 y[1] (numeric) 3.636300364405419 absolute error 1.7319479184152442e-14 relative error 4.762939649784535e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3199999999998555 y[1] (closed_form) 3.638944119492809 y[1] (numeric) 3.638944119492826 absolute error 1.687538997430238e-14 relative error 4.637441362153824e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3299999999998544 y[1] (closed_form) 3.6416559796007215 y[1] (numeric) 3.6416559796007393 absolute error 1.7763568394002505e-14 relative error 4.877882066155556e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3399999999998533 y[1] (closed_form) 3.6444366735370566 y[1] (numeric) 3.6444366735370743 absolute error 1.7763568394002505e-14 relative error 4.874160257190674e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.349999999999852 y[1] (closed_form) 3.6472869232264036 y[1] (numeric) 3.6472869232264227 absolute error 1.9095836023552692e-14 relative error 5.235627584423889e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.359999999999851 y[1] (closed_form) 3.6502074436378353 y[1] (numeric) 3.650207443637855 absolute error 1.9539925233402755e-14 relative error 5.353099936131043e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.36999999999985 y[1] (closed_form) 3.653198942713412 y[1] (numeric) 3.653198942713431 absolute error 1.9095836023552692e-14 relative error 5.227154700031e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.379999999999849 y[1] (closed_form) 3.6562621212973845 y[1] (numeric) 3.656262121297404 absolute error 1.9539925233402755e-14 relative error 5.344235337938306e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.389999999999848 y[1] (closed_form) 3.6593976730661146 y[1] (numeric) 3.659397673066134 absolute error 1.9539925233402755e-14 relative error 5.339656134456345e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3999999999998467 y[1] (closed_form) 3.662606284458705 y[1] (numeric) 3.662606284458725 absolute error 1.9984014443252818e-14 relative error 5.45622785830125e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4099999999998456 y[1] (closed_form) 3.6658886346083563 y[1] (numeric) 3.6658886346083768 absolute error 2.042810365310288e-14 relative error 5.572483424686824e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4199999999998445 y[1] (closed_form) 3.6692453952744564 y[1] (numeric) 3.6692453952744772 absolute error 2.0872192862952943e-14 relative error 5.688415631681054e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4299999999998434 y[1] (closed_form) 3.672677230775402 y[1] (numeric) 3.672677230775423 absolute error 2.0872192862952943e-14 relative error 5.683100243074248e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4399999999998423 y[1] (closed_form) 3.6761847979221702 y[1] (numeric) 3.6761847979221915 absolute error 2.1316282072803006e-14 relative error 5.798479468401931e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.449999999999841 y[1] (closed_form) 3.679768745952635 y[1] (numeric) 3.6797687459526576 absolute error 2.2648549702353193e-14 relative error 6.154883979397959e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.45999999999984 y[1] (closed_form) 3.6834297164666476 y[1] (numeric) 3.68342971646667 absolute error 2.220446049250313e-14 relative error 6.028202572520617e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.469999999999839 y[1] (closed_form) 3.687168343361874 y[1] (numeric) 3.687168343361896 absolute error 2.220446049250313e-14 relative error 6.022090239649222e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.479999999999838 y[1] (closed_form) 3.6909852527704063 y[1] (numeric) 3.6909852527704285 absolute error 2.220446049250313e-14 relative error 6.015862695695343e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.489999999999837 y[1] (closed_form) 3.6948810629961515 y[1] (numeric) 3.694881062996174 absolute error 2.2648549702353193e-14 relative error 6.129710081652169e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4999999999998357 y[1] (closed_form) 3.6988563844530002 y[1] (numeric) 3.6988563844530233 absolute error 2.3092638912203256e-14 relative error 6.243183436173956e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5099999999998346 y[1] (closed_form) 3.702911819603786 y[1] (numeric) 3.702911819603809 absolute error 2.3092638912203256e-14 relative error 6.236345891346174e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5199999999998335 y[1] (closed_form) 3.7070479629000403 y[1] (numeric) 3.707047962900064 absolute error 2.353672812205332e-14 relative error 6.34918359773269e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5299999999998324 y[1] (closed_form) 3.7112654007225467 y[1] (numeric) 3.7112654007225707 absolute error 2.398081733190338e-14 relative error 6.461628243357253e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5399999999998313 y[1] (closed_form) 3.7155647113227044 y[1] (numeric) 3.7155647113227293 absolute error 2.4868995751603507e-14 relative error 6.693194085899903e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.54999999999983 y[1] (closed_form) 3.7199464647647025 y[1] (numeric) 3.7199464647647282 absolute error 2.5757174171303632e-14 relative error 6.924071197065695e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.559999999999829 y[1] (closed_form) 3.7244112228685156 y[1] (numeric) 3.7244112228685418 absolute error 2.6201263381153694e-14 relative error 7.035008169955428e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.569999999999828 y[1] (closed_form) 3.7289595391537196 y[1] (numeric) 3.7289595391537462 absolute error 2.6645352591003757e-14 relative error 7.145519363036819e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.579999999999827 y[1] (closed_form) 3.7335919587841433 y[1] (numeric) 3.7335919587841713 absolute error 2.7977620220553945e-14 relative error 7.493486307396309e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5899999999998258 y[1] (closed_form) 3.7383090185133514 y[1] (numeric) 3.7383090185133803 absolute error 2.886579864025407e-14 relative error 7.721619185920966e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5999999999998247 y[1] (closed_form) 3.743111246630968 y[1] (numeric) 3.743111246630997 absolute error 2.886579864025407e-14 relative error 7.711712727276026e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6099999999998236 y[1] (closed_form) 3.7479991629098492 y[1] (numeric) 3.747999162909879 absolute error 2.9753977059954195e-14 relative error 7.938629590529038e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6199999999998225 y[1] (closed_form) 3.7529732785541086 y[1] (numeric) 3.7529732785541388 absolute error 3.019806626980426e-14 relative error 8.04643785831551e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6299999999998214 y[1] (closed_form) 3.758034096147992 y[1] (numeric) 3.7580340961480236 absolute error 3.1530333899354446e-14 relative error 8.390113844808707e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6399999999998203 y[1] (closed_form) 3.7631821096056255 y[1] (numeric) 3.7631821096056575 absolute error 3.197442310920451e-14 relative error 