##############ECHO OF PROBLEM################# ##############temp/h2sinpostode.ode################# diff ( y , x , 2 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(5.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $array_y_init[1 + 1] = exact_soln_yp(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=false $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(2.0) - sin(c(x))) end def exact_soln_yp (x) x = c(x) return(neg( cos(c(x)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 1.9001665833531718 y[1] (numeric) 1.9001665833531718 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y[1] (closed_form) 1.8902216991628251 y[1] (numeric) 1.8902216991628251 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) 1.8802877927110806 y[1] (numeric) 1.8802877927110808 absolute error 2.220446049250313e-16 relative error 1.1809075492899826e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y[1] (closed_form) 1.870365857380305 y[1] (numeric) 1.8703658573803057 absolute error 6.661338147750939e-16 relative error 3.5615161180716937e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (closed_form) 1.8604568853557635 y[1] (numeric) 1.8604568853557641 absolute error 6.661338147750939e-16 relative error 3.5804850949164207e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y[1] (closed_form) 1.8505618675264008 y[1] (numeric) 1.8505618675264015 absolute error 6.661338147750939e-16 relative error 3.599630071625209e-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) 1.840681793385754 y[1] (numeric) 1.8406817933857549 absolute error 8.881784197001252e-16 relative error 4.825268674312294e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (closed_form) 1.8308176509330039 y[1] (numeric) 1.830817650933005 absolute error 1.1102230246251565e-15 relative error 6.064083029019167e-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) 1.8209704265741757 y[1] (numeric) 1.8209704265741766 absolute error 8.881784197001252e-16 relative error 4.877500516969247e-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) 1.8111411050234993 y[1] (numeric) 1.8111411050235005 absolute error 1.1102230246251565e-15 relative error 6.12996426145798e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y[1] (closed_form) 1.8013306692049387 y[1] (numeric) 1.8013306692049398 absolute error 1.1102230246251565e-15 relative error 6.163349370580475e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y[1] (closed_form) 1.7915401001539004 y[1] (numeric) 1.7915401001539015 absolute error 1.1102230246251565e-15 relative error 6.197031395109626e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y[1] (closed_form) 1.7817703769191306 y[1] (numeric) 1.7817703769191318 absolute error 1.1102230246251565e-15 relative error 6.231010679080036e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y[1] (closed_form) 1.7720224764648114 y[1] (numeric) 1.7720224764648127 absolute error 1.3322676295501878e-15 relative error 7.518344982892456e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y[1] (closed_form) 1.7622973735728653 y[1] (numeric) 1.7622973735728662 absolute error 8.881784197001252e-16 relative error 5.0398895953606316e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (closed_form) 1.752596040745477 y[1] (numeric) 1.752596040745478 absolute error 8.881784197001252e-16 relative error 5.0677874367577213e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (closed_form) 1.7429194481078447 y[1] (numeric) 1.7429194481078456 absolute error 8.881784197001252e-16 relative error 5.09592351307086e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (closed_form) 1.7332685633111686 y[1] (numeric) 1.7332685633111697 absolute error 1.1102230246251565e-15 relative error 6.405372185971168e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (closed_form) 1.7236443514358861 y[1] (numeric) 1.7236443514358872 absolute error 1.1102230246251565e-15 relative error 6.441137486977998e-14% 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) 1.7140477748951644 y[1] (numeric) 1.7140477748951652 absolute error 8.881784197001252e-16 relative error 5.181759999393532e-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) 1.7044797933386602 y[1] (numeric) 1.7044797933386613 absolute error 1.1102230246251565e-15 relative error 6.513559321524724e-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) 1.6949413635565564 y[1] (numeric) 1.6949413635565573 absolute error 8.881784197001252e-16 relative error 5.2401719540104236e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (closed_form) 1.6854334393838821 y[1] (numeric) 1.6854334393838828 absolute error 6.661338147750939e-16 relative error 3.9522997420687355e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (closed_form) 1.6759569716051315 y[1] (numeric) 1.6759569716051324 absolute error 8.881784197001252e-16 relative error 5.299529968537802e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (closed_form) 1.6665129078591854 y[1] (numeric) 1.6665129078591865 absolute error 1.1102230246251565e-15 relative error 6.661952748096966e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (closed_form) 1.6571021925445484 y[1] (numeric) 1.6571021925445495 absolute error 1.1102230246251565e-15 relative error 6.69978610625313e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (closed_form) 1.64772576672491 y[1] (numeric) 1.6477257667249108 absolute error 8.881784197001252e-16 relative error 5.3903291290122054e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (closed_form) 1.6383845680350377 y[1] (numeric) 1.6383845680350388 absolute error 1.1102230246251565e-15 relative error 6.776327403746724e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (closed_form) 1.6290795305870172 y[1] (numeric) 1.629079530587018 absolute error 8.881784197001252e-16 relative error 5.452026147428677e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (closed_form) 1.6198115848768384 y[1] (numeric) 1.6198115848768393 absolute error 8.881784197001252e-16 relative error 5.4832205670862484e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (closed_form) 1.6105816576913492 y[1] (numeric) 1.6105816576913505 absolute error 1.3322676295501878e-15 relative error 8.271965740997547e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (closed_form) 1.6013906720155768 y[1] (numeric) 1.6013906720155782 absolute error 1.3322676295501878e-15 relative error 8.319441675486597e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (closed_form) 1.5922395469404296 y[1] (numeric) 