##############ECHO OF PROBLEM################# ##############temp/sub_sin_cpostode.ode################# diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; ! #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) 0.9049958347219743 y[1] (numeric) 0.9049958347219743 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) 0.8960439020433032 y[1] (numeric) 0.8960439020433032 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) 0.8871913641461339 y[1] (numeric) 0.8871913641461339 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) 0.8784381062852119 y[1] (numeric) 0.878438106285212 absolute error 1.1102230246251565e-16 relative error 1.2638602727745153e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (closed_form) 0.8697840037873629 y[1] (numeric) 0.8697840037873629 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) 0.8612289220639576 y[1] (numeric) 0.861228922063958 absolute error 3.3306690738754696e-16 relative error 3.8673446612701234e-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) 0.8527727166243732 y[1] (numeric) 0.8527727166243734 absolute error 2.220446049250313e-16 relative error 2.6037958367614717e-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) 0.8444152330904394 y[1] (numeric) 0.8444152330904398 absolute error 3.3306690738754696e-16 relative error 3.944349821456555e-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) 0.8361563072118786 y[1] (numeric) 0.8361563072118788 absolute error 2.220446049250313e-16 relative error 2.6555394369436492e-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) 0.8279957648827295 y[1] (numeric) 0.82799576488273 absolute error 4.440892098500626e-16 relative error 5.3634236874745336e-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) 0.8199334221587583 y[1] (numeric) 0.8199334221587586 absolute error 3.3306690738754696e-16 relative error 4.062121367252394e-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) 0.8119690852758515 y[1] (numeric) 0.811969085275852 absolute error 4.440892098500626e-16 relative error 5.4692871674934704e-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) 0.8041025506693945 y[1] (numeric) 0.8041025506693945 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] 0.23000000000000012 y[1] (closed_form) 0.7963336049946251 y[1] (numeric) 0.7963336049946251 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] 0.24000000000000013 y[1] (closed_form) 0.7886620251479705 y[1] (numeric) 0.7886620251479705 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] 0.2500000000000001 y[1] (closed_form) 0.7810875782893553 y[1] (numeric) 0.7810875782893554 absolute error 1.1102230246251565e-16 relative error 1.421380976326156e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (closed_form) 0.7736100218654866 y[1] (numeric) 0.7736100218654868 absolute error 2.220446049250313e-16 relative error 2.87023950891422e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (closed_form) 0.7662291036341092 y[1] (numeric) 0.7662291036341095 absolute error 2.220446049250313e-16 relative error 2.897887901567654e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (closed_form) 0.7589445616892291 y[1] (numeric) 0.7589445616892291 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) 0.7517561244873029 y[1] (numeric) 0.7517561244873027 absolute error 2.220446049250313e-16 relative error 2.953678695686923e-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) 0.7446635108743939 y[1] (numeric) 0.7446635108743936 absolute error 2.220446049250313e-16 relative error 2.9818112702246356e-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) 0.7376664301142865 y[1] (numeric) 0.7376664301142863 absolute error 1.1102230246251565e-16 relative error 1.5050475110452703e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (closed_form) 0.7307645819175589 y[1] (numeric) 0.7307645819175589 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) 0.7239576564716129 y[1] (numeric) 0.7239576564716127 absolute error 2.220446049250313e-16 relative error 3.0670938132931795e-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) 0.7172453344716537 y[1] (numeric) 0.7172453344716534 absolute error 3.3306690738754696e-16 relative error 4.64369569769171e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (closed_form) 0.7106272871526208 y[1] (numeric) 0.7106272871526208 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] 0.3600000000000002 y[1] (closed_form) 0.704103176322065 y[1] (numeric) 0.704103176322065 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) 0.6976726543939654 y[1] (numeric) 0.6976726543939653 absolute error 1.1102230246251565e-16 relative error 1.591323692612768e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (closed_form) 0.6913353644234898 y[1] (numeric) 0.6913353644234895 absolute error 2.220446049250313e-16 relative error 3.2118218790990986e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (closed_form) 0.6850909401426869 y[1] (numeric) 0.6850909401426869 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] 0.40000000000000024 y[1] (closed_form) 0.6789390059971147 y[1] (numeric) 0.6789390059971149 absolute error 2.220446049250313e-16 relative error 3.27046469511541e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (closed_form) 0.6728791771833947 y[1] (numeric) 0.6728791771833947 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] 0.42000000000000026 y[1] (closed_form) 0.6669110596876916 y[1] (numeric) 0.6669110596876915 absolute error 1.1102230246251565e-16 relative error 1.6647242664487585e-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) 0.6610342503251146 y[1] (numeric) 0.6610342503251145 absolute error 1.1102230246251565e-16 relative error 1.6795242063162666e-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) 0.6552483367800365 y[1] (numeric) 0.6552483367800364 absolute error 1.1102230246251565e-16 relative error 1.694354586355635e-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) 0.6495528976473229 y[1] (numeric) 0.6495528976473229 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] 0.4600000000000003 y[1] (closed_form) 0.6439475024744746 y[1] (numeric) 0.6439475024744745 absolute error 1.1102230246251565e-16 relative error 1.7240893401386623e-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) 0.6384317118046708 y[1] (numeric) 0.6384317118046708 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] 0.4800000000000003 y[1] (closed_form) 0.6330050772207155 y[1] (numeric) 0.6330050772207156 absolute error 1.1102230246251565e-16 relative error 1.7538927641776957e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (closed_form) 0.6276671413898783 y[1] (numeric) 0.6276671413898782 absolute error 1.1102230246251565e-16 relative error 1.7688085792841216e-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) 0.6224174381096271 y[1] (numeric) 0.622417438109627 absolute error 1.1102230246251565e-16 relative error 1.7837273775572008e-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) 0.6172554923542485 y[1] (numeric) 0.6172554923542486 absolute error 1.1102230246251565e-16 relative error 1.7986442216831497e-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) 0.6121808203223499 y[1] (numeric) 0.6121808203223501 absolute error 2.220446049250313e-16 relative error 3.627108160757332e-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) 0.6071929294852388 y[1] (numeric) 0.6071929294852388 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] 0.5400000000000004 y[1] (closed_form) 0.6022913186361757 y[1] (numeric) 0.6022913186361758 absolute error 1.1102230246251565e-16 relative error 1.843332271730461e-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) 0.5974754779404939 y[1] (numeric) 0.5974754779404942 absolute error 2.220446049250313e-16 relative error 3.716380221836418e-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) 0.5927448889865837 y[1] (numeric) 0.5927448889865838 absolute error 1.1102230246251565e-16 relative error 1.87301998760935e-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) 0.588099024837731 y[1] (numeric) 0.5880990248377311 absolute error 1.1102230246251565e-16 relative error 1.887816469227254e-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) 0.583537350084813 y[1] (numeric) 0.583537350084813 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] 0.5900000000000004 y[1] (closed_form) 0.5790593208998364 y[1] (numeric) 0.5790593208998364 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] 0.6000000000000004 y[1] (closed_form) 0.5746643850903214 y[1] (numeric) 0.5746643850903216 absolute error 2.220446049250313e-16 relative error 3.863900577206155e-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) 0.5703519821545203 y[1] (numeric) 0.5703519821545204 absolute error 1.1102230246251565e-16 relative error 1.9465576685317345e-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) 0.5661215433374659 y[1] (numeric) 0.566121543337466 absolute error 1.1102230246251565e-16 relative error 1.961103649368367e-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) 0.561972491687848 y[1] (numeric) 0.5619724916878481 absolute error 1.1102230246251565e-16 relative error 1.9755825081236158e-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) 0.5579042421157073 y[1] (numeric) 0.5579042421157075 absolute error 2.220446049250313e-16 relative error 3.979976995388755e-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) 0.5539162014509439 y[1] (numeric) 0.5539162014509444 absolute error 5.551115123125783e-16 relative error 1.0021579272433327e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (closed_form) 0.5500077685026349 y[1] (numeric) 0.5500077685026351 absolute error 2.220446049250313e-16 relative error 4.037117612530005e-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) 0.5461783341191505 y[1] (numeric) 0.546178334119151 absolute error 4.440892098500626e-16 relative error 8.130846320849907e-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) 0.5424272812490719 y[1] (numeric) 0.5424272812490724 absolute error 4.440892098500626e-16 relative error 8.187073644737009e-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) 0.5387539850028932 y[1] (numeric) 0.5387539850028937 absolute error 5.551115123125783e-16 relative error 1.0303617750680717e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (closed_form) 0.5351578127155113 y[1] (numeric) 0.5351578127155118 absolute error 4.440892098500626e-16 relative error 8.298285090834307e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (closed_form) 0.5316381240094915 y[1] (numeric) 0.531638124009492 absolute error 4.440892098500626e-16 relative error 8.353223551780762e-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) 0.5281942708591049 y[1] (numeric) 0.5281942708591051 absolute error 2.220446049250313e-16 relative error 4.203843494248377e-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) 0.5248255976551296 y[1] (numeric) 0.5248255976551296 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] 0.7400000000000005 y[1] (closed_form) 0.5215314412704118 y[1] (numeric) 0.521531441270412 absolute error 1.1102230246251565e-16 relative error 2.128774867188708e-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) 0.5183111311261789 y[1] (numeric) 0.5183111311261791 absolute error 2.220446049250313e-16 relative error 4.284002244801805e-14% 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) 0.5151639892590946 y[1] (numeric) 0.5151639892590947 absolute error 1.1102230246251565e-16 relative error 2.1550866282829122e-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) 0.5120893303890565 y[1] (numeric) 0.5120893303890565 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) 0.5090864619877223 y[1] (numeric) 0.5090864619877226 absolute error 2.220446049250313e-16 relative error 4.361628554372879e-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) 0.5061546843477637 y[1] (numeric) 0.5061546843477639 absolute error 2.220446049250313e-16 relative error 4.386892224679504e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (closed_form) 0.5032932906528346 y[1] (numeric) 0.5032932906528347 absolute error 1.1102230246251565e-16 relative error 2.205916600209508e-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) 0.5005015670482528 y[1] (numeric) 