8.496645173665371e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.649999999999819 y[1] (closed_form) 3.7684178041216185 y[1] (numeric) 3.768417804121652 absolute error 3.3306690738754696e-14 relative error 8.838375273125577e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.659999999999818 y[1] (closed_form) 3.7737416561225503 y[1] (numeric) 3.773741656122584 absolute error 3.375077994860476e-14 relative error 8.943585179935995e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.669999999999817 y[1] (closed_form) 3.7791541332193237 y[1] (numeric) 3.779154133219358 absolute error 3.419486915845482e-14 relative error 9.048286455923262e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.679999999999816 y[1] (closed_form) 3.784655694160406 y[1] (numeric) 3.7846556941604406 absolute error 3.4638958368304884e-14 relative error 9.152472818531845e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6899999999998148 y[1] (closed_form) 3.790246788785954 y[1] (numeric) 3.7902467887859896 absolute error 3.552713678800501e-14 relative error 9.373304369815093e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6999999999998137 y[1] (closed_form) 3.795927857982832 y[1] (numeric) 3.795927857982868 absolute error 3.597122599785507e-14 relative error 9.476267027100535e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7099999999998126 y[1] (closed_form) 3.8016993336405207 y[1] (numeric) 3.801699333640558 absolute error 3.730349362740526e-14 relative error 9.812320847499347e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7199999999998115 y[1] (closed_form) 3.8075616386079307 y[1] (numeric) 3.8075616386079685 absolute error 3.774758283725532e-14 relative error 9.913846818526116e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7299999999998104 y[1] (closed_form) 3.813515186651117 y[1] (numeric) 3.813515186651155 absolute error 3.8191672047105385e-14 relative error 1.0014821018883591e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7399999999998093 y[1] (closed_form) 3.819560382411903 y[1] (numeric) 3.8195603824119417 absolute error 3.863576125695545e-14 relative error 1.011523772077625e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.749999999999808 y[1] (closed_form) 3.825697621367418 y[1] (numeric) 3.825697621367458 absolute error 3.9968028886505635e-14 relative error 1.0447252460119908e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.759999999999807 y[1] (closed_form) 3.831927289790546 y[1] (numeric) 3.831927289790587 absolute error 4.085620730620576e-14 relative error 1.0662051812689529e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.769999999999806 y[1] (closed_form) 3.8382497647113043 y[1] (numeric) 3.838249764711346 absolute error 4.1744385725905886e-14 relative error 1.087589090988864e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.779999999999805 y[1] (closed_form) 3.844665413879135 y[1] (numeric) 3.844665413879177 absolute error 4.218847493575595e-14 relative error 1.097325004757416e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7899999999998037 y[1] (closed_form) 3.851174595726135 y[1] (numeric) 3.851174595726178 absolute error 4.3076653355456074e-14 relative error 1.1185328601632514e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7999999999998026 y[1] (closed_form) 3.8577776593312105 y[1] (numeric) 3.8577776593312536 absolute error 4.3076653355456074e-14 relative error 1.1166183528296936e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8099999999998015 y[1] (closed_form) 3.8644749443851705 y[1] (numeric) 3.864474944385214 absolute error 4.3520742565306136e-14 relative error 1.1261747893731056e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8199999999998004 y[1] (closed_form) 3.8712667811567565 y[1] (numeric) 3.8712667811568013 absolute error 4.4853010194856324e-14 relative error 1.1586132584087628e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8299999999997993 y[1] (closed_form) 3.8781534904596184 y[1] (numeric) 3.878153490459664 absolute error 4.574118861455645e-14 relative error 1.1794579231348433e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8399999999997982 y[1] (closed_form) 3.8851353836202316 y[1] (numeric) 3.885135383620278 absolute error 4.6629367034256575e-14 relative error 1.2001992834238527e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.849999999999797 y[1] (closed_form) 3.892212762446765 y[1] (numeric) 3.8922127624468126 absolute error 4.75175454539567e-14 relative error 1.2208362788494045e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.859999999999796 y[1] (closed_form) 3.8993859191989007 y[1] (numeric) 3.899385919198949 absolute error 4.8405723873656825e-14 relative error 1.2413678686002286e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.869999999999795 y[1] (closed_form) 3.906655136558607 y[1] (numeric) 3.9066551365586566 absolute error 4.973799150320701e-14 relative error 1.273160536689232e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.879999999999794 y[1] (closed_form) 3.914020687601872 y[1] (numeric) 3.9140206876019223 absolute error 5.0182080713057076e-14 relative error 1.282110768397694e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8899999999997927 y[1] (closed_form) 3.921482835771398 y[1] (numeric) 3.921482835771448 absolute error 5.0182080713057076e-14 relative error 1.2796710533908461e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8999999999997916 y[1] (closed_form) 3.929041834850251 y[1] (numeric) 3.929041834850302 absolute error 5.10702591327572e-14 relative error 1.2998145929566988e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9099999999997905 y[1] (closed_form) 3.93669792893649 y[1] (numeric) 3.936697928936542 absolute error 5.1958437552457326e-14 relative error 1.319848220269571e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9199999999997894 y[1] (closed_form) 3.9444513524187528 y[1] (numeric) 3.944451352418806 absolute error 5.3290705182007514e-14 relative error 1.3510295962790731e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9299999999997883 y[1] (closed_form) 3.9523023299528197 y[1] (numeric) 3.952302329952874 absolute error 5.417888360170764e-14 relative error 1.3708182997821018e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9399999999997872 y[1] (closed_form) 3.9602510764391456 y[1] (numeric) 3.9602510764392007 absolute error 5.5067062021407764e-14 relative error 1.3904942125770783e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.949999999999786 y[1] (closed_form) 3.968297797001373 y[1] (numeric) 3.968297797001429 absolute error 5.595524044110789e-14 relative error 1.41005648526152e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.959999999999785 y[1] (closed_form) 3.9764426869658176 y[1] (numeric) 3.976442686965874 absolute error 5.639932965095795e-14 relative error 1.4183362892624227e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.969999999999784 y[1] (closed_form) 3.984685931841937 y[1] (numeric) 3.984685931841995 absolute error 5.773159728050814e-14 relative error 1.4488368284980863e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.979999999999783 y[1] (closed_form) 3.99302770730378 y[1] (numeric) 3.9930277073038387 