1.5922395469404307 absolute error 1.1102230246251565e-15 relative error 6.97271353898041e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (closed_form) 1.583129197570789 y[1] (numeric) 1.5831291975707902 absolute error 1.1102230246251565e-15 relative error 7.012839042629768e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (closed_form) 1.5740605349340002 y[1] (numeric) 1.5740605349340013 absolute error 1.1102230246251565e-15 relative error 7.053242235513565e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (closed_form) 1.5650344658887696 y[1] (numeric) 1.565034465888771 absolute error 1.3322676295501878e-15 relative error 8.512704726880277e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (closed_form) 1.55605189303448 y[1] (numeric) 1.556051893034481 absolute error 1.1102230246251565e-15 relative error 7.134871462802529e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (closed_form) 1.5471137146209315 y[1] (numeric) 1.5471137146209326 absolute error 1.1102230246251565e-15 relative error 7.176091932564761e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (closed_form) 1.538220824458517 y[1] (numeric) 1.5382208244585176 absolute error 6.661338147750939e-16 relative error 4.3305473712435646e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (closed_form) 1.5293741118288418 y[1] (numeric) 1.5293741118288424 absolute error 6.661338147750939e-16 relative error 4.355597558654397e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y[1] (closed_form) 1.5205744613957968 y[1] (numeric) 1.520574461395798 absolute error 1.3322676295501878e-15 relative error 8.761607296279628e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (closed_form) 1.5118227531170922 y[1] (numeric) 1.5118227531170936 absolute error 1.3322676295501878e-15 relative error 8.812326886887397e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (closed_form) 1.503119862156263 y[1] (numeric) 1.5031198621562643 absolute error 1.3322676295501878e-15 relative error 8.863349245076282e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (closed_form) 1.4944666587951527 y[1] (numeric) 1.494466658795154 absolute error 1.3322676295501878e-15 relative error 8.914669468934618e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y[1] (closed_form) 1.4858640083468866 y[1] (numeric) 1.485864008346888 absolute error 1.3322676295501878e-15 relative error 8.966282392373283e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (closed_form) 1.4773127710693406 y[1] (numeric) 1.4773127710693421 absolute error 1.5543122344752192e-15 relative error 1.0521213008604421e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y[1] (closed_form) 1.4688138020791164 y[1] (numeric) 1.468813802079118 absolute error 1.5543122344752192e-15 relative error 1.0582091700629986e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (closed_form) 1.4603679512660306 y[1] (numeric) 1.4603679512660321 absolute error 1.5543122344752192e-15 relative error 1.0643291871255773e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (closed_form) 1.451976063208126 y[1] (numeric) 1.451976063208128 absolute error 1.9984014443252818e-15 relative error 1.3763322240380702e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (closed_form) 1.443638977087216 y[1] (numeric) 1.4436389770872178 absolute error 1.7763568394002505e-15 relative error 1.2304716536431764e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (closed_form) 1.4353575266049643 y[1] (numeric) 1.4353575266049663 absolute error 1.9984014443252818e-15 relative error 1.3922673670385657e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (closed_form) 1.4271325398995183 y[1] (numeric) 1.4271325398995203 absolute error 1.9984014443252818e-15 relative error 1.4002914154462385e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (closed_form) 1.4189648394626946 y[1] (numeric) 1.4189648394626964 absolute error 1.7763568394002505e-15 relative error 1.2518681154022716e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (closed_form) 1.41085524205773 y[1] (numeric) 1.4108552420577323 absolute error 2.220446049250313e-15 relative error 1.5738298182964513e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (closed_form) 1.4028045586376074 y[1] (numeric) 1.4028045586376092 absolute error 1.7763568394002505e-15 relative error 1.2662896113806716e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (closed_form) 1.3948135942639601 y[1] (numeric) 1.3948135942639615 absolute error 1.3322676295501878e-15 relative error 9.551581910507708e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (closed_form) 1.3868831480265658 y[1] (numeric) 1.386883148026567 absolute error 1.3322676295501878e-15 relative error 9.606199566603056e-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) 1.3790140129634398 y[1] (numeric) 1.379014012963441 absolute error 1.1102230246251565e-15 relative error 8.050846577253676e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (closed_form) 1.371206975981531 y[1] (numeric) 1.371206975981532 absolute error 8.881784197001252e-16 relative error 6.477347586890399e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (closed_form) 1.3634628177780317 y[1] (numeric) 1.3634628177780321 absolute error 4.440892098500626e-16 relative error 3.257068722811033e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (closed_form) 1.3557823127623085 y[1] (numeric) 1.355782312762309 absolute error 4.440892098500626e-16 relative error 3.275520012834973e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (closed_form) 1.3481662289784628 y[1] (numeric) 1.3481662289784635 absolute error 6.661338147750939e-16 relative error 4.941036205007443e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (closed_form) 1.3406153280285265 y[1] (numeric) 1.340615328028527 absolute error 4.440892098500626e-16 relative error 3.3125774453371985e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (closed_form) 1.3331303649963018 y[1] (numeric) 1.3331303649963022 absolute error 4.440892098500626e-16 relative error 3.3311761663406005e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (closed_form) 1.3257120883718545 y[1] (numeric) 1.325712088371855 absolute error 4.440892098500626e-16 relative error 3.349816402409527e-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) 1.3183612399766655 y[1] (numeric) 1.3183612399766655 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (closed_form) 1.3110785548894484 y[1] (numeric) 1.3110785548894484 