0.5005015670482531 absolute error 3.3306690738754696e-16 relative error 6.654662628767281e-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) 0.49777879271238634 y[1] (numeric) 0.49777879271238656 absolute error 2.220446049250313e-16 relative error 4.460708414577384e-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) 0.4951242399287329 y[1] (numeric) 0.49512423992873306 absolute error 1.6653345369377348e-16 relative error 3.363467999824528e-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) 0.4925371741586916 y[1] (numeric) 0.4925371741586921 absolute error 4.996003610813204e-16 relative error 1.0143404138676305e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (closed_form) 0.4900168541150177 y[1] (numeric) 0.490016854115018 absolute error 2.7755575615628914e-16 relative error 5.664208359885121e-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) 0.4875625318359479 y[1] (numeric) 0.48756253183594833 absolute error 4.440892098500626e-16 relative error 9.108353920835883e-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) 0.4851734527599988 y[1] (numeric) 0.485173452759999 absolute error 2.220446049250313e-16 relative error 4.5766025255893445e-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) 0.4828488558014198 y[1] (numeric) 0.48284885580141995 absolute error 1.6653345369377348e-16 relative error 3.4489768732570704e-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) 0.4805879734263029 y[1] (numeric) 0.48058797342630327 absolute error 3.885780586188048e-16 relative error 8.085471965693964e-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) 0.47839003172933536 y[1] (numeric) 0.4783900317293357 absolute error 3.3306690738754696e-16 relative error 6.962245977064805e-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) 0.4762542505111883 y[1] (numeric) 0.4762542505111886 absolute error 2.7755575615628914e-16 relative error 5.82789037280768e-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) 0.47417984335653707 y[1] (numeric) 0.47417984335653723 absolute error 1.6653345369377348e-16 relative error 3.51203147976403e-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) 0.4721660177127015 y[1] (numeric) 0.47216601771270184 absolute error 3.3306690738754696e-16 relative error 7.054021147074755e-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) 0.47021197496890166 y[1] (numeric) 0.4702119749689018 absolute error 1.6653345369377348e-16 relative error 3.5416676426581325e-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) 0.46831691053611635 y[1] (numeric) 0.4683169105361165 absolute error 1.6653345369377348e-16 relative error 3.555999152435699e-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) 0.46648001392754324 y[1] (numeric) 0.46648001392754335 absolute error 1.1102230246251565e-16 relative error 2.3800012679591535e-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) 0.46470046883964555 y[1] (numeric) 0.4647004688396457 absolute error 1.6653345369377348e-16 relative error 3.5836730294162726e-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) 0.4629774532337826 y[1] (numeric) 0.4629774532337827 absolute error 1.1102230246251565e-16 relative error 2.398006678015364e-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) 0.46131013941841237 y[1] (numeric) 0.4613101394184124 absolute error 5.551115123125783e-17 relative error 1.2033368982793747e-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) 0.45969769413186 y[1] (numeric) 0.4596976941318603 absolute error 2.7755575615628914e-16 relative error 6.037788740281887e-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) 0.45813927862564463 y[1] (numeric) 0.4581392786256446 absolute error 5.551115123125783e-17 relative error 1.2116654000456742e-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) 0.4566340487483507 y[1] (numeric) 0.45663404874835045 absolute error 2.220446049250313e-16 relative error 4.86263793805265e-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) 0.4551811550300451 y[1] (numeric) 0.4551811550300447 absolute error 3.885780586188048e-16 relative error 8.536778254652391e-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) 0.4537797427672221 y[1] (numeric) 0.45377974276722166 absolute error 4.440892098500626e-16 relative error 9.786448534302896e-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) 0.4524289521082736 y[1] (numeric) 0.45242895210827305 absolute error 5.551115123125783e-16 relative error 1.226958420158158e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.059999999999994 y[1] (closed_form) 0.45112791813947317 y[1] (numeric) 0.45112791813947245 absolute error 7.216449660063518e-16 relative error 1.5996459917234474e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.069999999999993 y[1] (closed_form) 0.4498757709714667 y[1] (numeric) 0.44987577097146597 absolute error 7.216449660063518e-16 relative error 1.604098314625888e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y[1] (closed_form) 0.448671635826261 y[1] (numeric) 0.44867163582626013 absolute error 8.881784197001252e-16 relative error 1.9795733645263331e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y[1] (closed_form) 0.4475146331247002 y[1] (numeric) 0.4475146331246992 absolute error 9.992007221626409e-16 relative error 2.232777764574713e-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) 0.44640387857442376 y[1] (numeric) 0.4464038785744226 absolute error 1.1657341758564144e-15 relative error 2.611388995048942e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y[1] (closed_form) 0.4453384832582943 y[1] (numeric) 0.4453384832582931 absolute error 1.1657341758564144e-15 relative error 2.617636291675009e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y[1] (closed_form) 0.44431755372328907 y[1] (numeric) 0.44431755372328774 absolute error 1.3322676295501878e-15 relative error 2.9984582386765077e-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) 0.4433401920698439 y[1] (numeric) 0.4433401920698426 absolute error 1.27675647831893e-15 relative error 2.879857277000028e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y[1] (closed_form) 0.44240549604164325 y[1] (numeric) 0.44240549604164175 absolute error 1.4988010832439613e-15 relative error 3.3878446281844575e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y[1] (closed_form) 0.44151255911584397 y[1] (numeric) 0.4415125591158425 absolute error 1.4988010832439613e-15 relative error 3.394696373406461e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.159999999999983 y[1] (closed_form) 0.44066047059372826 y[1] (numeric) 0.4406604705937265 absolute error 1.7763568394002505e-15 relative error 4.0311236381308686e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.169999999999982 y[1] (closed_form) 0.4398483156917712 y[1] (numeric) 0.43984831569176935 absolute error 1.8318679906315083e-15 relative error 4.164772093648782e-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) 0.4390751756331197 y[1] (numeric) 0.4390751756331177 absolute error 1.9984014443252818e-15 relative error 4.551387906282127e-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) 0.4383401277394685 y[1] (numeric) 0.4383401277394665 absolute error 1.9984014443252818e-15 relative error 4.55902008020824e-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) 0.437642245523328 y[1] (numeric) 0.43764224552332576 absolute error 2.220446049250313e-15 relative error 5.07365564445253e-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) 0.4369805987806712 y[1] (numeric) 0.4369805987806689 absolute error 2.275957200481571e-15 relative error 5.208371279714221e-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) 0.4363542536839544 y[1] (numeric) 0.4363542536839521 absolute error 2.3314683517128287e-15 relative error 5.343063192415858e-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) 0.43576227287549885 y[1] (numeric) 0.4357622728754964 absolute error 2.4424906541753444e-15 relative error 5.605098940892448e-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) 0.43520371556122517 y[1] (numeric) 0.43520371556122267 absolute error 2.4980018054066022e-15 relative error 5.7398448498659e-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) 0.43467763760473277 y[1] (numeric) 0.43467763760473016 absolute error 2.609024107869118e-15 relative error 6.002204581413486e-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) 0.434183091621712 y[1] (numeric) 0.4341830916217094 absolute error 2.55351295663786e-15 relative error 5.881189309100603e-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) 0.4337191270746825 y[1] (numeric) 0.43371912707467997 absolute error 2.55351295663786e-15 relative error 5.887480623371651e-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) 0.4332847903680457 y[1] (numeric) 0.43328479036804307 absolute error 2.609024107869118e-15 relative error 6.021499406090232e-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) 0.4328791249434436 y[1] (numeric) 0.4328791249434409 absolute error 2.7200464103316335e-15 relative error 6.28361649614546e-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) 0.4325011713754139 y[1] (numeric) 0.432501171375411 absolute error 2.886579864025407e-15 relative error 6.674155019848111e-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) 0.4321499674673315 y[1] (numeric) 0.43214996746732864 absolute error 2.831068712794149e-15 relative error 6.55112559509371e-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) 0.4318245483476282 y[1] (numeric) 0.43182454834762524 absolute error 2.942091015256665e-15 relative error 6.813162953598964e-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) 0.4315239465662779 y[1] (numeric) 0.43152394656627485 absolute error 3.0531133177191805e-15 relative error 7.075188623976519e-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) 0.4312471921915415 y[1] (numeric) 0.43124719219153856 absolute error 2.942091015256665e-15 relative error 6.822284454318056e-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) 0.4309933129069594 y[1] (numeric) 0.43099331290695636 absolute error 3.0531133177191805e-15 relative error 7.083899509081874e-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) 0.4307613341085814 y[1] (numeric) 0.4307613341085785 absolute error 2.942091015256665e-15 relative error 6.829979346556337e-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) 0.4305502790024278 y[1] (numeric) 0.43055027900242476 absolute error 3.0531133177191805e-15 relative error 7.091188803298777e-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) 0.4303591687021664 y[1] (numeric) 0.4303591687021632 absolute error 3.219646771412954e-15 relative error 7.481301679065973e-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) 0.43018702232700123 y[1] (numeric) 0.43018702232699796 absolute error 3.2751579226442118e-15 relative error 7.613335020958958e-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) 0.4300328570997596 y[1] (numeric) 0.4300328570997564 absolute error 3.164135620181696e-15 relative error 7.357892700388882e-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) 0.42989568844516945 y[1] (numeric) 0.4298956884451661 absolute error 3.3306690738754696e-15 relative error 7.747621489114507e-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) 0.4297745300883147 y[1] (numeric) 0.4297745300883115 absolute error 3.164135620181696e-15 relative error 7.362315350636287e-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) 0.42966839415326374 y[1] (numeric) 0.42966839415326047 absolute error 3.2751579226442118e-15 relative error 7.622524642750324e-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) 0.4295762912618548 y[1] (numeric) 0.42957629126185154 absolute error 3.2751579226442118e-15 relative error 7.6241589428123e-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) 0.4294972306326337 y[1] (numeric) 0.4294972306326304 absolute error 3.2751579226442118e-15 relative error 7.625562376316197e-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) 0.4294302201799307 y[1] (numeric) 0.42943022017992744 absolute error 3.2751579226442118e-15 relative error 7.626752307445724e-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) 0.42937426661306866 y[1] (numeric) 0.4293742666130652 absolute error 