absolute error 5.861977570020827e-14 relative error 1.4680533168599075e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9899999999997817 y[1] (closed_form) 4.001468179172418 y[1] (numeric) 4.001468179172478 absolute error 5.950795411990839e-14 relative error 1.4871530012320577e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9999999999997806 y[1] (closed_form) 4.0100075033993665 y[1] (numeric) 4.010007503399426 absolute error 5.950795411990839e-14 relative error 1.483986104002605e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0099999999997795 y[1] (closed_form) 4.0186458260509825 y[1] (numeric) 4.018645826051043 absolute error 6.039613253960852e-14 relative error 1.5028976215840898e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0199999999997784 y[1] (closed_form) 4.027383283293869 y[1] (numeric) 4.027383283293931 absolute error 6.217248937900877e-14 relative error 1.5437440393842988e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0299999999997773 y[1] (closed_form) 4.036220001381246 y[1] (numeric) 4.03622000138131 absolute error 6.394884621840902e-14 relative error 1.584374642525058e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.039999999999776 y[1] (closed_form) 4.04515609664034 y[1] (numeric) 4.0451560966404045 absolute error 6.483702463810914e-14 relative error 1.602831215634888e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.049999999999775 y[1] (closed_form) 4.054191675460734 y[1] (numeric) 4.054191675460801 absolute error 6.750155989720952e-14 relative error 1.664981956965278e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.059999999999774 y[1] (closed_form) 4.063326834283746 y[1] (numeric) 4.063326834283814 absolute error 6.750155989720952e-14 relative error 1.6612387496785797e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.069999999999773 y[1] (closed_form) 4.07256165959277 y[1] (numeric) 4.0725616595928384 absolute error 6.838973831690964e-14 relative error 1.6792806109103374e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.079999999999772 y[1] (closed_form) 4.0818962279046405 y[1] (numeric) 4.081896227904709 absolute error 6.838973831690964e-14 relative error 1.6754403957989922e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0899999999997707 y[1] (closed_form) 4.091330605761969 y[1] (numeric) 4.09133060576204 absolute error 7.105427357601002e-14 relative error 1.7367032983338407e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0999999999997696 y[1] (closed_form) 4.1008648497264995 y[1] (numeric) 4.100864849726572 absolute error 7.283063041541027e-14 relative error 1.7759822155628365e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1099999999997685 y[1] (closed_form) 4.110499006373448 y[1] (numeric) 4.110499006373521 absolute error 7.283063041541027e-14 relative error 1.7718196818071056e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1199999999997674 y[1] (closed_form) 4.120233112286844 y[1] (numeric) 4.120233112286917 absolute error 7.37188088351104e-14 relative error 1.7891902430295846e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1299999999997663 y[1] (closed_form) 4.130067194055876 y[1] (numeric) 4.1300671940559495 absolute error 7.37188088351104e-14 relative error 1.7849300113375602e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.139999999999765 y[1] (closed_form) 4.140001268272226 y[1] (numeric) 4.1400012682723 absolute error 7.460698725481052e-14 relative error 1.8021005893543302e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.149999999999764 y[1] (closed_form) 4.150035341528421 y[1] (numeric) 4.150035341528494 absolute error 7.37188088351104e-14 relative error 1.7763417120192625e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.159999999999763 y[1] (closed_form) 4.1601694104171605 y[1] (numeric) 4.160169410417235 absolute error 7.460698725481052e-14 relative error 1.7933641612765311e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.169999999999762 y[1] (closed_form) 4.170403461531669 y[1] (numeric) 4.170403461531745 absolute error 7.549516567451064e-14 relative error 1.8102604788934124e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.179999999999761 y[1] (closed_form) 4.1807374714670305 y[1] (numeric) 4.180737471467107 absolute error 7.638334409421077e-14 relative error 1.8270303891482494e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1899999999997597 y[1] (closed_form) 4.191171406822529 y[1] (numeric) 4.191171406822606 absolute error 7.638334409421077e-14 relative error 1.822481990831284e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1999999999997586 y[1] (closed_form) 4.201705224204991 y[1] (numeric) 4.201705224205069 absolute error 7.815970093361102e-14 relative error 1.8601900124585654e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2099999999997575 y[1] (closed_form) 4.212338870233124 y[1] (numeric) 4.212338870233201 absolute error 7.72715225139109e-14 relative error 1.834408980245088e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2199999999997564 y[1] (closed_form) 4.2230722815428505 y[1] (numeric) 4.223072281542929 absolute error 7.815970093361102e-14 relative error 1.8507781947093808e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2299999999997553 y[1] (closed_form) 4.233905384793653 y[1] (numeric) 4.233905384793732 absolute error 7.904787935331115e-14 relative error 1.8670204496590018e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.239999999999754 y[1] (closed_form) 4.2448380966759 y[1] (numeric) 4.244838096675981 absolute error 8.08242361927114e-14 relative error 1.904059338706092e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.249999999999753 y[1] (closed_form) 4.25587032391918 y[1] (numeric) 4.255870323919262 absolute error 8.171241461241152e-14 relative error 1.919993054139007e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.259999999999752 y[1] (closed_form) 4.26700196330163 y[1] (numeric) 4.2670019633017136 absolute error 8.348877145181177e-14 relative error 1.956614320074313e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.269999999999751 y[1] (closed_form) 4.278232901660254 y[1] (numeric) 4.278232901660338 absolute error 8.43769498715119e-14 relative error 1.9722383472570585e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.27999999999975 y[1] (closed_form) 4.289563015902242 y[1] (numeric) 4.289563015902328 absolute error 8.526512829121202e-14 relative error 1.9877346008233855e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2899999999997487 y[1] (closed_form) 4.300992173017279 y[1] (numeric) 4.300992173017366 absolute error 8.704148513061227e-14 relative error 2.0237536277484084e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2999999999997476 y[1] (closed_form) 4.312520230090843 y[1] (numeric) 4.312520230090931 absolute error 8.79296635503124e-14 relative error 2.038939155271166e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3099999999997465 y[1] (closed_form) 4.324147034318501 y[1] (numeric) 4.32414703431859 absolute error 8.881784197001252e-14 relative error 2.0539968059622303e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3199999999997454 y[1] (closed_form) 