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (closed_form) 1.3038647613726428 y[1] (numeric) 1.303864761372643 absolute error 2.220446049250313e-16 relative error 1.7029726663620695e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (closed_form) 1.2967205807995894 y[1] (numeric) 1.2967205807995899 absolute error 4.440892098500626e-16 relative error 3.4247101220235624e-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) 1.2896467275823917 y[1] (numeric) 1.289646727582392 absolute error 2.220446049250313e-16 relative error 1.7217475156261003e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (closed_form) 1.2826439091004769 y[1] (numeric) 1.282643909100477 absolute error 2.220446049250313e-16 relative error 1.731147696953179e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (closed_form) 1.275712825629857 y[1] (numeric) 1.275712825629857 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] 0.8200000000000006 y[1] (closed_form) 1.2688541702731038 y[1] (numeric) 1.2688541702731038 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] 0.8300000000000006 y[1] (closed_form) 1.262068628890037 y[1] (numeric) 1.262068628890037 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] 0.8400000000000006 y[1] (closed_form) 1.2553568800291401 y[1] (numeric) 1.2553568800291406 absolute error 4.440892098500626e-16 relative error 3.5375534791329944e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (closed_form) 1.2487195948597067 y[1] (numeric) 1.2487195948597072 absolute error 4.440892098500626e-16 relative error 3.5563565405566964e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (closed_form) 1.2421574371047226 y[1] (numeric) 1.2421574371047228 absolute error 2.220446049250313e-16 relative error 1.7875721570575068e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (closed_form) 1.2356710629744945 y[1] (numeric) 1.235671062974495 absolute error 4.440892098500626e-16 relative error 3.593911220847527e-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) 1.2292611211010303 y[1] (numeric) 1.2292611211010307 absolute error 4.440892098500626e-16 relative error 3.612651553254192e-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) 1.2229282524731757 y[1] (numeric) 1.2229282524731762 absolute error 4.440892098500626e-16 relative error 3.6313594763385635e-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) 1.2166730903725163 y[1] (numeric) 1.2166730903725167 absolute error 4.440892098500626e-16 relative error 3.650029028866687e-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) 1.210496260310049 y[1] (numeric) 1.2104962603100498 absolute error 6.661338147750939e-16 relative error 5.502981187273346e-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) 1.2043983799636335 y[1] (numeric) 1.204398379963634 absolute error 4.440892098500626e-16 relative error 3.687228555251559e-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) 1.1983800591162224 y[1] (numeric) 1.198380059116223 absolute error 6.661338147750939e-16 relative error 5.5586189849182926e-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) 1.1924418995948853 y[1] (numeric) 1.1924418995948862 absolute error 8.881784197001252e-16 relative error 7.4483999597957e-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) 1.1865844952106257 y[1] (numeric) 1.186584495210627 absolute error 1.3322676295501878e-15 relative error 1.1227751878838621e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (closed_form) 1.1808084316990013 y[1] (numeric) 1.1808084316990028 absolute error 1.5543122344752192e-15 relative error 1.316311937440016e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (closed_form) 1.1751142866615494 y[1] (numeric) 1.1751142866615507 absolute error 1.3322676295501878e-15 relative error 1.1337345181421499e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (closed_form) 1.169502629508029 y[1] (numeric) 1.16950262950803 absolute error 8.881784197001252e-16 relative error 7.594496987781484e-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) 1.1639740213994791 y[1] (numeric) 1.1639740213994798 absolute error 6.661338147750939e-16 relative error 5.722926822491985e-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) 1.1585290151921033 y[1] (numeric) 1.158529015192104 absolute error 6.661338147750939e-16 relative error 5.749824182561694e-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) 1.153168155381985 y[1] (numeric) 1.153168155381985 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] 1.0199999999999985 y[1] (closed_form) 1.1478919780506378 y[1] (numeric) 1.1478919780506374 absolute error 4.440892098500626e-16 relative error 3.8687369399010835e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0299999999999974 y[1] (closed_form) 1.142701010811398 y[1] (numeric) 1.1427010108113969 absolute error 1.1102230246251565e-15 relative error 9.715778791836547e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0399999999999963 y[1] (closed_form) 1.1375957727566635 y[1] (numeric) 1.137595772756662 absolute error 1.5543122344752192e-15 relative error 1.366313300117803e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0499999999999952 y[1] (closed_form) 1.1325767744059854 y[1] (numeric) 1.1325767744059834 absolute error 1.9984014443252818e-15 relative error 1.764473269702537e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.059999999999994 y[1] (closed_form) 1.1276445176550167 y[1] (numeric) 1.127644517655014 absolute error 2.6645352591003757e-15 relative error 2.362921308429173e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.069999999999993 y[1] (closed_form) 1.1227994957253218 y[1] (numeric) 1.1227994957253185 absolute error 3.3306690738754696e-15 relative error 2.966397016168837e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y[1] (closed_form) 1.1180421931150564 y[1] (numeric) 1.1180421931150528 absolute error 3.552713678800501e-15 relative error 3.177620398119354e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y[1] (closed_form) 1.113373085550517 y[1] (numeric) 1.113373085550513 absolute error 3.9968028886505635e-15 relative error 3.5898145379312e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0999999999999897 y[1] (closed_form) 1.1087926399385695 y[1] (numeric) 1.108792639938565 absolute error 4.440892098500626e-15 relative error 4.005160152169359e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y[1] (closed_form) 1.1043013143199576 y[1] (numeric) 1.1043013143199523 absolute error 5.329070518200751e-15 relative error 