3.4416913763379853e-15 relative error 8.015597682381537e-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) 0.4293283755356905 y[1] (numeric) 0.4293283755356872 absolute error 3.2751579226442118e-15 relative error 7.628561514383167e-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) 0.4292915515451996 y[1] (numeric) 0.4292915515451961 absolute error 3.497202527569243e-15 relative error 8.146450856023955e-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) 0.4292627983322972 y[1] (numeric) 0.42926279833229386 absolute error 3.3306690738754696e-15 relative error 7.759044312284338e-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) 0.4292411187806142 y[1] (numeric) 0.42924111878061083 absolute error 3.3861802251067274e-15 relative error 7.888760132594401e-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) 0.4292255150664208 y[1] (numeric) 0.42922551506641754 absolute error 3.2751579226442118e-15 relative error 7.630389638270677e-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) 0.4292149887584089 y[1] (numeric) 0.42921498875840564 absolute error 3.2751579226442118e-15 relative error 7.630576770206157e-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) 0.4292085409175339 y[1] (numeric) 0.4292085409175306 absolute error 3.3306690738754696e-15 relative error 7.760025154101975e-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) 0.42920517219690746 y[1] (numeric) 0.42920517219690424 absolute error 3.219646771412954e-15 relative error 7.501416525185464e-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) 0.4292038829417326 y[1] (numeric) 0.42920388294172934 absolute error 3.2751579226442118e-15 relative error 7.630774214334955e-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) 0.4292036732892668 y[1] (numeric) 0.4292036732892634 absolute error 3.3861802251067274e-15 relative error 7.889448380430267e-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) 0.42920354326880816 y[1] (numeric) 0.429203543268805 absolute error 3.164135620181696e-15 relative error 7.372109736288949e-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) 0.42920249290169266 y[1] (numeric) 0.42920249290168927 absolute error 3.3861802251067274e-15 relative error 7.889470077897055e-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) 0.42919952230128877 y[1] (numeric) 0.42919952230128555 absolute error 3.219646771412954e-15 relative error 7.501515272313914e-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) 0.42919363177298764 y[1] (numeric) 0.4291936317729845 absolute error 3.164135620181696e-15 relative error 7.372279982605369e-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) 0.42918382191417037 y[1] (numeric) 0.4291838219141674 absolute error 2.9976021664879227e-15 relative error 6.984424886097858e-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) 0.4291690937141486 y[1] (numeric) 0.42916909371414524 absolute error 3.3306690738754696e-15 relative error 7.760738419094754e-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) 0.4291484486540622 y[1] (numeric) 0.4291484486540591 absolute error 3.1086244689504383e-15 relative error 7.243704314206456e-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) 0.4291208888067344 y[1] (numeric) 0.42912088880673105 absolute error 3.3306690738754696e-15 relative error 7.761610214634697e-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) 0.4290854169364595 y[1] (numeric) 0.4290854169364561 absolute error 3.4416913763379853e-15 relative error 8.020993584239296e-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) 0.4290410365987285 y[1] (numeric) 0.4290410365987253 absolute error 3.219646771412954e-15 relative error 7.504286296101345e-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) 0.4289867522398716 y[1] (numeric) 0.4289867522398685 absolute error 3.1086244689504383e-15 relative error 7.246434657292691e-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) 0.4289215692966126 y[1] (numeric) 0.42892156929660963 absolute error 2.9976021664879227e-15 relative error 6.988695325823047e-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) 0.4288444942955254 y[1] (numeric) 0.4288444942955221 absolute error 3.2751579226442118e-15 relative error 7.637169104909236e-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) 0.42875453495237825 y[1] (numeric) 0.42875453495237525 absolute error 2.9976021664879227e-15 relative error 6.991417984233954e-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) 0.4286507002713644 y[1] (numeric) 0.42865070027136143 absolute error 2.9976021664879227e-15 relative error 6.993111558176019e-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) 0.42853200064419883 y[1] (numeric) 0.42853200064419567 absolute error 3.164135620181696e-15 relative error 7.383662399599445e-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) 0.42839744794907797 y[1] (numeric) 0.4283974479490751 absolute error 2.886579864025407e-15 relative error 6.738088375280248e-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) 0.42824605564949336 y[1] (numeric) 0.42824605564949025 absolute error 3.1086244689504383e-15 relative error 7.25896812811454e-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) 0.4280768388928815 y[1] (numeric) 0.42807683889287845 absolute error 3.0531133177191805e-15 relative error 7.132161893213678e-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) 0.42788881460911043 y[1] (numeric) 0.42788881460910744 absolute error 2.9976021664879227e-15 relative error 7.005563277521812e-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) 0.4276810016087855 y[1] (numeric) 0.42768100160878236 absolute error 3.164135620181696e-15 relative error 7.398354400310817e-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) 0.4274524206813666 y[1] (numeric) 0.4274524206813633 absolute error 3.2751579226442118e-15 relative error 7.662040882640349e-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) 0.42720209469308945 y[1] (numeric) 0.42720209469308595 absolute error 3.497202527569243e-15 relative error 8.186295364683789e-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) 0.4269290486846773 y[1] (numeric) 0.4269290486846738 absolute error 3.497202527569243e-15 relative error 8.191530977673573e-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) 0.4266323099688367 y[1] (numeric) 0.4266323099688333 absolute error 3.4416913763379853e-15 relative error 8.067113755611672e-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) 0.4263109082275258 y[1] (numeric) 0.42631090822752227 absolute error 3.552713678800501e-15 relative error 8.333621331838844e-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) 0.42596387560898363 y[1] (numeric) 0.42596387560898014 absolute error 3.497202527569243e-15 relative error 8.210091812526195e-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) 0.4255902468245163 y[1] (numeric) 0.42559024682451285 absolute error 3.4416913763379853e-15 relative error 8.08686618647325e-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) 0.4251890592450247 y[1] (numeric) 0.425189059245021 absolute error 3.7192471324942744e-15 relative error 8.747278537924409e-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) 0.4247593529972653 y[1] (numeric) 0.4247593529972615 absolute error 3.83026943495679e-15 relative error 9.017504636281547e-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) 0.42430017105983775 y[1] (numeric) 0.4243001710598341 absolute error 3.6637359812630166e-15 relative error 8.634773754890453e-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) 0.42381055935888745 y[1] (numeric) 0.42381055935888334 absolute error 4.107825191113079e-15 relative error 9.692597554263691e-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) 0.4232895668635088 y[1] (numeric) 0.4232895668635046 absolute error 4.218847493575595e-15 relative error 9.966811903341753e-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) 0.422736245680851 y[1] (numeric) 0.4227362456808467 absolute error 4.274358644806853e-15 relative error 1.0111171418298072e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9199999999998993 y[1] (closed_form) 0.4221496511509042 y[1] (numeric) 0.42214965115090014 absolute error 4.052314039881821e-15 relative error 9.599235789568985e-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) 0.4215288419409664 y[1] (numeric) 0.42152884194096213 absolute error 4.274358644806853e-15 relative error 1.0140133294616793e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9399999999998971 y[1] (closed_form) 0.4208728801397743 y[1] (numeric) 0.4208728801397698 absolute error 4.496403249731884e-15 relative error 1.0683518615498823e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.949999999999896 y[1] (closed_form) 0.42018083135129447 y[1] (numeric) 0.4201808313512899 absolute error 4.551914400963142e-15 relative error 1.0833227175842986e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.959999999999895 y[1] (closed_form) 0.4194517647881624 y[1] (numeric) 0.41945176478815793 absolute error 4.440892098500626e-15 relative error 1.0587372545073043e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9699999999998938 y[1] (closed_form) 0.4186847533647604 y[1] (numeric) 0.41868475336475586 absolute error 4.551914400963142e-15 relative error 1.087193733323623e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9799999999998927 y[1] (closed_form) 0.41787887378992505 y[1] (numeric) 0.4178788737899202 absolute error 4.829470157119431e-15 relative error 1.1557105324131052e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9899999999998916 y[1] (closed_form) 0.4170332066592748 y[1] (numeric) 0.4170332066592702 absolute error 4.6074255521944e-15 relative error 1.104810235401414e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9999999999998905 y[1] (closed_form) 0.4161468365471521 y[1] (numeric) 0.41614683654714746 absolute error 4.6629367034256575e-15 relative error 1.120502739397207e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0099999999998897 y[1] (closed_form) 0.415218852098163 y[1] (numeric) 0.41521885209815795 absolute error 5.051514762044462e-15 relative error 1.216590898153685e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0199999999998886 y[1] (closed_form) 0.4142483461183115 y[1] (numeric) 0.4142483461183064 absolute error 5.10702591327572e-15 relative error 1.2328415939691226e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0299999999998875 y[1] (closed_form) 0.4132344156657206 y[1] (numeric) 0.41323441566571556 absolute error 5.051514762044462e-15 relative error 1.222433217210738e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0399999999998863 y[1] (closed_form) 0.41217616214092434 y[1] (numeric) 0.41217616214091896 absolute error 5.384581669432009e-15 relative error 1.3063787195900484e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0499999999998852 y[1] (closed_form) 0.411072691376726 y[1] (numeric) 0.4110726913767204 absolute error 5.551115123125783e-15 relative error 1.3503974454091102e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.059999999999884 y[1] (closed_form) 0.4099231137276158 y[1] (numeric) 0.4099231137276102 absolute error 5.6066262743570405e-15 relative error 1.3677263093006536e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.069999999999883 y[1] (closed_form) 0.4087265441587342 y[1] (numeric) 0.40872654415872856 absolute error 5.662137425588298e-15 relative error 1.3853118928799825e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.079999999999882 y[1] (closed_form) 0.4074821023343742 y[1] (numeric) 0.40748210233436855 absolute error 5.662137425588298e-15 relative error 1.3895426064485224e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.089999999999881 y[1] (closed_form) 0.40618891270601454 y[1] (numeric) 0.4061889127060087 absolute error 5.828670879282072e-15 relative error 1.4349655288352644e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.0999999999998797 y[1] (closed_form) 0.4048461045998737 y[1] (numeric) 0.4048461045998678 absolute error 5.88418203051333e-15 relative error 1.4534367414326271e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1099999999998786 y[1] (closed_form) 0.40345281230397667 y[1] (numeric) 0.4034528123039706 absolute error 6.050715484207103e-15 