4.335872423021186 y[1] (numeric) 4.335872423021276 absolute error 8.970602038971265e-14 relative error 2.0689266573762917e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3299999999997443 y[1] (closed_form) 4.3476962236614645 y[1] (numeric) 4.347696223661556 absolute error 9.14823772291129e-14 relative error 2.104157524420368e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.339999999999743 y[1] (closed_form) 4.359618253860794 y[1] (numeric) 4.359618253860886 absolute error 9.237055564881302e-14 relative error 2.118776238424349e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.349999999999742 y[1] (closed_form) 4.3716383214177545 y[1] (numeric) 4.371638321417847 absolute error 9.237055564881302e-14 relative error 2.1129505429638693e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.359999999999741 y[1] (closed_form) 4.383756224327275 y[1] (numeric) 4.383756224327368 absolute error 9.325873406851315e-14 relative error 2.1273704397836242e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.36999999999974 y[1] (closed_form) 4.395971750800829 y[1] (numeric) 4.395971750800922 absolute error 9.325873406851315e-14 relative error 2.121458902722109e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3799999999997388 y[1] (closed_form) 4.408284679287615 y[1] (numeric) 4.40828467928771 absolute error 9.50350909079134e-14 relative error 2.155829258360674e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3899999999997377 y[1] (closed_form) 4.4206947784967126 y[1] (numeric) 4.420694778496808 absolute error 9.50350909079134e-14 relative error 2.1497772560590743e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3999999999997366 y[1] (closed_form) 4.433201807420208 y[1] (numeric) 4.433201807420305 absolute error 9.681144774731365e-14 relative error 2.183781653821229e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4099999999997355 y[1] (closed_form) 4.4458055153573 y[1] (numeric) 4.445805515357398 absolute error 9.769962616701378e-14 relative error 2.19756860324921e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4199999999997344 y[1] (closed_form) 4.458505641939363 y[1] (numeric) 4.45850564193946 absolute error 9.769962616701378e-14 relative error 2.1913087929729823e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4299999999997333 y[1] (closed_form) 4.471301917155989 y[1] (numeric) 4.4713019171560875 absolute error 9.85878045867139e-14 relative error 2.2049015345718712e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.439999999999732 y[1] (closed_form) 4.484194061381987 y[1] (numeric) 4.484194061382086 absolute error 9.85878045867139e-14 relative error 2.198562400226052e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.449999999999731 y[1] (closed_form) 4.497181785405345 y[1] (numeric) 4.497181785405445 absolute error 1.0036416142611415e-13 relative error 2.2317123526521625e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.45999999999973 y[1] (closed_form) 4.51026479045615 y[1] (numeric) 4.510264790456252 absolute error 1.021405182655144e-13 relative error 2.26462354231722e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.469999999999729 y[1] (closed_form) 4.523442768236465 y[1] (numeric) 4.523442768236569 absolute error 1.0391687510491465e-13 relative error 2.2972961177848235e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4799999999997278 y[1] (closed_form) 4.536715400951161 y[1] (numeric) 4.536715400951265 absolute error 1.0391687510491465e-13 relative error 2.2905751390781004e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4899999999997267 y[1] (closed_form) 4.550082361339696 y[1] (numeric) 4.5500823613398005 absolute error 1.0480505352461478e-13 relative error 2.3033660756364128e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4999999999997256 y[1] (closed_form) 4.563543312708833 y[1] (numeric) 4.56354331270894 absolute error 1.0658141036401503e-13 relative error 2.3354968510367947e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5099999999997245 y[1] (closed_form) 4.577097908966321 y[1] (numeric) 4.57709790896643 absolute error 1.092459456231154e-13 relative error 2.3867950346683146e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5199999999997234 y[1] (closed_form) 4.590745794655498 y[1] (numeric) 4.590745794655608 absolute error 1.1013412404281553e-13 relative error 2.399046450601395e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5299999999997222 y[1] (closed_form) 4.604486604990832 y[1] (numeric) 4.604486604990943 absolute error 1.1102230246251565e-13 relative error 2.4111765759548062e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.539999999999721 y[1] (closed_form) 4.618319965894409 y[1] (numeric) 4.618319965894522 absolute error 1.127986593019159e-13 relative error 2.4424175920013523e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.54999999999972 y[1] (closed_form) 4.632245494033333 y[1] (numeric) 4.632245494033447 absolute error 1.1457501614131615e-13 relative error 2.473422798703071e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.559999999999719 y[1] (closed_form) 4.6462627968580605 y[1] (numeric) 4.646262796858176 absolute error 1.1546319456101628e-13 relative error 2.4850767080823727e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.569999999999718 y[1] (closed_form) 4.660371472641656 y[1] (numeric) 4.660371472641775 absolute error 1.1901590823981678e-13 relative error 2.553785871759157e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5799999999997167 y[1] (closed_form) 4.674571110519967 y[1] (numeric) 4.674571110520087 absolute error 1.199040866595169e-13 relative error 2.565028615987395e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5899999999997156 y[1] (closed_form) 4.688861290532704 y[1] (numeric) 4.688861290532825 absolute error 1.2079226507921703e-13 relative error 2.5761535177657975e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5999999999997145 y[1] (closed_form) 4.7032415836654415 y[1] (numeric) 4.703241583665562 absolute error 1.2079226507921703e-13 relative error 2.568276856088654e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6099999999997134 y[1] (closed_form) 4.717711551892515 y[1] (numeric) 4.717711551892639 absolute error 1.234568003383174e-13 relative error 2.6168789460812325e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6199999999997123 y[1] (closed_form) 4.73227074822083 y[1] (numeric) 4.732270748220954 absolute error 1.2434497875801753e-13 relative error 2.6275964621163516e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6299999999997112 y[1] (closed_form) 4.74691871673455 y[1] (numeric) 4.746918716734675 absolute error 1.2523315717771766e-13 relative error 2.6381988959749185e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.63999999999971 y[1] (closed_form) 4.761654992640698 y[1] (numeric) 4.761654992640826 absolute error 1.2789769243681803e-13 relative error 2.6859924256269792e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.649999999999709 y[1] (closed_form) 4.77647910231563 y[1] (numeric) 4.7764791023157604 absolute error 1.305622276959184e-13 relative error 2.7334407813617784e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.659999999999708 