4.82573954146062e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y[1] (closed_form) 1.0998995578235005 y[1] (numeric) 1.0998995578234947 absolute error 5.773159728050814e-15 relative error 5.248806299617793e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1299999999999863 y[1] (closed_form) 1.09558781062118 y[1] (numeric) 1.095587810621174 absolute error 5.995204332975845e-15 relative error 5.472134935105443e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y[1] (closed_form) 1.091366503884123 y[1] (numeric) 1.0913665038841165 absolute error 6.439293542825908e-15 relative error 5.900211816936621e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y[1] (closed_form) 1.0872360597394854 y[1] (numeric) 1.0872360597394788 absolute error 6.661338147750939e-15 relative error 6.12685542213075e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.159999999999983 y[1] (closed_form) 1.0831968912282397 y[1] (numeric) 1.083196891228233 absolute error 6.661338147750939e-15 relative error 6.149702054810766e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.169999999999982 y[1] (closed_form) 1.0792494022638714 y[1] (numeric) 1.0792494022638646 absolute error 6.8833827526759706e-15 relative error 6.377935200369021e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1799999999999808 y[1] (closed_form) 1.075393987591987 y[1] (numeric) 1.0753939875919798 absolute error 7.105427357601002e-15 relative error 6.607278299473679e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1899999999999797 y[1] (closed_form) 1.0716310327508407 y[1] (numeric) 1.0716310327508336 absolute error 7.105427357601002e-15 relative error 6.630479279198932e-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) 1.0679609140327813 y[1] (numeric) 1.067960914032774 absolute error 7.327471962526033e-15 relative error 6.861179904849135e-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) 1.0643839984466221 y[1] (numeric) 1.0643839984466148 absolute error 7.327471962526033e-15 relative error 6.884237242592763e-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) 1.0609006436809405 y[1] (numeric) 1.0609006436809332 absolute error 7.327471962526033e-15 relative error 6.906840905574684e-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) 1.0575111980683107 y[1] (numeric) 1.057511198068303 absolute error 7.771561172376096e-15 relative error 7.348916197362182e-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) 1.0542160005504693 y[1] (numeric) 1.054216000550461 absolute error 8.215650382226158e-15 relative error 7.793137628281372e-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) 1.0510153806444222 y[1] (numeric) 1.0510153806444138 absolute error 8.43769498715119e-15 relative error 8.028136545421133e-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) 1.047909658409493 y[1] (numeric) 1.047909658409484 absolute error 8.881784197001252e-15 relative error 8.475715559757258e-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) 1.0448991444153164 y[1] (numeric) 1.0448991444153075 absolute error 8.881784197001252e-15 relative error 8.500135390551155e-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) 1.0419841397107836 y[1] (numeric) 1.0419841397107747 absolute error 8.881784197001252e-15 relative error 8.523914960420135e-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) 1.039164935793936 y[1] (numeric) 1.039164935793927 absolute error 9.103828801926284e-15 relative error 8.760715925206651e-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) 1.0364418145828158 y[1] (numeric) 1.0364418145828067 absolute error 9.103828801926284e-15 relative error 8.783733610352954e-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) 1.0338150483872746 y[1] (numeric) 1.0338150483872655 absolute error 9.103828801926284e-15 relative error 8.806051736360413e-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) 1.0312848998817432 y[1] (numeric) 1.031284899881734 absolute error 9.103828801926284e-15 relative error 8.827656453585439e-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) 1.0288516220789639 y[1] (numeric) 1.028851622078955 absolute error 8.881784197001252e-15 relative error 8.632716327991151e-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) 1.0265154583046892 y[1] (numeric) 1.0265154583046798 absolute error 9.325873406851315e-15 relative error 9.084980972671548e-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) 1.0242766421733491 y[1] (numeric) 1.02427664217334 absolute error 9.103828801926284e-15 relative error 8.88805663146768e-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) 1.0221353975646918 y[1] (numeric) 1.022135397564683 absolute error 8.881784197001252e-15 relative error 8.689439988246876e-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) 1.0200919386013938 y[1] (numeric) 1.0200919386013851 absolute error 8.659739592076221e-15 relative error 8.489175597200812e-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) 1.018146469627648 y[1] (numeric) 1.0181464696276397 absolute error 8.43769498715119e-15 relative error 8.287309575641887e-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) 1.016299185188731 y[1] (numeric) 1.016299185188723 absolute error 7.993605777301127e-15 relative error 7.865406067226828e-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) 1.0145502700115472 y[1] (numeric) 1.0145502700115396 absolute error 7.549516567451064e-15 relative error 7.441244451460388e-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) 1.0128998989861566 y[1] (numeric) 1.0128998989861495 absolute error 7.105427357601002e-15 relative error 7.014935399552362e-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) 1.0113482371482871 y[1] (numeric) 1.01134823714828 absolute error 7.105427357601002e-15 relative error 7.025698069772955e-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) 1.0098954396628288 y[1] (numeric) 1.0098954396628221 absolute error 6.661338147750939e-15 relative error 6.596067163126257e-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) 1.00854165180832 y[1] (numeric) 1.0085416518083135 absolute error 6.439293542825908e-15 relative error 6.384757170197408e-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) 1.0072870089624173 y[1] (numeric) 1.0072870089624113 absolute error 5.995204332975845e-15 relative error 5.951833270590241e-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) 1.0061316365883606 y[1] (numeric) 1.0061316365883546 absolute error 5.995204332975845e-15 relative error 