relative error 1.4997331285543907e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1199999999998775 y[1] (closed_form) 0.4020081751547253 y[1] (numeric) 0.40200817515471887 absolute error 6.439293542825908e-15 relative error 1.6017817399727123e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1299999999998764 y[1] (closed_form) 0.40051133762296365 y[1] (numeric) 0.4005113376229571 absolute error 6.5503158452884236e-15 relative error 1.6354882446436032e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1399999999998753 y[1] (closed_form) 0.3989614493995308 y[1] (numeric) 0.3989614493995244 absolute error 6.439293542825908e-15 relative error 1.6140139736602531e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1499999999998742 y[1] (closed_form) 0.3973576654802917 y[1] (numeric) 0.39735766548028467 absolute error 7.049916206369744e-15 relative error 1.7741991205450667e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.159999999999873 y[1] (closed_form) 0.39569914625063385 y[1] (numeric) 0.3956991462506269 absolute error 6.938893903907228e-15 relative error 1.7535781842481327e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.169999999999872 y[1] (closed_form) 0.3939850575694326 y[1] (numeric) 0.3939850575694252 absolute error 7.382983113757291e-15 relative error 1.8739246506718536e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.179999999999871 y[1] (closed_form) 0.39221457085246003 y[1] (numeric) 0.3922145708524525 absolute error 7.549516567451064e-15 relative error 1.924843473061835e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.18999999999987 y[1] (closed_form) 0.3903868631552463 y[1] (numeric) 0.3903868631552385 absolute error 7.771561172376096e-15 relative error 1.9907332714947315e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.1999999999998687 y[1] (closed_form) 0.38850111725537095 y[1] (numeric) 0.388501117255363 absolute error 7.93809462606987e-15 relative error 2.04326172396873e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2099999999998676 y[1] (closed_form) 0.3865565217341862 y[1] (numeric) 0.386556521734178 absolute error 8.215650382226158e-15 relative error 2.1253425877718377e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2199999999998665 y[1] (closed_form) 0.38455227105795675 y[1] (numeric) 0.38455227105794837 absolute error 8.382183835919932e-15 relative error 2.179725479935245e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2299999999998654 y[1] (closed_form) 0.38248756565841324 y[1] (numeric) 0.3824875656584049 absolute error 8.326672684688674e-15 relative error 2.176978660823956e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2399999999998643 y[1] (closed_form) 0.3803616120127087 y[1] (numeric) 0.38036161201270025 absolute error 8.43769498715119e-15 relative error 2.21833505818386e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.249999999999863 y[1] (closed_form) 0.37817362272276966 y[1] (numeric) 0.37817362272276045 absolute error 9.2148511043888e-15 relative error 2.4366720867637014e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.259999999999862 y[1] (closed_form) 0.37592281659403426 y[1] (numeric) 0.37592281659402477 absolute error 9.492406860545088e-15 relative error 2.525094631538715e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.269999999999861 y[1] (closed_form) 0.3736084187135731 y[1] (numeric) 0.3736084187135636 absolute error 9.492406860545088e-15 relative error 2.54073687451418e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.27999999999986 y[1] (closed_form) 0.37122966052757933 y[1] (numeric) 0.37122966052756967 absolute error 9.658940314238862e-15 relative error 2.601877312419459e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.289999999999859 y[1] (closed_form) 0.3687857799182228 y[1] (numeric) 0.3687857799182126 absolute error 1.021405182655144e-14 relative error 2.7696436204282e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.2999999999998577 y[1] (closed_form) 0.3662760212798606 y[1] (numeric) 0.3662760212798501 absolute error 1.049160758270773e-14 relative error 2.8643992435124234e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3099999999998566 y[1] (closed_form) 0.3636996355945983 y[1] (numeric) 0.3636996355945877 absolute error 1.0602629885170245e-14 relative error 2.9152159770070765e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3199999999998555 y[1] (closed_form) 0.36105588050719106 y[1] (numeric) 0.36105588050718035 absolute error 1.071365218763276e-14 relative error 2.9673113681413586e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3299999999998544 y[1] (closed_form) 0.3583440203992785 y[1] (numeric) 0.3583440203992671 absolute error 1.1379786002407855e-14 relative error 3.1756595211852926e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3399999999998533 y[1] (closed_form) 0.3555633264629434 y[1] (numeric) 0.35556332646293193 absolute error 1.149080830487037e-14 relative error 3.2317192043336152e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.349999999999852 y[1] (closed_form) 0.3527130767735964 y[1] (numeric) 0.35271307677358466 absolute error 1.176836406102666e-14 relative error 3.3365261556720432e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.359999999999851 y[1] (closed_form) 0.34979255636216466 y[1] (numeric) 0.34979255636215234 absolute error 1.2323475573339238e-14 relative error 3.523081137432748e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.36999999999985 y[1] (closed_form) 0.34680105728658805 y[1] (numeric) 0.3468010572865757 absolute error 1.2378986724570495e-14 relative error 3.569477792664513e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.379999999999849 y[1] (closed_form) 0.3437378787026155 y[1] (numeric) 0.34373787870260253 absolute error 1.2989609388114332e-14 relative error 3.778928710778564e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.389999999999848 y[1] (closed_form) 0.34060232693388537 y[1] (numeric) 0.34060232693387216 absolute error 1.3211653993039363e-14 relative error 3.878908905870126e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3999999999998467 y[1] (closed_form) 0.33739371554129516 y[1] (numeric) 0.33739371554128156 absolute error 1.3600232051658168e-14 relative error 4.030967805621019e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4099999999998456 y[1] (closed_form) 0.33411136539164366 y[1] (numeric) 0.33411136539162967 absolute error 1.3988810110276972e-14 relative error 4.186870474723109e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4199999999998445 y[1] (closed_form) 0.33075460472554363 y[1] (numeric) 0.3307546047255293 absolute error 1.432187701766452e-14 relative error 4.330061263863174e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4299999999998434 y[1] (closed_form) 0.3273227692245979 y[1] (numeric) 0.32732276922458325 absolute error 1.4654943925052066e-14 relative error 4.477214939788174e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4399999999998423 y[1] (closed_form) 0.32381520207782977 y[1] (numeric) 0.3238152020778149 absolute error 1.4876988529977098e-14 relative error 4.594283540277203e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.449999999999841 y[1] (closed_form) 0.3202312540473651 y[1] (numeric) 0.3202312540473493 absolute error 1.5765166949677223e-14 relative error 4.92305693164647e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.45999999999984 y[1] (closed_form) 0.31657028353335237 y[1] (numeric) 0.31657028353333627 absolute error 1.609823385706477e-14 relative error 5.085200568223497e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.469999999999839 y[1] (closed_form) 0.3128316566381262 y[1] (numeric) 0.3128316566381097 absolute error 1.6486811915683575e-14 relative error 5.270186557479699e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.479999999999838 y[1] (closed_form) 0.30901474722959366 y[1] (numeric) 0.30901474722957695 absolute error 1.6708856520608606e-14 relative error 5.407138872952933e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.489999999999837 y[1] (closed_form) 0.3051189370038485 y[1] (numeric) 0.3051189370038313 absolute error 1.7208456881689926e-14 relative error 5.639917682812612e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4999999999998357 y[1] (closed_form) 0.30114361554699975 y[1] (numeric) 0.30114361554698216 absolute error 1.759703494030873e-14 relative error 5.8434029585336985e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5099999999998346 y[1] (closed_form) 0.297088180396214 y[1] (numeric) 0.2970881803961958 absolute error 1.8207657603852567e-14 relative error 6.1287048106625385e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5199999999998335 y[1] (closed_form) 0.29295203709995965 y[1] (numeric) 0.292952037099941 absolute error 1.865174681370263e-14 relative error 6.366826118822438e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5299999999998324 y[1] (closed_form) 0.28873459927745326 y[1] (numeric) 0.2887345992774341 absolute error 1.915134717478395e-14 relative error 6.6328549549341945e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5399999999998313 y[1] (closed_form) 0.2844352886772956 y[1] (numeric) 0.284435288677276 absolute error 1.9595436384634013e-14 relative error 6.889242356586035e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.54999999999983 y[1] (closed_form) 0.2800535352352975 y[1] (numeric) 0.2800535352352774 absolute error 2.015054789694659e-14 relative error 7.1952485370400165e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.559999999999829 y[1] (closed_form) 0.27558877713148444 y[1] (numeric) 0.2755887771314641 absolute error 2.0317081350640365e-14 relative error 7.372245547193313e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.569999999999828 y[1] (closed_form) 0.2710404608462804 y[1] (numeric) 0.2710404608462595 absolute error 2.09277040141842e-14 relative error 7.721247207461498e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.579999999999827 y[1] (closed_form) 0.2664080412158567 y[1] (numeric) 0.26640804121583495 absolute error 2.1760371282653068e-14 relative error 8.168060987701855e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5899999999998258 y[1] (closed_form) 0.2616909814866486 y[1] (numeric) 0.26169098148662656 absolute error 2.2037927038809357e-14 relative error 8.421355185269817e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5999999999998247 y[1] (closed_form) 0.25688875336903205 y[1] (numeric) 0.25688875336900957 absolute error 2.248201624865942e-14 relative error 8.75165454065753e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6099999999998236 y[1] (closed_form) 0.25200083709015075 y[1] (numeric) 0.2520008370901274 absolute error 2.3370194668359545e-14 relative error 9.273855967390733e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6199999999998225 y[1] (closed_form) 0.24702672144589144 y[1] (numeric) 0.24702672144586782 absolute error 2.3619994848900205e-14 relative error 9.561716526312686e-12% Desired digits 8 Estimated correct digits 11 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6299999999998214 y[1] (closed_form) 0.2419659038520079 y[1] (numeric) 0.24196590385198355 absolute error 2.4341639814906557e-14 relative error 1.0059946226884299e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6399999999998203 y[1] (closed_form) 0.2368178903943745 y[1] (numeric) 0.2368178903943499 absolute error 2.4619195571062846e-14 relative error 1.0395834339231857e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.649999999999819 y[1] (closed_form) 0.23158219587838147 y[1] (numeric) 0.23158219587835596 absolute error 2.550737399076297e-14 relative error 1.1014393353519505e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.659999999999818 y[1] (closed_form) 0.2262583438774497 y[1] (numeric) 0.22625834387742363 absolute error 2.606248550307555e-14 relative error 1.151890580317869e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.669999999999817 y[1] (closed_form) 0.2208458667806763 y[1] (numeric) 0.22084586678064977 absolute error 2.653433028854124e-14 relative error 1.2014863884635289e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.679999999999816 y[1] (closed_form) 0.21534430583959407 y[1] (numeric) 0.21534430583956693 