y[1] (closed_form) 4.791390563352398 y[1] (numeric) 4.791390563352531 absolute error 1.3233858453531866e-13 relative error 2.76200787194282e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.669999999999707 y[1] (closed_form) 4.806388884608992 y[1] (numeric) 4.806388884609127 absolute error 1.3500311979441904e-13 relative error 2.808826398270138e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6799999999997057 y[1] (closed_form) 4.821473566257453 y[1] (numeric) 4.821473566257589 absolute error 1.3677947663381929e-13 relative error 2.8368811890011234e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6899999999997046 y[1] (closed_form) 4.836644099833851 y[1] (numeric) 4.836644099833989 absolute error 1.376676550535194e-13 relative error 2.846346603386604e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6999999999997035 y[1] (closed_form) 4.851899968289138 y[1] (numeric) 4.851899968289278 absolute error 1.3944401189291966e-13 relative error 2.8740083844327477e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7099999999997024 y[1] (closed_form) 4.867240646040848 y[1] (numeric) 4.86724064604099 absolute error 1.4210854715202004e-13 relative error 2.919694288541397e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7199999999997013 y[1] (closed_form) 4.882665599025658 y[1] (numeric) 4.882665599025801 absolute error 1.4299672557172016e-13 relative error 2.9286610494123402e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7299999999997 y[1] (closed_form) 4.898174284752788 y[1] (numeric) 4.898174284752932 absolute error 1.4477308241112041e-13 relative error 2.9556539640040015e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.739999999999699 y[1] (closed_form) 4.913766152358257 y[1] (numeric) 4.913766152358403 absolute error 1.4566126083082054e-13 relative error 2.964350689763971e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.749999999999698 y[1] (closed_form) 4.929440642659965 y[1] (numeric) 4.929440642660111 absolute error 1.4654943925052066e-13 relative error 2.9729425684176904e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.759999999999697 y[1] (closed_form) 4.9451971882136085 y[1] (numeric) 4.945197188213757 absolute error 1.4832579608992091e-13 relative error 2.9993909331551203e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.769999999999696 y[1] (closed_form) 4.961035213369431 y[1] (numeric) 4.961035213369582 absolute error 1.509903313490213e-13 relative error 3.0435246849713814e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7799999999996947 y[1] (closed_form) 4.976954134329782 y[1] (numeric) 4.976954134329936 absolute error 1.5365486660812167e-13 relative error 3.0873273584791332e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7899999999996936 y[1] (closed_form) 4.9929533592074975 y[1] (numeric) 4.992953359207652 absolute error 1.545430450278218e-13 relative error 3.0952230856078235e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7999999999996925 y[1] (closed_form) 5.009032288085088 y[1] (numeric) 5.009032288085245 absolute error 1.5720758028692217e-13 relative error 3.138482070895601e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8099999999996914 y[1] (closed_form) 5.025190313074733 y[1] (numeric) 5.025190313074891 absolute error 1.580957587066223e-13 relative error 3.146065101162093e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8199999999996903 y[1] (closed_form) 5.041426818379064 y[1] (numeric) 5.041426818379225 absolute error 1.616484723854228e-13 relative error 3.2064032308495664e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.829999999999689 y[1] (closed_form) 5.057741180352748 y[1] (numeric) 5.057741180352911 absolute error 1.6342482922482304e-13 relative error 3.231182130466888e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.839999999999688 y[1] (closed_form) 5.07413276756485 y[1] (numeric) 5.074132767565016 absolute error 1.652011860642233e-13 relative error 3.255752137985655e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.849999999999687 y[1] (closed_form) 5.090600940861975 y[1] (numeric) 5.090600940862142 absolute error 1.6697754290362354e-13 relative error 3.280114564928945e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.859999999999686 y[1] (closed_form) 5.107145053432184 y[1] (numeric) 5.107145053432352 absolute error 1.6786572132332367e-13 relative error 3.286879843181895e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.869999999999685 y[1] (closed_form) 5.123764450869672 y[1] (numeric) 5.123764450869843 absolute error 1.7141843500212417e-13 relative error 3.345556507247885e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8799999999996837 y[1] (closed_form) 5.140458471240212 y[1] (numeric) 5.140458471240384 absolute error 1.723066134218243e-13 relative error 3.351969758842401e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8899999999996826 y[1] (closed_form) 5.157226445147346 y[1] (numeric) 5.157226445147519 absolute error 1.7319479184152442e-13 relative error 3.3582933323490338e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8999999999996815 y[1] (closed_form) 5.174067695799322 y[1] (numeric) 5.174067695799497 absolute error 1.7497114868092467e-13 relative error 3.3816942291454507e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9099999999996804 y[1] (closed_form) 5.190981539076777 y[1] (numeric) 5.1909815390769545 absolute error 1.7763568394002505e-13 relative error 3.422005695894226e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9199999999996793 y[1] (closed_form) 5.207967283601144 y[1] (numeric) 5.207967283601323 absolute error 1.7852386235972517e-13 relative error 3.4278990753621167e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.929999999999678 y[1] (closed_form) 5.225024230803792 y[1] (numeric) 5.225024230803973 absolute error 1.8030021919912542e-13 relative error 3.4507058959875658e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.939999999999677 y[1] (closed_form) 5.242151674995882 y[1] (numeric) 5.242151674996065 absolute error 1.829647544582258e-13 relative error 3.4902605991149527e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.949999999999676 y[1] (closed_form) 5.259348903438934 y[1] (numeric) 5.25934890343912 absolute error 1.865174681370263e-13 relative error 3.546398452764144e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.959999999999675 y[1] (closed_form) 5.276615196416101 y[1] (numeric) 5.276615196416289 absolute error 1.8829382497642655e-13 relative error 3.5684585281927797e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.969999999999674 y[1] (closed_form) 5.293949827304141 y[1] (numeric) 5.293949827304331 absolute error 1.900701818158268e-13 relative error 3.590328356259035e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9799999999996727 y[1] (closed_form) 5.311352062646078 y[1] (numeric) 5.311352062646269 absolute error 1.9095836023552692e-13 relative error 3.5952871883320953e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9899999999996716 y[1] (closed_form) 5.328821162224545 y[1] (numeric) 5.328821162224739 absolute error 1.936228954946273e-13 