5.958667946576724e-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) 1.0050756502224243 y[1] (numeric) 1.0050756502224187 absolute error 5.551115123125783e-15 relative error 5.52308189129576e-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) 1.0041191554623645 y[1] (numeric) 1.0041191554623594 absolute error 5.10702591327572e-15 relative error 5.08607557727957e-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) 1.003262247956861 y[1] (numeric) 1.0032622479568563 absolute error 4.6629367034256575e-15 relative error 4.647774510524748e-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) 1.0025050133959494 y[1] (numeric) 1.0025050133959452 absolute error 4.218847493575595e-15 relative error 4.2083056315942017e-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) 1.0018475275024552 y[1] (numeric) 1.0018475275024517 absolute error 3.552713678800501e-15 relative error 3.5461620468907074e-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) 1.0012898560244199 y[1] (numeric) 1.0012898560244166 absolute error 3.3306690738754696e-15 relative error 3.326378524496147e-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) 1.0008320547285263 y[1] (numeric) 1.0008320547285237 absolute error 2.6645352591003757e-15 relative error 2.6623200631030206e-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) 1.0004741693945227 y[1] (numeric) 1.0004741693945205 absolute error 2.220446049250313e-15 relative error 2.2193936806925315e-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) 1.0002162358106443 y[1] (numeric) 1.0002162358106423 absolute error 1.9984014443252818e-15 relative error 1.9979694117898808e-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) 1.0000582797700344 y[1] (numeric) 1.0000582797700333 absolute error 1.1102230246251565e-15 relative error 1.1101583248532824e-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) 1.0000003170681655 y[1] (numeric) 1.0000003170681653 absolute error 2.220446049250313e-16 relative error 2.220445345217781e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5799999999999368 y[1] (closed_form) 1.0000423535012595 y[1] (numeric) 1.0000423535012597 absolute error 2.220446049250313e-16 relative error 2.2203520095686792e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5899999999999357 y[1] (closed_form) 1.000184384865708 y[1] (numeric) 1.0001843848657088 absolute error 8.881784197001252e-16 relative error 8.880146832320108e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5999999999999346 y[1] (closed_form) 1.0004263969584928 y[1] (numeric) 1.0004263969584943 absolute error 1.5543122344752192e-15 relative error 1.5536497629417377e-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) 1.0007683655786068 y[1] (numeric) 1.000768365578609 absolute error 2.220446049250313e-15 relative error 2.218741244849935e-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) 1.0012102565294727 y[1] (numeric) 1.0012102565294756 absolute error 2.886579864025407e-15 relative error 2.883090584820067e-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) 1.0017520256223635 y[1] (numeric) 1.001752025622367 absolute error 3.552713678800501e-15 relative error 3.5465001197210344e-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) 1.0023936186808216 y[1] (numeric) 1.0023936186808258 absolute error 4.218847493575595e-15 relative error 4.2087732951928784e-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) 1.0031349715460756 y[1] (numeric) 1.0031349715460804 absolute error 4.884981308350689e-15 relative error 4.869714890730747e-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) 1.003976010083457 y[1] (numeric) 1.0039760100834625 absolute error 5.551115123125783e-15 relative error 5.529131241556597e-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) 1.0049166501898126 y[1] (numeric) 1.0049166501898188 absolute error 6.217248937900877e-15 relative error 6.186830456761303e-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) 1.005956797801916 y[1] (numeric) 1.0059567978019228 absolute error 6.8833827526759706e-15 relative error 6.842622633215094e-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) 1.0070963489058724 y[1] (numeric) 1.0070963489058804 absolute error 7.993605777301127e-15 relative error 7.937280068570921e-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) 1.0083351895475214 y[1] (numeric) 1.0083351895475303 absolute error 8.881784197001252e-15 relative error 8.808364806733412e-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) 1.0096731958438312 y[1] (numeric) 1.009673195843841 absolute error 9.769962616701378e-15 relative error 9.676361278994004e-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) 1.0111102339952869 y[1] (numeric) 1.0111102339952973 absolute error 1.0436096431476471e-14 relative error 1.0321423006707613e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7299999999999203 y[1] (closed_form) 1.012646160299271 y[1] (numeric) 1.0126461602992822 absolute error 1.1324274851176597e-14 relative error 1.1182854678311222e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7399999999999192 y[1] (closed_form) 1.0142808211644327 y[1] (numeric) 1.0142808211644454 absolute error 1.2656542480726785e-14 relative error 1.247834151709247e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.749999999999918 y[1] (closed_form) 1.0160140531260486 y[1] (numeric) 1.016014053126062 absolute error 1.3322676295501878e-14 relative error 1.3112688997274176e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.759999999999917 y[1] (closed_form) 1.0178456828623659 y[1] (numeric) 1.0178456828623805 absolute error 1.4654943925052066e-14 relative error 1.4398001751935242e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7699999999999159 y[1] (closed_form) 1.0197755272119378 y[1] (numeric) 1.0197755272119537 absolute error 1.5987211554602254e-14 relative error 1.5677186918096796e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7799999999999148 y[1] (closed_form) 1.0218033931919375 y[1] (numeric) 1.021803393191955 absolute error 1.7541523789077473e-14 relative error 1.716722013838766e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7899999999999137 y[1] (closed_form) 1.023929078017457 y[1] (numeric) 1.0239290780174755 absolute error 1.84297022087776e-14 relative error 1.7999002669658914e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7999999999999126 y[1] (closed_form) 1.0261523691217849 y[1] (numeric) 1.0261523691218046 absolute error 1.9761969838327786e-14 relative error 