absolute error 2.7144952952085077e-14 relative error 1.2605372984556575e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6899999999998148 y[1] (closed_form) 0.2097532112140459 y[1] (numeric) 0.20975321121401794 absolute error 2.7949864644938316e-14 relative error 1.3325118830441383e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6999999999998137 y[1] (closed_form) 0.20407214201716783 y[1] (numeric) 0.20407214201713939 absolute error 2.8449465006019636e-14 relative error 1.3940886161535115e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7099999999998126 y[1] (closed_form) 0.1983006663594793 y[1] (numeric) 0.19830066635945007 absolute error 2.9226621123257246e-14 relative error 1.473853903762242e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7199999999998115 y[1] (closed_form) 0.19243836139206927 y[1] (numeric) 0.19243836139203957 absolute error 2.969846590872294e-14 relative error 1.5432716062373864e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7299999999998104 y[1] (closed_form) 0.186484813348883 y[1] (numeric) 0.18648481334885267 absolute error 3.03368441478824e-14 relative error 1.626772904618622e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7399999999998093 y[1] (closed_form) 0.1804396175880969 y[1] (numeric) 0.18043961758806573 absolute error 3.116951141635127e-14 relative error 1.7274206093422486e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.749999999999808 y[1] (closed_form) 0.17430237863258213 y[1] (numeric) 0.17430237863255046 absolute error 3.166911177743259e-14 relative error 1.8169064602491158e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.759999999999807 y[1] (closed_form) 0.1680727102094539 y[1] (numeric) 0.16807271020942136 absolute error 3.2557290197132716e-14 relative error 1.9370955675409464e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.769999999999806 y[1] (closed_form) 0.1617502352886957 y[1] (numeric) 0.16175023528866267 absolute error 3.302913498259841e-14 relative error 2.0419837364469496e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.779999999999805 y[1] (closed_form) 0.15533458612086504 y[1] (numeric) 0.1553345861208311 absolute error 3.394506897791416e-14 relative error 2.1852872451407364e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7899999999998037 y[1] (closed_form) 0.14882540427386504 y[1] (numeric) 0.14882540427383031 absolute error 3.472222509515177e-14 relative error 2.333084547262962e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7999999999998026 y[1] (closed_form) 0.14222234066878947 y[1] (numeric) 0.14222234066875408 absolute error 3.5388358909926865e-14 relative error 2.4882419135781245e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8099999999998015 y[1] (closed_form) 0.13552505561482953 y[1] (numeric) 0.1355250556147937 absolute error 3.583244811977693e-14 relative error 2.643972212903194e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8199999999998004 y[1] (closed_form) 0.1287332188432435 y[1] (numeric) 0.12873321884320674 absolute error 3.677613769070831e-14 relative error 2.8567713928982118e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8299999999997993 y[1] (closed_form) 0.12184650954038156 y[1] (numeric) 0.1218465095403439 absolute error 3.7664316110408436e-14 relative error 3.091128030871166e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8399999999997982 y[1] (closed_form) 0.11486461637976841 y[1] (numeric) 0.11486461637972983 absolute error 3.858025010572419e-14 relative error 3.358758451616567e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.849999999999797 y[1] (closed_form) 0.10778723755323494 y[1] (numeric) 0.1077872375531957 absolute error 3.923250613269147e-14 relative error 3.639809964822131e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.859999999999796 y[1] (closed_form) 0.10061408080109935 y[1] (numeric) 0.10061408080105967 absolute error 3.967659534254153e-14 relative error 3.943443604178712e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.869999999999795 y[1] (closed_form) 0.09334486344139314 y[1] (numeric) 0.0933448634413526 absolute error 4.055089597443384e-14 relative error 4.344202185254023e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.879999999999794 y[1] (closed_form) 0.08597931239812784 y[1] (numeric) 0.08597931239808612 absolute error 4.171663015029026e-14 relative error 4.85193809844874e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8899999999997927 y[1] (closed_form) 0.078517164228602 y[1] (numeric) 0.07851716422855994 absolute error 4.206357484548562e-14 relative error 5.357245802079391e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8999999999997916 y[1] (closed_form) 0.07095816514974906 y[1] (numeric) 0.07095816514970586 absolute error 4.3201553445726404e-14 relative error 6.088313213081888e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9099999999997905 y[1] (closed_form) 0.06330207106350993 y[1] (numeric) 0.06330207106346597 absolute error 4.39648317751562e-14 relative error 6.945243818491658e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9199999999997894 y[1] (closed_form) 0.055548647581247224 y[1] (numeric) 0.05554864758120209 absolute error 4.5130565951012613e-14 relative error 8.124512101757871e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9299999999997883 y[1] (closed_form) 0.047697670047180285 y[1] (numeric) 0.04769767004713463 absolute error 4.565792188770956e-14 relative error 9.572358952239575e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9399999999997872 y[1] (closed_form) 0.039748923560854355 y[1] (numeric) 0.039748923560807836 absolute error 4.651834473179406e-14 relative error 1.170304515556904e-10% Desired digits 8 Estimated correct digits 10 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 2.949999999999786 y[1] (closed_form) 0.031702202998626916 y[1] (numeric) 0.0317022029985797 absolute error 4.721917301608869e-14 relative error 1.4894603071633175e-10% Desired digits 8 Estimated correct digits 10 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 2.959999999999785 y[1] (closed_form) 0.023557313034182403 y[1] (numeric) 0.02355731303413417 absolute error 4.8232251526059144e-14 relative error 2.0474428240637048e-10% Desired digits 8 Estimated correct digits 10 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 2.969999999999784 y[1] (closed_form) 0.015314068158062799 y[1] (numeric) 0.015314068158013618 absolute error 4.918114526741846e-14 relative error 3.211501004161639e-10% Desired digits 8 Estimated correct digits 10 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 2.979999999999783 y[1] (closed_form) 0.006972292696219906 y[1] (numeric) 0.006972292696169607 absolute error 5.029917454768551e-14 relative error 7.214151318540554e-10% Desired digits 8 Estimated correct digits 10 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9899999999997817 y[1] (closed_form) -0.0014681791724187043 y[1] (numeric) -0.0014681791724698234 absolute error 5.111904823051905e-14 relative error 3.4817990331728127e-09% Desired digits 8 Estimated correct digits 9 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9999999999997806 y[1] (closed_form) -0.010007503399366069 y[1] (numeric) -0.010007503399418206 absolute error 5.213711407048294e-14 relative error 5.209802284332533e-10% Desired digits 8 Estimated correct digits 10 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0099999999997795 y[1] (closed_form) -0.018645826050982528 y[1] (numeric) -0.018645826051035624 absolute error 5.309641615269811e-14 relative error 2.847630134890175e-10% Desired digits 8 Estimated correct digits 10 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0199999999997784 y[1] (closed_form) -0.0273832832938683 y[1] (numeric) -0.027383283293922187 absolute error 5.3887450057743536e-14 relative error 1.9678958684187473e-10% Desired digits 8 Estimated correct digits 10 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0299999999997773 y[1] (closed_form) -0.03622000138124637 y[1] (numeric) -0.036220001381301485 absolute error 5.5115634278735115e-14 relative error 1.5216905625871216e-10% Desired digits 8 Estimated correct digits 10 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 3.039999999999776 y[1] (closed_form) -0.045156096640339705 y[1] (numeric) -0.04515609664039539 absolute error 5.568462357885551e-14 relative error 1.23315848184075e-10% Desired digits 8 Estimated correct digits 11 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 3.049999999999775 y[1] (closed_form) -0.054191675460734334 y[1] (numeric) -0.0541916754607914 absolute error 5.706546346573305e-14 relative error 1.0530300637610101e-10% Desired digits 8 Estimated correct digits 11 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] 3.059999999999774 y[1] (closed_form) -0.06332683428374608 y[1] (numeric) -0.0633268342838038 absolute error 5.771771949270033e-14 relative error 9.114259404486697e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.069999999999773 y[1] (closed_form) -0.0725616595927705 y[1] (numeric) -0.07256165959282958 absolute error 5.907774269786614e-14 relative error 8.141729810125816e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.079999999999772 y[1] (closed_form) -0.08189622790464046 y[1] (numeric) -0.0818962279047002 absolute error 5.974387651264124e-14 relative error 7.295070608405394e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0899999999997707 y[1] (closed_form) -0.09133060576196872 y[1] (numeric) -0.09133060576202998 absolute error 6.125655538369301e-14 relative error 6.707122423269973e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0999999999997696 y[1] (closed_form) -0.10086484972649945 y[1] (numeric) -0.1008648497265618 absolute error 6.235290062051035e-14 relative error 6.181826552023193e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1099999999997685 y[1] (closed_form) -0.1104990063734479 y[1] (numeric) -0.11049900637351107 absolute error 6.317169010117141e-14 relative error 5.7169464391085335e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1199999999997674 y[1] (closed_form) -0.12023311228684408 y[1] (numeric) -0.12023311228690825 absolute error 6.417089082333405e-14 relative error 5.337206165822228e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1299999999997663 y[1] (closed_form) -0.1300671940558753 y[1] (numeric) -0.1300671940559404 absolute error 6.50868248186498e-14 relative error 5.004092330206592e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.139999999999765 y[1] (closed_form) -0.14000126827222603 y[1] (numeric) -0.1400012682722924 absolute error 6.636358129696873e-14 relative error 4.7402128649240375e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.149999999999764 y[1] (closed_form) -0.15003534152842013 y[1] (numeric) -0.15003534152848763 absolute error 6.750155989720952e-14 relative error 4.4990439725445074e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.159999999999763 y[1] (closed_form) -0.16016941041716048 y[1] (numeric) -0.16016941041722887 absolute error 6.838973831690964e-14 relative error 4.269837676169806e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.169999999999762 y[1] (closed_form) -0.1704034615316692 y[1] (numeric) -0.170403461531739 absolute error 6.980527267330672e-14 relative error 4.0964703443147797e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.179999999999761 y[1] (closed_form) -0.18073747146703045 y[1] (numeric) -0.1807374714671016 absolute error 7.11375403028569e-14 relative error 3.935959694768309e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1899999999997597 y[1] (closed_form) -0.1911714068225292 y[1] (numeric) -0.19117140682260145 absolute error 7.224776332748206e-14 relative error 3.7792138755641464e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1999999999997586 y[1] (closed_form) -0.20170522420499148 y[1] (numeric) -0.20170522420506462 absolute error 7.313594174718219e-14 relative error 3.6258823754041534e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2099999999997575 y[1] (closed_form) -0.21233887023312326 y[1] (numeric) -0.21233887023319772 absolute error 7.446820937673237e-14 relative error 3.507045568009992e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2199999999997564 