relative error 3.6335033509324673e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9999999999996705 y[1] (closed_form) 5.346356379135809 y[1] (numeric) 5.346356379136005 absolute error 1.9628743075372768e-13 relative error 3.671424365194596e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.009999999999674 y[1] (closed_form) 5.363956959864466 y[1] (numeric) 5.363956959864656 absolute error 1.900701818158268e-13 relative error 3.5434695549948895e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.019999999999677 y[1] (closed_form) 5.3816221443587695 y[1] (numeric) 5.381622144358954 absolute error 1.8474111129762605e-13 relative error 3.4328146113208456e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.0299999999996805 y[1] (closed_form) 5.399351166106657 y[1] (numeric) 5.399351166106835 absolute error 1.7852386235972517e-13 relative error 3.3063947290625008e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.039999999999684 y[1] (closed_form) 5.417143252212395 y[1] (numeric) 5.417143252212567 absolute error 1.7141843500212417e-13 relative error 3.1643696136725903e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.049999999999687 y[1] (closed_form) 5.434997623473866 y[1] (numeric) 5.434997623474032 absolute error 1.652011860642233e-13 relative error 3.039581569469616e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.0599999999996905 y[1] (closed_form) 5.45291349446049 y[1] (numeric) 5.452913494460648 absolute error 1.580957587066223e-13 relative error 2.8992896892134587e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.069999999999694 y[1] (closed_form) 5.470890073591764 y[1] (numeric) 5.4708900735919155 absolute error 1.5187850976872141e-13 relative error 2.7761206627390654e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.079999999999697 y[1] (closed_form) 5.488926563216421 y[1] (numeric) 5.488926563216568 absolute error 1.4654943925052066e-13 relative error 2.6699107295879923e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.0899999999997005 y[1] (closed_form) 5.507022159692198 y[1] (numeric) 5.5070221596923385 absolute error 1.4033219031261979e-13 relative error 2.5482408866948037e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.099999999999704 y[1] (closed_form) 5.5251760534661924 y[1] (numeric) 5.5251760534663275 absolute error 1.3500311979441904e-13 relative error 2.4434175216864896e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.109999999999707 y[1] (closed_form) 5.543387429155822 y[1] (numeric) 5.543387429155952 absolute error 1.2967404927621828e-13 relative error 2.3392564732926445e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.119999999999711 y[1] (closed_form) 5.56165546563036 y[1] (numeric) 5.561655465630484 absolute error 1.2434497875801753e-13 relative error 2.235754795068454e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.129999999999714 y[1] (closed_form) 5.57997933609305 y[1] (numeric) 5.579979336093168 absolute error 1.1812772982011666e-13 relative error 2.1169922450434465e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.139999999999717 y[1] (closed_form) 5.5983582081637815 y[1] (numeric) 5.5983582081638925 absolute error 1.1102230246251565e-13 relative error 1.983122521538866e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.149999999999721 y[1] (closed_form) 5.6167912439623295 y[1] (numeric) 5.616791243962435 absolute error 1.056932319443149e-13 relative error 1.881736873484981e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.159999999999724 y[1] (closed_form) 5.6352776001921425 y[1] (numeric) 5.635277600192241 absolute error 9.85878045867139e-14 relative error 1.7494755641381787e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.169999999999727 y[1] (closed_form) 5.653816428224669 y[1] (numeric) 5.6538164282247605 absolute error 9.14823772291129e-14 relative error 1.618064158794043e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.179999999999731 y[1] (closed_form) 5.6724068741842215 y[1] (numeric) 5.672406874184307 absolute error 8.526512829121202e-14 relative error 1.5031560708253047e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.189999999999734 y[1] (closed_form) 5.691048079033362 y[1] (numeric) 5.6910480790334415 absolute error 7.904787935331115e-14 relative error 1.388986321246079e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.199999999999737 y[1] (closed_form) 5.7097391786588085 y[1] (numeric) 5.7097391786588805 absolute error 7.194245199571014e-14 relative error 1.2599954173845309e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.209999999999741 y[1] (closed_form) 5.728479303957839 y[1] (numeric) 5.728479303957906 absolute error 6.661338147750939e-14 relative error 1.1628458085112715e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.219999999999744 y[1] (closed_form) 5.747267580925209 y[1] (numeric) 5.74726758092527 absolute error 6.039613253960852e-14 relative error 1.0508668978639377e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.229999999999747 y[1] (closed_form) 5.766103130740543 y[1] (numeric) 5.766103130740597 absolute error 5.417888360170764e-14 relative error 9.396100342511465e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.239999999999751 y[1] (closed_form) 5.784985069856224 y[1] (numeric) 5.784985069856271 absolute error 4.707345624410664e-14 relative error 8.137178519161946e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.249999999999754 y[1] (closed_form) 5.803912510085741 y[1] (numeric) 5.803912510085783 absolute error 4.1744385725905886e-14 relative error 7.192456063623398e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.259999999999757 y[1] (closed_form) 5.822884558692511 y[1] (numeric) 5.822884558692547 absolute error 3.552713678800501e-14 relative error 6.101295059159199e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.269999999999761 y[1] (closed_form) 5.841900318479151 y[1] (numeric) 5.841900318479181 absolute error 2.930988785010413e-14 relative error 5.01718383612107e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.279999999999764 y[1] (closed_form) 5.860958887877194 y[1] (numeric) 5.860958887877217 absolute error 2.3092638912203256e-14 relative error 3.9400786379798813e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.289999999999767 y[1] (closed_form) 5.880059361037249 y[1] (numeric) 5.880059361037266 absolute error 1.687538997430238e-14 relative error 2.8699353081574234e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.299999999999771 y[1] (closed_form) 5.899200827919586 y[1] (numeric) 5.8992008279195955 absolute error 9.769962616701378e-15 relative error 1.656150197576314e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.309999999999774 y[1] (closed_form) 5.918382374385131 y[1] (numeric) 5.918382374385135 absolute error 3.552713678800501e-15 relative error 6.002845801543191e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 4.319999999999777 y[1] (closed_form) 5.937603082286891 y[1] (numeric) 5.937603082286888 absolute error 3.552713678800501e-15 relative error 5.983413895413432e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 4.329999999999781 y[1] (closed_form) 