1.925831916681217e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8099999999999115 y[1] (closed_form) 1.0284730441776637 y[1] (numeric) 1.0284730441776846 absolute error 2.0872192862952943e-14 relative error 2.0294350912854235e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8199999999999104 y[1] (closed_form) 1.0308908711195215 y[1] (numeric) 1.0308908711195433 absolute error 2.1760371282653068e-14 relative error 2.110831698317578e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8299999999999093 y[1] (closed_form) 1.0334056081666791 y[1] (numeric) 1.0334056081667016 absolute error 2.2426505097428162e-14 relative error 2.170155156910177e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8399999999999082 y[1] (closed_form) 1.0360170038475274 y[1] (numeric) 1.0360170038475514 absolute error 2.398081733190338e-14 relative error 2.3147127163786094e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.849999999999907 y[1] (closed_form) 1.0387247970246745 y[1] (numeric) 1.0387247970246996 absolute error 2.5091040356528538e-14 relative error 2.415561891696373e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.859999999999906 y[1] (closed_form) 1.041528716921059 y[1] (numeric) 1.041528716921085 absolute error 2.5979218776228663e-14 relative error 2.4943353317254447e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8699999999999048 y[1] (closed_form) 1.044428483147028 y[1] (numeric) 1.0444284831470552 absolute error 2.708944180085382e-14 relative error 2.5937095969681957e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8799999999999037 y[1] (closed_form) 1.0474238057283753 y[1] (numeric) 1.0474238057284035 absolute error 2.8199664825478976e-14 relative error 2.692287942211607e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8899999999999026 y[1] (closed_form) 1.050514385135339 y[1] (numeric) 1.050514385135368 absolute error 2.90878432451791e-14 relative error 2.76891432014343e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8999999999999015 y[1] (closed_form) 1.0536999123125537 y[1] (numeric) 1.0536999123125843 absolute error 3.064215547965432e-14 relative error 2.9080533386781845e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9099999999999004 y[1] (closed_form) 1.0569800687099562 y[1] (numeric) 1.0569800687099886 absolute error 3.241851231905457e-14 relative error 3.0670883282237626e-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) 1.0603545263146406 y[1] (numeric) 1.060354526314674 absolute error 3.352873534367973e-14 relative error 3.162030671025843e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9299999999998982 y[1] (closed_form) 1.0638229476836583 y[1] (numeric) 1.0638229476836931 absolute error 3.4861002973229915e-14 relative error 3.2769553476107465e-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) 1.0673849859777624 y[1] (numeric) 1.0673849859777989 absolute error 3.6415315207705135e-14 relative error 3.4116383203898466e-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) 1.0710402849960923 y[1] (numeric) 1.0710402849961302 absolute error 3.7969627442180354e-14 relative error 3.545116647252805e-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) 1.0747884792117919 y[1] (numeric) 1.0747884792118314 absolute error 3.952393967665557e-14 relative error 3.677369123424257e-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) 1.0786291938085633 y[1] (numeric) 1.0786291938086046 absolute error 4.1300296516055823e-14 relative error 3.828961496047349e-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) 1.0825620447181474 y[1] (numeric) 1.0825620447181898 absolute error 4.241051954068098e-14 relative error 3.917606362388481e-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) 1.0865866386587308 y[1] (numeric) 1.0865866386587744 absolute error 4.3520742565306136e-14 relative error 4.0052712795205734e-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) 1.0907025731742728 y[1] (numeric) 1.0907025731743183 absolute error 4.551914400963142e-14 relative error 4.1733782544545586e-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) 1.0949094366747523 y[1] (numeric) 1.0949094366747991 absolute error 4.6851411639181606e-14 relative error 4.279021631366123e-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) 1.0992068084773243 y[1] (numeric) 1.099206808477373 absolute error 4.8627768478581856e-14 relative error 4.423896222581031e-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) 1.1035942588483902 y[1] (numeric) 1.1035942588484404 absolute error 5.0182080713057076e-14 relative error 4.54714949001479e-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) 1.108071349046569 y[1] (numeric) 1.1080713490466212 absolute error 5.218048215738236e-14 relative error 4.709126556000264e-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) 1.1126376313665718 y[1] (numeric) 1.1126376313666257 absolute error 5.395683899678261e-14 relative error 4.849453000300857e-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) 1.1172926491839714 y[1] (numeric) 1.1172926491840272 absolute error 5.573319583618286e-14 relative error 4.988236150742448e-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) 1.122035937000866 y[1] (numeric) 1.1220359370009232 absolute error 5.728750807065808e-14 relative error 5.105674977201187e-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) 1.1268670204924258 y[1] (numeric) 1.1268670204924849 absolute error 5.906386491005833e-14 relative error 5.2414227975407614e-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) 1.1317854165543282 y[1] (numeric) 1.1317854165543886 absolute error 6.039613253960852e-14 relative error 5.3363589648894694e-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) 1.1367906333510656 y[1] (numeric) 1.1367906333511275 absolute error 6.195044477408373e-14 relative error 5.449591416096063e-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) 1.141882170365129 y[1] (numeric) 1.1418821703651925 absolute error 6.350475700855895e-14 relative error 5.5614106828774314e-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) 1.1470595184470598 y[1] (numeric) 1.1470595184471253 absolute error 6.550315845288424e-14 relative error 5.710528302974664e-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) 1.1523221598663647 y[1] (numeric) 1.1523221598664317 absolute error 6.705747068735946e-14 relative error 5.819333605034215e-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) 1.157669568363287 y[1] (numeric) 1.1576695683633558 absolute error 