y[1] (closed_form) -0.22307228154285053 y[1] (numeric) -0.22307228154292597 absolute error 7.543965452327939e-14 relative error 3.3818479822553836e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2299999999997553 y[1] (closed_form) -0.23390538479365297 y[1] (numeric) -0.23390538479372955 absolute error 7.657763312352017e-14 relative error 3.273872176610023e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.239999999999754 y[1] (closed_form) -0.24483809667589984 y[1] (numeric) -0.2448380966759777 absolute error 7.78543896018391e-14 relative error 3.17983151555444e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.249999999999753 y[1] (closed_form) -0.2558703239191802 y[1] (numeric) -0.2558703239192594 absolute error 7.921441280700492e-14 relative error 3.095881210203407e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.259999999999752 y[1] (closed_form) -0.26700196330163006 y[1] (numeric) -0.2670019633017105 absolute error 8.043565813409259e-14 relative error 3.01254931384999e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.269999999999751 y[1] (closed_form) -0.27823290166025405 y[1] (numeric) -0.2782329016603358 absolute error 8.176792576364278e-14 relative error 2.938830212951894e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.27999999999975 y[1] (closed_form) -0.2895630159022424 y[1] (numeric) -0.28956301590232525 absolute error 8.282263763703668e-14 relative error 2.860262985553304e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2899999999997487 y[1] (closed_form) -0.30099217301727865 y[1] (numeric) -0.300992173017363 absolute error 8.432143872028064e-14 relative error 2.8014495485050406e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2999999999997476 y[1] (closed_form) -0.31252023009084295 y[1] (numeric) -0.3125202300909285 absolute error 8.554268404736831e-14 relative error 2.7371886940727926e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3099999999997465 y[1] (closed_form) -0.3241470343185009 y[1] (numeric) -0.3241470343185878 absolute error 8.693046282814976e-14 relative error 2.6818219395687417e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3199999999997454 y[1] (closed_form) -0.3358724230211858 y[1] (numeric) -0.3358724230212739 absolute error 8.809619700400617e-14 relative error 2.6229065253877462e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3299999999997443 y[1] (closed_form) -0.34769622366146447 y[1] (numeric) -0.3476962236615542 absolute error 8.97615315409439e-14 relative error 2.58160789311133e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.339999999999743 y[1] (closed_form) -0.35961825386079393 y[1] (numeric) -0.35961825386088464 absolute error 9.070522111187529e-14 relative error 2.5222640991685236e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.349999999999742 y[1] (closed_form) -0.37163832141775455 y[1] (numeric) -0.37163832141784675 absolute error 9.220402219511925e-14 relative error 2.481014924493584e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.359999999999741 y[1] (closed_form) -0.38375622432727496 y[1] (numeric) -0.38375622432736856 absolute error 9.35918009759007e-14 relative error 2.4388347352532775e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.36999999999974 y[1] (closed_form) -0.3959717508008289 y[1] (numeric) -0.3959717508009237 absolute error 9.481304630298837e-14 relative error 2.3944396566481e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3799999999997388 y[1] (closed_form) -0.40828467928761514 y[1] (numeric) -0.4082846792877112 absolute error 9.60898027813073e-14 relative error 2.3535000859931135e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3899999999997377 y[1] (closed_form) -0.42069477849671255 y[1] (numeric) -0.4206947784968099 absolute error 9.736655925962623e-14 relative error 2.314422812841902e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3999999999997366 y[1] (closed_form) -0.4332018074202084 y[1] (numeric) -0.4332018074203071 absolute error 9.869882688917642e-14 relative error 2.2783567657980232e-11% Desired digits 8 Estimated correct digits 11 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4099999999997355 y[1] (closed_form) -0.4458055153572995 y[1] (numeric) -0.4458055153573999 absolute error 1.0036416142611415e-13 relative error 2.2512992318113278e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4199999999997344 y[1] (closed_form) -0.4585056419393627 y[1] (numeric) -0.45850564193946414 absolute error 1.0141887329950805e-13 relative error 2.2119438458931913e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4299999999997333 y[1] (closed_form) -0.4713019171559889 y[1] (numeric) -0.47130191715609177 absolute error 1.0286216323152075e-13 relative error 2.1825110292830828e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.439999999999732 y[1] (closed_form) -0.48419406138198706 y[1] (numeric) -0.4841940613820914 absolute error 1.0436096431476471e-13 relative error 2.155354074705038e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.449999999999731 y[1] (closed_form) -0.49718178540534463 y[1] (numeric) -0.49718178540545055 absolute error 1.0591527654923993e-13 relative error 2.1303128887332194e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.45999999999973 y[1] (closed_form) -0.5102647904561493 y[1] (numeric) -0.5102647904562566 absolute error 1.0735856648125264e-13 relative error 2.1039775522289095e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.469999999999729 y[1] (closed_form) -0.5234427682364649 y[1] (numeric) -0.5234427682365738 absolute error 1.0891287871572786e-13 relative error 2.0807027114476543e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4799999999997278 y[1] (closed_form) -0.5367154009511617 y[1] (numeric) -0.5367154009512719 absolute error 1.1024514634527804e-13 relative error 2.0540708567315696e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4899999999997267 y[1] (closed_form) -0.5500823613396952 y[1] (numeric) -0.550082361339807 absolute error 1.1179945857975326e-13 relative error 2.0324130791518537e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4999999999997256 y[1] (closed_form) -0.5635433127088332 y[1] (numeric) -0.5635433127089462 absolute error 1.1302070390684094e-13 relative error 2.005537131894519e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5099999999997245 y[1] (closed_form) -0.5770979089663215 y[1] (numeric) -0.5770979089664365 absolute error 1.1501910535116622e-13 relative error 1.993060511294948e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5199999999997234 y[1] (closed_form) -0.5907457946554979 y[1] (numeric) -0.5907457946556144 absolute error 1.1646239528317892e-13 relative error 1.9714468784512578e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5299999999997222 y[1] (closed_form) -0.6044866049908326 y[1] (numeric) -0.6044866049909506 absolute error 1.1801670751765414e-13 relative error 1.9523461155842144e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.539999999999721 y[1] (closed_form) -0.6183199658944094 y[1] (numeric) -0.6183199658945291 absolute error 1.1968204205459188e-13 relative error 1.935600476388789e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.54999999999972 y[1] (closed_form) -0.6322454940333331 y[1] (numeric) -0.6322454940334541 absolute error 1.2101430968414206e-13 relative error 1.9140398915640508e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.559999999999719 y[1] (closed_form) -0.6462627968580601 y[1] (numeric) -0.6462627968581827 absolute error 1.2256862191861728e-13 relative error 1.8965755496759202e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.569999999999718 y[1] (closed_form) -0.6603714726416561 y[1] (numeric) -0.6603714726417803 absolute error 1.2423395645555502e-13 relative error 1.8812738224228125e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5799999999997167 y[1] (closed_form) -0.6745711105199668 y[1] (numeric) -0.6745711105200923 absolute error 1.255662240851052e-13 relative error 1.861423089825436e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5899999999997156 y[1] (closed_form) -0.6888612905327038 y[1] (numeric) -0.688861290532831 absolute error 1.2712053631958042e-13 relative error 1.8453720373992382e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.5999999999997145 y[1] (closed_form) -0.7032415836654411 y[1] (numeric) -0.7032415836655697 absolute error 1.2856382625159313e-13 relative error 1.828160183325505e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6099999999997134 y[1] (closed_form) -0.7177115518925157 y[1] (numeric) -0.7177115518926459 absolute error 1.3022916078853086e-13 relative error 1.814505569056717e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6199999999997123 y[1] (closed_form) -0.7322707482208299 y[1] (numeric) -0.7322707482209615 absolute error 1.3156142841808105e-13 relative error 1.7966227483172145e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6299999999997112 y[1] (closed_form) -0.7469187167345499 y[1] (numeric) -0.7469187167346831 absolute error 1.3322676295501878e-13 relative error 1.7836848906059308e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.63999999999971 y[1] (closed_form) -0.7616549926406977 y[1] (numeric) -0.7616549926408326 absolute error 1.3489209749195652e-13 relative error 1.7710393655305606e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.649999999999709 y[1] (closed_form) -0.7764791023156294 y[1] (numeric) -0.7764791023157662 absolute error 1.3677947663381929e-13 relative error 1.761534550329985e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.659999999999708 y[1] (closed_form) -0.7913905633523983 y[1] (numeric) -0.7913905633525365 absolute error 1.38222766565832e-13 relative error 1.7465809293998717e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.669999999999707 y[1] (closed_form) -0.8063888846089928 y[1] (numeric) -0.8063888846091327 absolute error 1.3988810110276972e-13 relative error 1.7347473876775918e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6799999999997057 y[1] (closed_form) -0.821473566257453 y[1] (numeric) -0.8214735662575945 absolute error 1.4144241333724494e-13 relative error 1.72181332604093e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6899999999997046 y[1] (closed_form) -0.8366440998338511 y[1] (numeric) -0.8366440998339942 absolute error 1.4310774787418268e-13 relative error 1.7104973058747727e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.6999999999997035 y[1] (closed_form) -0.8518999682891382 y[1] (numeric) -0.8518999682892829 absolute error 1.4477308241112041e-13 relative error 1.6994141072908675e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7099999999997024 y[1] (closed_form) -0.8672406460408486 y[1] (numeric) -0.867240646040995 absolute error 1.4643841694805815e-13 relative error 1.6885557384398773e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7199999999997013 y[1] (closed_form) -0.8826655990256578 y[1] (numeric) -0.8826655990258059 absolute error 1.4810375148499588e-13 relative error 1.6779146218962447e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7299999999997 y[1] (closed_form) -0.898174284752788 y[1] (numeric) -0.8981742847529378 absolute error 1.4976908602193362e-13 relative error 1.667483567102523e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.739999999999699 y[1] (closed_form) -0.9137661523582574 y[1] (numeric) -0.9137661523584085 absolute error 1.511013536514838e-13 relative error 1.6536107543655433e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.749999999999698 y[1] (closed_form) -0.9294406426599648 y[1] (numeric) -0.9294406426601176 absolute error 1.5276668818842154e-13 relative error 1.643641144755826e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.759999999999697 y[1] (closed_form) -0.945197188213609 y[1] (numeric) -0.9451971882137634 absolute error 1.5443202272535927e-13 relative error 1.633860369572519e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.769999999999696 y[1] (closed_form) -0.9610352133694313 y[1] (numeric) -0.9610352133695879 absolute error 1.5654144647214707e-13 relative error 1.6288835652889963e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7799999999996947 y[1] (closed_form) -0.9769541343297821 y[1] (numeric) -0.9769541343299402 absolute error 