5.956862029561759 y[1] (numeric) 5.95686202956175 absolute error 9.769962616701378e-15 relative error 1.6401190036325458e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.339999999999784 y[1] (closed_form) 5.976158290322725 y[1] (numeric) 5.976158290322707 absolute error 1.7763568394002505e-14 relative error 2.9724059389068214e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.349999999999787 y[1] (closed_form) 5.995490934951457 y[1] (numeric) 5.995490934951433 absolute error 2.398081733190338e-14 relative error 3.9998087883186075e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.359999999999791 y[1] (closed_form) 6.014859030191271 y[1] (numeric) 6.01485903019124 absolute error 3.108624468950438e-14 relative error 5.168241605242716e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.369999999999794 y[1] (closed_form) 6.03426163924045 y[1] (numeric) 6.034261639240412 absolute error 3.8191672047105385e-14 relative error 6.329137569830777e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.379999999999797 y[1] (closed_form) 6.0536978218459225 y[1] (numeric) 6.053697821845877 absolute error 4.529709940470639e-14 relative error 7.482550457216938e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.389999999999801 y[1] (closed_form) 6.073166634397293 y[1] (numeric) 6.073166634397242 absolute error 5.1514348342607263e-14 relative error 8.482287979855437e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.399999999999804 y[1] (closed_form) 6.092667130021198 y[1] (numeric) 6.092667130021139 absolute error 5.861977570020827e-14 relative error 9.62136523286548e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.409999999999807 y[1] (closed_form) 6.1121983586759905 y[1] (numeric) 6.112198358675925 absolute error 6.572520305780927e-14 relative error 1.0753120105226182e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.419999999999811 y[1] (closed_form) 6.131759367246747 y[1] (numeric) 6.1317593672466755 absolute error 7.194245199571014e-14 relative error 1.17327585260433e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.429999999999814 y[1] (closed_form) 6.151349199640581 y[1] (numeric) 6.151349199640503 absolute error 7.815970093361102e-14 relative error 1.270610696888706e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.439999999999817 y[1] (closed_form) 6.170966896882242 y[1] (numeric) 6.170966896882159 absolute error 8.348877145181177e-14 relative error 1.3529285255766452e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.449999999999821 y[1] (closed_form) 6.190611497210021 y[1] (numeric) 6.190611497209931 absolute error 9.059419880941277e-14 relative error 1.4634127638318392e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.459999999999824 y[1] (closed_form) 6.2102820361719235 y[1] (numeric) 6.210282036171826 absolute error 9.769962616701378e-14 relative error 1.5731914524648022e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.4699999999998274 y[1] (closed_form) 6.22997754672211 y[1] (numeric) 6.229977546722006 absolute error 1.0391687510491465e-13 relative error 1.6680136376990686e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.479999999999831 y[1] (closed_form) 6.249697059317607 y[1] (numeric) 6.249697059317495 absolute error 1.1191048088221578e-13 relative error 1.7906544880502589e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.489999999999834 y[1] (closed_form) 6.269439602015254 y[1] (numeric) 6.269439602015136 absolute error 1.1812772982011666e-13 relative error 1.884183233572353e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.4999999999998375 y[1] (closed_form) 6.289204200568899 y[1] (numeric) 6.289204200568774 absolute error 1.2523315717771766e-13 relative error 1.991240118525481e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.509999999999841 y[1] (closed_form) 6.308989878526825 y[1] (numeric) 6.308989878526693 absolute error 1.3233858453531866e-13 relative error 2.097619224049544e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.519999999999844 y[1] (closed_form) 6.32879565732939 y[1] (numeric) 6.328795657329252 absolute error 1.3855583347321954e-13 relative error 2.1892922599382357e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.5299999999998475 y[1] (closed_form) 6.348620556406885 y[1] (numeric) 6.348620556406743 absolute error 1.4210854715202004e-13 relative error 2.238416139213223e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.539999999999851 y[1] (closed_form) 6.368463593277593 y[1] (numeric) 6.368463593277442 absolute error 1.509903313490213e-13 relative error 2.3709067208675464e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.549999999999854 y[1] (closed_form) 6.388323783646024 y[1] (numeric) 6.388323783645867 absolute error 1.5720758028692217e-13 relative error 2.46085805308382e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.5599999999998575 y[1] (closed_form) 6.408200141501362 y[1] (numeric) 6.408200141501197 absolute error 1.6431300764452317e-13 relative error 2.5641054276751516e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.569999999999861 y[1] (closed_form) 6.428091679216049 y[1] (numeric) 6.428091679215878 absolute error 1.7053025658242404e-13 relative error 2.652890859254537e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.579999999999864 y[1] (closed_form) 6.447997407644559 y[1] (numeric) 6.447997407644381 absolute error 1.7763568394002505e-13 relative error 2.7548969503217435e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.5899999999998675 y[1] (closed_form) 6.467916336222302 y[1] (numeric) 6.4679163362221175 absolute error 1.8474111129762605e-13 relative error 2.856269340761561e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.599999999999871 y[1] (closed_form) 6.487847473064688 y[1] (numeric) 6.487847473064494 absolute error 1.9451107391432743e-13 relative error 2.998083335372333e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.609999999999874 y[1] (closed_form) 6.507789825066307 y[1] (numeric) 6.507789825066106 absolute error 2.007283228522283e-13 relative error 3.0844315543055067e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.6199999999998775 y[1] (closed_form) 6.527742398000244 y[1] (numeric) 6.527742398000036 absolute error 2.078337502098293e-13 relative error 3.1838534295332886e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.629999999999881 y[1] (closed_form) 6.5477041966175 y[1] (numeric) 6.5477041966172855 absolute error 2.1405099914773018e-13 relative error 3.269100019183938e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.639999999999884 y[1] (closed_form) 6.567674224746515 y[1] (numeric) 6.567674224746293 absolute error 2.220446049250313e-13 relative error 3.3808711779336362e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.649999999999888 y[1] (closed_form) 6.587651485392783 y[1] (numeric) 6.587651485392555 absolute error 2.282618538629322e-13 relative error 3.464995899814549e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.659999999999891 y[1] (closed_form) 6.607634980838556 y[1] (numeric) 6.60763498083832 absolute error 2.362554596402333e-13 relative error 3.575491992601728e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.669999999999894 