6.88338275267597e-14 relative error 5.945895910875239e-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) 1.1631012092014335 y[1] (numeric) 1.163101209201504 absolute error 7.061018436615996e-14 relative error 6.0708546949787605e-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) 1.1686165392212464 y[1] (numeric) 1.168616539221319 absolute error 7.260858581048524e-14 relative error 6.213208813463382e-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) 1.1742150068943198 y[1] (numeric) 1.1742150068943944 absolute error 7.460698725481052e-14 relative error 6.353775655800761e-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) 1.179896052378552 y[1] (numeric) 1.1798960523786284 absolute error 7.638334409421077e-14 relative error 6.4737350328640915e-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) 1.1856591075741285 y[1] (numeric) 1.185659107574207 absolute error 7.838174553853605e-14 relative error 6.610816299375118e-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) 1.1915035961803326 y[1] (numeric) 1.1915035961804128 absolute error 8.01581023779363e-14 relative error 6.7274746492501956e-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) 1.1974289337531738 y[1] (numeric) 1.197428933753256 absolute error 8.215650382226158e-14 relative error 6.861075551661633e-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) 1.2034345277638328 y[1] (numeric) 1.2034345277639165 absolute error 8.37108160567368e-14 relative error 6.955992546788934e-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) 1.209519777657913 y[1] (numeric) 1.2095197776579985 absolute error 8.548717289613705e-14 relative error 7.067860689444244e-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) 1.2156840749154958 y[1] (numeric) 1.2156840749155833 absolute error 8.748557434046234e-14 relative error 7.1964070391021284e-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) 1.2219268031119928 y[1] (numeric) 1.2219268031120822 absolute error 8.948397578478762e-14 relative error 7.323186262621509e-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) 1.2282473379797865 y[1] (numeric) 1.228247337979878 absolute error 9.14823772291129e-14 relative error 7.44820480373135e-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) 1.2346450474706572 y[1] (numeric) 1.2346450474707504 absolute error 9.325873406851315e-14 relative error 7.553485453942142e-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) 1.2411192918189868 y[1] (numeric) 1.2411192918190823 absolute error 9.547918011776346e-14 relative error 7.692989767150343e-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) 1.2476694236057364 y[1] (numeric) 1.247669423605834 absolute error 9.769962616701378e-14 relative error 7.830569886425851e-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) 1.2542947878231852 y[1] (numeric) 1.2542947878232849 absolute error 9.969802761133906e-14 relative error 7.948532400773496e-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) 1.2609947219404325 y[1] (numeric) 1.2609947219405346 absolute error 1.021405182655144e-13 relative error 8.099995700881242e-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) 1.26776855596965 y[1] (numeric) 1.2677685559697542 absolute error 1.0413891970983968e-13 relative error 8.214347896504599e-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) 1.27461561253308 y[1] (numeric) 1.2746156125331862 absolute error 1.0613732115416497e-13 relative error 8.327006205677587e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3399999999998533 y[1] (closed_form) 1.281535206930772 y[1] (numeric) 1.28153520693088 absolute error 1.0813572259849025e-13 relative error 8.437982976485772e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.349999999999852 y[1] (closed_form) 1.2885266472090517 y[1] (numeric) 1.2885266472091623 absolute error 1.1057821325266559e-13 relative error 8.581756030593388e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.359999999999851 y[1] (closed_form) 1.2955892342297182 y[1] (numeric) 1.2955892342298307 absolute error 1.1257661469699087e-13 relative error 8.689221222490504e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.36999999999985 y[1] (closed_form) 1.3027222617399548 y[1] (numeric) 1.3027222617400696 absolute error 1.1479706074624119e-13 relative error 8.812090198943465e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.379999999999849 y[1] (closed_form) 1.3099250164429543 y[1] (numeric) 1.3099250164430711 absolute error 1.1679546219056647e-13 relative error 8.916194493919932e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.389999999999848 y[1] (closed_form) 1.317196778069249 y[1] (numeric) 1.3171967780693679 absolute error 1.1879386363489175e-13 relative error 9.01868768681777e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.3999999999998467 y[1] (closed_form) 1.3245368194487361 y[1] (numeric) 1.324536819448857 absolute error 1.2079226507921703e-13 relative error 9.119585299976032e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4099999999998456 y[1] (closed_form) 1.331944406583394 y[1] (numeric) 1.331944406583517 absolute error 1.2301271112846734e-13 relative error 9.235573986455675e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4199999999998445 y[1] (closed_form) 1.3394187987206827 y[1] (numeric) 1.3394187987208075 absolute error 1.247890679678676e-13 relative error 9.316657947988875e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4299999999998434 y[1] (closed_form) 1.3469592484276165 y[1] (numeric) 1.3469592484277435 absolute error 1.270095140171179e-13 relative error 9.42935090021346e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4399999999998423 y[1] (closed_form) 1.3545650016655089 y[1] (numeric) 1.354565001665638 absolute error 1.2922996006636822e-13 relative error 9.540329176338765e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.449999999999841 y[1] (closed_form) 1.3622352978653738 y[1] (numeric) 1.3622352978655057 absolute error 1.318944953254686e-13 relative error 9.682210961068739e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.45999999999984 y[1] (closed_form) 1.3699693700039837 y[1] (numeric) 1.3699693700041176 absolute error 1.3389289676979388e-13 relative error 9.773422654654282e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.469999999999839 y[1] (closed_form) 1.377766444680569 y[1] (numeric) 1.3777664446807054 absolute error 1.3633538742396922e-13 relative error 9.895391773427765e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.479999999999838 