1.580957587066223e-13 relative error 1.618251595967506e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7899999999996936 y[1] (closed_form) -0.992953359207497 y[1] (numeric) -0.9929533592076569 absolute error 1.5987211554602254e-13 relative error 1.610066717268783e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.7999999999996925 y[1] (closed_form) -1.0090322880850877 y[1] (numeric) -1.0090322880852494 absolute error 1.616484723854228e-13 relative error 1.6020148640852177e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8099999999996914 y[1] (closed_form) -1.0251903130747322 y[1] (numeric) -1.025190313074896 absolute error 1.638689184346731e-13 relative error 1.5984243739408774e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8199999999996903 y[1] (closed_form) -1.0414268183790636 y[1] (numeric) -1.0414268183792292 absolute error 1.6564527527407336e-13 relative error 1.59056087620149e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.829999999999689 y[1] (closed_form) -1.057741180352748 y[1] (numeric) -1.057741180352915 absolute error 1.6719958750854857e-13 relative error 1.5807230598017266e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.839999999999688 y[1] (closed_form) -1.0741327675648504 y[1] (numeric) -1.0741327675650192 absolute error 1.687538997430238e-13 relative error 1.571071145381805e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.849999999999687 y[1] (closed_form) -1.0906009408619752 y[1] (numeric) -1.0906009408621462 absolute error 1.709743457922741e-13 relative error 1.567707668188344e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.859999999999686 y[1] (closed_form) -1.107145053432184 y[1] (numeric) -1.1071450534323566 absolute error 1.7252865802674933e-13 relative error 1.5583202715118955e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.869999999999685 y[1] (closed_form) -1.1237644508696722 y[1] (numeric) -1.1237644508698468 absolute error 1.745270594710746e-13 relative error 1.553057309616882e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8799999999996837 y[1] (closed_form) -1.1404584712402124 y[1] (numeric) -1.140458471240389 absolute error 1.765254609153999e-13 relative error 1.5478464614624156e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8899999999996826 y[1] (closed_form) -1.1572264451473462 y[1] (numeric) -1.1572264451475247 absolute error 1.7852386235972517e-13 relative error 1.542687372107144e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.8999999999996815 y[1] (closed_form) -1.1740676957993221 y[1] (numeric) -1.1740676957995029 absolute error 1.8074430840897548e-13 relative error 1.5394709270654293e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9099999999996804 y[1] (closed_form) -1.1909815390767768 y[1] (numeric) -1.1909815390769594 absolute error 1.8252066524837574e-13 relative error 1.5325230430512114e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9199999999996793 y[1] (closed_form) -1.207967283601144 y[1] (numeric) -1.2079672836013284 absolute error 1.8451906669270102e-13 relative error 1.527517087570618e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.929999999999678 y[1] (closed_form) -1.2250242308037924 y[1] (numeric) -1.2250242308039785 absolute error 1.8607337892717624e-13 relative error 1.518936313652223e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.939999999999677 y[1] (closed_form) -1.242151674995882 y[1] (numeric) -1.2421516749960704 absolute error 1.8829382497642655e-13 relative error 1.515868220980749e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.949999999999676 y[1] (closed_form) -1.259348903438934 y[1] (numeric) -1.259348903439124 absolute error 1.900701818158268e-13 relative error 1.5092734134027323e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.959999999999675 y[1] (closed_form) -1.2766151964161012 y[1] (numeric) -1.276615196416293 absolute error 1.9184653865522705e-13 relative error 1.5027749880606652e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.969999999999674 y[1] (closed_form) -1.2939498273041417 y[1] (numeric) -1.293949827304335 absolute error 1.9340085088970227e-13 relative error 1.494654945722587e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9799999999996727 y[1] (closed_form) -1.311352062646078 y[1] (numeric) -1.311352062646274 absolute error 1.9606538614880265e-13 relative error 1.4951391905631898e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9899999999996716 y[1] (closed_form) -1.3288211622245454 y[1] (numeric) -1.328821162224743 absolute error 1.9761969838327786e-13 relative error 1.4871805477002474e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.9999999999996705 y[1] (closed_form) -1.346356379135809 y[1] (numeric) -1.346356379136009 absolute error 1.9984014443252818e-13 relative error 1.4843034691958778e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.009999999999674 y[1] (closed_form) -1.363956959864466 y[1] (numeric) -1.3639569598646601 absolute error 1.9406698470447736e-13 relative error 1.4228233765071402e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.019999999999677 y[1] (closed_form) -1.3816221443587695 y[1] (numeric) -1.3816221443589571 absolute error 1.8762769116165146e-13 relative error 1.3580246373999175e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.0299999999996805 y[1] (closed_form) -1.399351166106657 y[1] (numeric) -1.3993511661068387 absolute error 1.816324868286756e-13 relative error 1.2979764567175969e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.039999999999684 y[1] (closed_form) -1.4171432522123952 y[1] (numeric) -1.4171432522125706 absolute error 1.7541523789077473e-13 relative error 1.2378087932671768e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.049999999999687 y[1] (closed_form) -1.4349976234738664 y[1] (numeric) -1.434997623474036 absolute error 1.6964207816272392e-13 relative error 1.1821767185373557e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.0599999999996905 y[1] (closed_form) -1.45291349446049 y[1] (numeric) -1.4529134944606539 absolute error 1.638689184346731e-13 relative error 1.1278642469730967e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.069999999999694 y[1] (closed_form) -1.4708900735917636 y[1] (numeric) -1.4708900735919217 absolute error 1.580957587066223e-13 relative error 1.0748305501890333e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.079999999999697 y[1] (closed_form) -1.4889265632164213 y[1] (numeric) -1.4889265632165734 absolute error 1.5210055437364645e-13 relative error 1.0215450387631915e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.0899999999997005 y[1] (closed_form) -1.5070221596921982 y[1] (numeric) -1.5070221596923443 absolute error 1.461053500406706e-13 relative error 9.694970249841043e-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) -1.5251760534661924 y[1] (numeric) -1.5251760534663328 absolute error 1.4033219031261979e-13 relative error 9.201048626071313e-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) -1.543387429155822 y[1] (numeric) -1.5433874291559562 absolute error 1.341149413747189e-13 relative error 8.689648421464402e-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) -1.56165546563036 y[1] (numeric) -1.5616554656304882 absolute error 1.2811973704174306e-13 relative error 8.204097501751304e-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) -1.57997933609305 y[1] (numeric) -1.5799793360931715 absolute error 1.2145839889399213e-13 relative error 7.687340974618864e-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) -1.5983582081637815 y[1] (numeric) -1.598358208163897 absolute error 1.1546319456101628e-13 relative error 7.2238622088137665e-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) -1.6167912439623295 y[1] (numeric) -1.616791243962439 absolute error 1.0946799022804043e-13 relative error 6.770694153424732e-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) -1.6352776001921425 y[1] (numeric) -1.6352776001922458 absolute error 1.0325074129013956e-13 relative error 6.313958026331906e-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) -1.653816428224669 y[1] (numeric) -1.6538164282247658 absolute error 9.681144774731365e-14 relative error 5.853820659602369e-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) -1.6724068741842215 y[1] (numeric) -1.6724068741843119 absolute error 9.037215420448774e-14 relative error 5.403718174057979e-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) -1.6910480790333628 y[1] (numeric) -1.691048079033447 absolute error 8.415490526658687e-14 relative error 4.976493945381583e-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) -1.7097391786588085 y[1] (numeric) -1.7097391786588865 absolute error 7.793765632868599e-14 relative error 4.558452967652269e-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) -1.7284793039578394 y[1] (numeric) -1.7284793039579107 absolute error 7.127631818093505e-14 relative error 4.1236431363527394e-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) -1.7472675809252087 y[1] (numeric) -1.7472675809252736 absolute error 6.483702463810914e-14 relative error 3.7107667621107466e-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) -1.766103130740543 y[1] (numeric) -1.7661031307406014 absolute error 5.839773109528323e-14 relative error 3.3065866924088707e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.239999999999751 y[1] (closed_form) -1.7849850698562237 y[1] (numeric) -1.7849850698562761 absolute error 5.240252676230739e-14 relative error 2.9357403401995003e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.249999999999754 y[1] (closed_form) -1.8039125100857412 y[1] (numeric) -1.8039125100857871 absolute error 4.596323321948148e-14 relative error 2.547974636380609e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.259999999999757 y[1] (closed_form) -1.8228845586925115 y[1] (numeric) -1.822884558692551 absolute error 3.952393967665557e-14 relative error 2.168208594898881e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.269999999999761 y[1] (closed_form) -1.841900318479151 y[1] (numeric) -1.841900318479184 absolute error 3.3084646133829665e-14 relative error 1.796223487335488e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.279999999999764 y[1] (closed_form) -1.860958887877194 y[1] (numeric) -1.8609588878772207 absolute error 2.6645352591003757e-14 relative error 1.4318076968050733e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.289999999999767 y[1] (closed_form) -1.8800593610372496 y[1] (numeric) -1.8800593610372698 absolute error 2.020605904817785e-14 relative error 1.0747564394472067e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.299999999999771 y[1] (closed_form) -1.8992008279195853 y[1] (numeric) -1.8992008279195989 absolute error 1.354472090042691e-14 relative error 7.131800229501801e-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) -1.9183823743851312 y[1] (numeric) -1.918382374385138 absolute error 6.8833827526759706e-15 relative error 3.588118221156089e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 4.319999999999777 y[1] (closed_form) -1.9376030822868913 y[1] (numeric) -1.937603082286892 absolute error 6.661338147750939e-16 relative error 3.43792710109068e-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) -1.9568620295617594 y[1] (numeric) -1.9568620295617538 absolute error 5.551115123125783e-15 relative error 2.836743234457341e-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) -1.9761582903227248 y[1] (numeric) -1.9761582903227124 absolute error 1.2434497875801753e-14 relative error 6.292258032513724e-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) -1.995490934951457 y[1] (numeric) -1.9954909349514385 absolute error 1.84297022087776e-14 relative error 9.235673230069535e-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) -2.0148590301912708 y[1] (numeric) -2.0148590301912463 absolute error 2.4424906541753444e-14 relative error 1.2122389792915082e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.369999999999794 y[1] (closed_form) -2.0342616392404493 y[1] (numeric) -2.034261639240418 absolute error 3.1530333899354446e-14 relative error 1.5499645321497194e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.379999999999797 y[1] (closed_form) -2.0536978218459225 