y[1] (closed_form) 6.627623712742607 y[1] (numeric) 6.627623712742365 absolute error 2.4158453015843406e-13 relative error 3.645115363051637e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.679999999999898 y[1] (closed_form) 6.647616682240071 y[1] (numeric) 6.647616682239822 absolute error 2.4868995751603507e-13 relative error 3.741039374012659e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.689999999999901 y[1] (closed_form) 6.667612890042324 y[1] (numeric) 6.6676128900420695 absolute error 2.5490720645393594e-13 relative error 3.82306547572107e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.699999999999904 y[1] (closed_form) 6.687611336536918 y[1] (numeric) 6.687611336536657 absolute error 2.611244553918368e-13 relative error 3.904599747973038e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.709999999999908 y[1] (closed_form) 6.7076110218875336 y[1] (numeric) 6.707611021887266 absolute error 2.673417043297377e-13 relative error 3.985647102334615e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.719999999999911 y[1] (closed_form) 6.72761094613397 y[1] (numeric) 6.727610946133694 absolute error 2.753353101070388e-13 relative error 4.092616417797771e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.729999999999914 y[1] (closed_form) 6.747610109292135 y[1] (numeric) 6.747610109291852 absolute error 2.8332891588433995e-13 relative error 4.198952092595979e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.739999999999918 y[1] (closed_form) 6.767607511454047 y[1] (numeric) 6.767607511453757 absolute error 2.9043434324194095e-13 relative error 4.291536451403045e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.749999999999921 y[1] (closed_form) 6.7876021528878185 y[1] (numeric) 6.787602152887522 absolute error 2.9665159217984183e-13 relative error 4.370491750958473e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.759999999999924 y[1] (closed_form) 6.8075930341376365 y[1] (numeric) 6.807593034137334 absolute error 3.028688411177427e-13 relative error 4.448985707561603e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.769999999999928 y[1] (closed_form) 6.8275791561237025 y[1] (numeric) 6.8275791561233925 absolute error 3.099742684753437e-13 relative error 4.540031852978602e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.779999999999931 y[1] (closed_form) 6.847559520242137 y[1] (numeric) 6.847559520241821 absolute error 3.161915174132446e-13 relative error 4.617579686288929e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.789999999999934 y[1] (closed_form) 6.8675331284648475 y[1] (numeric) 6.867533128464523 absolute error 3.241851231905457e-13 relative error 4.720546914391271e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.799999999999938 y[1] (closed_form) 6.887498983439322 y[1] (numeric) 6.8874989834389915 absolute error 3.304023721284466e-13 relative error 4.797131337846787e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.809999999999941 y[1] (closed_form) 6.9074560885883685 y[1] (numeric) 6.907456088588032 absolute error 3.3661962106634746e-13 relative error 4.873279203648766e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.819999999999944 y[1] (closed_form) 6.927403448209769 y[1] (numeric) 6.927403448209426 absolute error 3.4283687000424834e-13 relative error 4.9489952847029115e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.829999999999948 y[1] (closed_form) 6.947340067575851 y[1] (numeric) 6.9473400675755 absolute error 3.5083047578154947e-13 relative error 5.049853215317923e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.839999999999951 y[1] (closed_form) 6.967264953032959 y[1] (numeric) 6.9672649530326 absolute error 3.597122599785507e-13 relative error 5.1628904943820505e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.849999999999954 y[1] (closed_form) 6.987177112100817 y[1] (numeric) 6.987177112100452 absolute error 3.6504133049675147e-13 relative error 5.224446505936579e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.859999999999958 y[1] (closed_form) 7.007075553571779 y[1] (numeric) 7.007075553571408 absolute error 3.7125857943465235e-13 relative error 5.298338466543398e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.869999999999961 y[1] (closed_form) 7.026959287609946 y[1] (numeric) 7.026959287609569 absolute error 3.774758283725532e-13 relative error 5.371823187279952e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.879999999999964 y[1] (closed_form) 7.046827325850151 y[1] (numeric) 7.046827325849767 absolute error 3.836930773104541e-13 relative error 5.444905339214683e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.889999999999968 y[1] (closed_form) 7.066678681496794 y[1] (numeric) 7.066678681496403 absolute error 3.907985046680551e-13 relative error 5.530158116447429e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.899999999999971 y[1] (closed_form) 7.086512369422518 y[1] (numeric) 7.0865123694221195 absolute error 3.9879211044535623e-13 relative error 5.627480623135551e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.909999999999974 y[1] (closed_form) 7.106327406266727 y[1] (numeric) 7.106327406266322 absolute error 4.050093593832571e-13 relative error 5.699278069092326e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.919999999999978 y[1] (closed_form) 7.126122810533914 y[1] (numeric) 7.126122810533505 absolute error 4.0945025148175773e-13 relative error 5.745764735860345e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.929999999999981 y[1] (closed_form) 7.145897602691817 y[1] (numeric) 7.145897602691399 absolute error 4.18332035678759e-13 relative error 5.85415659358421e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.939999999999984 y[1] (closed_form) 7.165650805269364 y[1] (numeric) 7.16565080526894 absolute error 4.2454928461665986e-13 relative error 5.924783333070897e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.949999999999988 y[1] (closed_form) 7.1853814429544265 y[1] (numeric) 7.185381442953997 absolute error 4.298783551348606e-13 relative error 5.98267967466605e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.959999999999991 y[1] (closed_form) 7.205088542691344 y[1] (numeric) 7.205088542690907 absolute error 4.369837824924616e-13 relative error 6.0649328582606615e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.969999999999994 y[1] (closed_form) 7.224771133778232 y[1] (numeric) 7.224771133777789 absolute error 4.4231285301066237e-13 relative error 6.122171136227433e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.979999999999998 y[1] (closed_form) 7.244428247964051 y[1] (numeric) 7.244428247963602 absolute error 4.4941828036826337e-13 relative error 6.203640439044535e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.990000000000001 y[1] (closed_form) 7.2640589195454295 y[1] (numeric) 7.264058919544975 absolute error 4.547473508864641e-13 relative error 6.260237642936428e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Finished! diff ( y , x , 1 ) = 1.0 - sin ( x ) ; Iterations 4900 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.0204081632654%