y[1] (numeric) -2.0536978218458857 absolute error 3.68594044175552e-14 relative error 1.794782271542992e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.389999999999801 y[1] (closed_form) -2.0731666343972934 y[1] (numeric) -2.073166634397251 absolute error 4.263256414560601e-14 relative error 2.056398334714665e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.399999999999804 y[1] (closed_form) -2.092667130021198 y[1] (numeric) -2.092667130021148 absolute error 4.973799150320701e-14 relative error 2.3767751110375203e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 4.409999999999807 y[1] (closed_form) -2.1121983586759905 y[1] (numeric) -2.112198358675934 absolute error 5.639932965095795e-14 relative error 2.6701720233468643e-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) -2.131759367246748 y[1] (numeric) -2.1317593672466852 absolute error 6.261657858885883e-14 relative error 2.9373192655290468e-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) -2.151349199640581 y[1] (numeric) -2.151349199640512 absolute error 6.927791673660977e-14 relative error 3.220207893176236e-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) -2.170966896882242 y[1] (numeric) -2.1709668968821667 absolute error 7.549516567451064e-14 relative error 3.4774904114351247e-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) -2.1906114972100212 y[1] (numeric) -2.1906114972099395 absolute error 8.171241461241152e-14 relative error 3.730118951556725e-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) -2.210282036171923 y[1] (numeric) -2.2102820361718347 absolute error 8.837375276016246e-14 relative error 3.998302086064118e-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) -2.22997754672211 y[1] (numeric) -2.2299775467220155 absolute error 9.459100169806334e-14 relative error 4.241791664544094e-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) -2.249697059317607 y[1] (numeric) -2.2496970593175054 absolute error 1.0169642905566434e-13 relative error 4.520449926111899e-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) -2.2694396020152534 y[1] (numeric) -2.269439602015145 absolute error 1.0835776720341528e-13 relative error 4.774648644854616e-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) -2.289204200568899 y[1] (numeric) -2.289204200568783 absolute error 1.1590728377086634e-13 relative error 5.063212960296935e-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) -2.3089898785268246 y[1] (numeric) -2.308989878526703 absolute error 1.2168044349891716e-13 relative error 5.269856079947452e-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) -2.32879565732939 y[1] (numeric) -2.328795657329261 absolute error 1.2878587085651816e-13 relative error 5.5301490472636345e-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) -2.348620556406886 y[1] (numeric) -2.34862055640675 absolute error 1.3589129821411916e-13 relative error 5.7860048036885495e-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) -2.368463593277592 y[1] (numeric) -2.36846359327745 absolute error 1.4210854715202004e-13 relative error 6.000030887338382e-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) -2.388323783646024 y[1] (numeric) -2.3883237836458755 absolute error 1.4832579608992091e-13 relative error 6.210455931711496e-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) -2.4082001415013616 y[1] (numeric) -2.4082001415012066 absolute error 1.5498713423767185e-13 relative error 6.4358078702315455e-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) -2.4280916792160494 y[1] (numeric) -2.428091679215888 absolute error 1.6120438317557273e-13 relative error 6.639139063629603e-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) -2.4479974076445594 y[1] (numeric) -2.4479974076443907 absolute error 1.687538997430238e-13 relative error 6.893548956222027e-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) -2.4679163362223027 y[1] (numeric) -2.4679163362221272 absolute error 1.7541523789077473e-13 relative error 7.1078275756822025e-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) -2.4878474730646882 y[1] (numeric) -2.4878474730645066 absolute error 1.816324868286756e-13 relative error 7.300788685607369e-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) -2.5077898250663067 y[1] (numeric) -2.507789825066119 absolute error 1.8784973576657649e-13 relative error 7.490649092238409e-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) -2.527742398000244 y[1] (numeric) -2.5277423980000497 absolute error 1.9406698470447736e-13 relative error 7.677482676162266e-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) -2.5477041966175 y[1] (numeric) -2.547704196617299 absolute error 2.0117241206207837e-13 relative error 7.89622328719198e-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) -2.5676742247465145 y[1] (numeric) -2.5676742247463067 absolute error 2.078337502098293e-13 relative error 8.094241403632388e-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) -2.5876514853927834 y[1] (numeric) -2.5876514853925685 absolute error 2.149391775674303e-13 relative error 8.306341823107001e-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) -2.6076349808385557 y[1] (numeric) -2.607634980838334 absolute error 2.2160051571518125e-13 relative error 8.498141700949248e-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) -2.627623712742607 y[1] (numeric) -2.6276237127423787 absolute error 2.282618538629322e-13 relative error 8.687006924012028e-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) -2.647616682240071 y[1] (numeric) -2.647616682239836 absolute error 2.349231920106831e-13 relative error 8.873006186527027e-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) -2.6676128900423244 y[1] (numeric) -2.667612890042083 absolute error 2.4158453015843406e-13 relative error 9.056206433108107e-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) -2.687611336536918 y[1] (numeric) -2.687611336536669 absolute error 2.4868995751603507e-13 relative error 9.253196477303182e-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) -2.7076110218875336 y[1] (numeric) -2.707611021887278 absolute error 2.55351295663786e-13 relative error 9.430870741757254e-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) -2.7276109461339697 y[1] (numeric) -2.7276109461337086 absolute error 2.611244553918368e-13 relative error 9.573376135696568e-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) -2.7476101092921352 y[1] (numeric) -2.747610109291868 absolute error 2.673417043297377e-13 relative error 9.729972364915076e-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) -2.7676075114540466 y[1] (numeric) -2.767607511453772 absolute error 2.744471316873387e-13 relative error 9.916403628459208e-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) -2.7876021528878185 y[1] (numeric) -2.787602152887537 absolute error 2.815525590449397e-13 relative error 1.0100170096125987e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.759999999999924 y[1] (closed_form) -2.8075930341376365 y[1] (numeric) -2.8075930341373487 absolute error 2.877698079828406e-13 relative error 1.0249698032579363e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.769999999999928 y[1] (closed_form) -2.8275791561237016 y[1] (numeric) -2.827579156123407 absolute error 2.944311461305915e-13 relative error 1.0412834791660582e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.779999999999931 y[1] (closed_form) -2.847559520242137 y[1] (numeric) -2.8475595202418353 absolute error 3.015365734881925e-13 relative error 1.0589298356880418e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.789999999999934 y[1] (closed_form) -2.8675331284648475 y[1] (numeric) -2.8675331284645393 absolute error 3.0819791163594346e-13 relative error 1.0747841361502917e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.799999999999938 y[1] (closed_form) -2.887498983439322 y[1] (numeric) -2.887498983439007 absolute error 3.148592497836944e-13 relative error 1.0904220281617663e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.809999999999941 y[1] (closed_form) -2.9074560885883685 y[1] (numeric) -2.907456088588047 absolute error 3.2152058793144533e-13 relative error 1.1058484741812572e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.819999999999944 y[1] (closed_form) -2.927403448209769 y[1] (numeric) -2.927403448209441 absolute error 3.277378368693462e-13 relative error 1.119551311144939e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.829999999999948 y[1] (closed_form) -2.947340067575851 y[1] (numeric) -2.9473400675755173 absolute error 3.339550858072471e-13 relative error 1.133072798355165e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.839999999999951 y[1] (closed_form) -2.9672649530329585 y[1] (numeric) -2.9672649530326183 absolute error 3.4017233474514796e-13 relative error 1.1464171219271957e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.849999999999954 y[1] (closed_form) -2.9871771121008166 y[1] (numeric) -2.987177112100469 absolute error 3.4772185131259903e-13 relative error 1.1640483247679071e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.859999999999958 y[1] (closed_form) -3.0070755535717786 y[1] (numeric) -3.007075553571424 absolute error 3.5438318946034997e-13 relative error 1.1784977901184314e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.869999999999961 y[1] (closed_form) -3.026959287609946 y[1] (numeric) -3.0269592876095848 absolute error 3.610445276081009e-13 relative error 1.1927630777392375e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.879999999999964 y[1] (closed_form) -3.046827325850151 y[1] (numeric) -3.0468273258497827 absolute error 3.681499549657019e-13 relative error 1.2083059379250437e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.889999999999968 y[1] (closed_form) -3.0666786814967937 y[1] (numeric) -3.0666786814964184 absolute error 3.752553823233029e-13 relative error 1.2236540612730485e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.899999999999971 y[1] (closed_form) -3.0865123694225183 y[1] (numeric) -3.086512369422136 absolute error 3.823608096809039e-13 relative error 1.2388118494805936e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.909999999999974 y[1] (closed_form) -3.1063274062667268 y[1] (numeric) -3.1063274062663386 absolute error 3.8813396940895473e-13 relative error 1.2494947204403842e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.919999999999978 y[1] (closed_form) -3.1261228105339143 y[1] (numeric) -3.1261228105335195 absolute error 3.9479530755670567e-13 relative error 1.2628912281577258e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.929999999999981 y[1] (closed_form) -3.145897602691817 y[1] (numeric) -3.145897602691416 absolute error 4.0101255649460654e-13 relative error 1.274715859001502e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.939999999999984 y[1] (closed_form) -3.1656508052693644 y[1] (numeric) -3.1656508052689576 absolute error 4.0678571622265736e-13 relative error 1.284998697726056e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.949999999999988 y[1] (closed_form) -3.185381442954427 y[1] (numeric) -3.1853814429540135 absolute error 4.134470543704083e-13 relative error 1.2979514754344084e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.959999999999991 y[1] (closed_form) -3.2050885426913442 y[1] (numeric) -3.2050885426909246 absolute error 4.1966430330830917e-13 relative error 1.3093688293425833e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.969999999999994 y[1] (closed_form) -3.224771133778232 y[1] (numeric) -3.2247711337778058 absolute error 4.263256414560601e-13 relative error 1.322033793314706e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.979999999999998 y[1] (closed_form) -3.244428247964051 y[1] (numeric) -3.2444282479636173 absolute error 4.338751580235112e-13 relative error 1.3372931218182348e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.990000000000001 y[1] (closed_form) -3.2640589195454295 y[1] (numeric) -3.2640589195449894 absolute error 4.4009240696141205e-13 relative error 1.3482979866757482e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; Iterations 4900 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.0204081632654%