y[1] (closed_form) 1.3856257421941605 y[1] (numeric) 1.385625742194299 absolute error 1.3855583347321954e-13 relative error 9.999513523313602e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 2.489999999999837 y[1] (closed_form) 1.3935464766215553 y[1] (numeric) 1.3935464766216963 absolute error 1.4099832412739488e-13 relative error 1.0117949167309023e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.4999999999998357 y[1] (closed_form) 1.401527855895912 y[1] (numeric) 1.401527855896055 absolute error 1.432187701766452e-13 relative error 1.0218760160503132e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5099999999998346 y[1] (closed_form) 1.4095690818859536 y[1] (numeric) 1.4095690818860995 absolute error 1.4588330543574557e-13 relative error 1.0349496687353475e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5199999999998335 y[1] (closed_form) 1.4176693504757827 y[1] (numeric) 1.417669350475931 absolute error 1.4832579608992091e-13 relative error 1.0462650972890217e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5299999999998324 y[1] (closed_form) 1.4258278516452902 y[1] (numeric) 1.4258278516454406 absolute error 1.503241975342462e-13 relative error 1.0542941587287989e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5399999999998313 y[1] (closed_form) 1.434043769551158 y[1] (numeric) 1.4340437695513109 absolute error 1.5276668818842154e-13 relative error 1.065286091206519e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.54999999999983 y[1] (closed_form) 1.4423162826084421 y[1] (numeric) 1.4423162826085973 absolute error 1.5520917884259688e-13 relative error 1.0761105640567246e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.559999999999829 y[1] (closed_form) 1.4506445635727305 y[1] (numeric) 1.450644563572888 absolute error 1.574296248918472e-13 relative error 1.0852391333140939e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.569999999999828 y[1] (closed_form) 1.459027779622867 y[1] (numeric) 1.4590277796230269 absolute error 1.5987211554602254e-13 relative error 1.0957441508574063e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.579999999999827 y[1] (closed_form) 1.4674650924442323 y[1] (numeric) 1.4674650924443946 absolute error 1.6231460620019789e-13 relative error 1.1060883630958758e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5899999999998258 y[1] (closed_form) 1.4759556583125755 y[1] (numeric) 1.4759556583127407 absolute error 1.652011860642233e-13 relative error 1.1192828533419074e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.5999999999998247 y[1] (closed_form) 1.4844986281783856 y[1] (numeric) 1.4844986281785528 absolute error 1.6719958750854857e-13 relative error 1.126303415407784e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6099999999998236 y[1] (closed_form) 1.4930931477517946 y[1] (numeric) 1.4930931477519642 absolute error 1.6964207816272392e-13 relative error 1.1361788004864951e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6199999999998225 y[1] (closed_form) 1.5017383575880074 y[1] (numeric) 1.5017383575881798 absolute error 1.723066134218243e-13 relative error 1.1473810504419142e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6299999999998214 y[1] (closed_form) 1.5104333931732448 y[1] (numeric) 1.5104333931734197 absolute error 1.7497114868092467e-13 relative error 1.1584168456003919e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6399999999998203 y[1] (closed_form) 1.519177385011194 y[1] (numeric) 1.5191773850113715 absolute error 1.7741363933510002e-13 relative error 1.1678270166837215e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.649999999999819 y[1] (closed_form) 1.527969458709958 y[1] (numeric) 1.5279694587101378 absolute error 1.7985612998927536e-13 relative error 1.1770924409780104e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.659999999999818 y[1] (closed_form) 1.5368087350694934 y[1] (numeric) 1.5368087350696757 absolute error 1.822986206434507e-13 relative error 1.1862154117389714e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.669999999999817 y[1] (closed_form) 1.5456943301695305 y[1] (numeric) 1.5456943301697155 absolute error 1.8496315590255108e-13 relative error 1.1966347569008969e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.679999999999816 y[1] (closed_form) 1.5546253554579639 y[1] (numeric) 1.5546253554581513 absolute error 1.8740564655672642e-13 relative error 1.2054714397831251e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6899999999998148 y[1] (closed_form) 1.563600917839707 y[1] (numeric) 1.563600917839897 absolute error 1.900701818158268e-13 relative error 1.2155926723196762e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.6999999999998137 y[1] (closed_form) 1.5726201197660017 y[1] (numeric) 1.5726201197661938 absolute error 1.9206858326015208e-13 relative error 1.2213285385712283e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7099999999998126 y[1] (closed_form) 1.5816820593241707 y[1] (numeric) 1.5816820593243657 absolute error 1.949551631241775e-13 relative error 1.232581238276667e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7199999999998115 y[1] (closed_form) 1.5907858303278104 y[1] (numeric) 1.590785830328008 absolute error 1.9761969838327786e-13 relative error 1.2422772105189969e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7299999999998104 y[1] (closed_form) 1.5999305224074067 y[1] (numeric) 1.5999305224076068 absolute error 2.000621890374532e-13 relative error 1.2504429800890399e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7399999999998093 y[1] (closed_form) 1.609115221101372 y[1] (numeric) 1.609115221101575 absolute error 2.0294876890147862e-13 relative error 1.2612444792024817e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.749999999999808 y[1] (closed_form) 1.6183390079474909 y[1] (numeric) 1.6183390079476967 absolute error 2.0583534876550402e-13 relative error 1.2718926489114364e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.759999999999807 y[1] (closed_form) 1.6276009605747654 y[1] (numeric) 1.6276009605749733 absolute error 2.078337502098293e-13 relative error 1.2769330766211615e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.769999999999806 y[1] (closed_form) 1.6369001527956508 y[1] (numeric) 1.6369001527958613 absolute error 2.1049828546892968e-13 relative error 1.2859567830659742e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.779999999999805 y[1] (closed_form) 1.6462356546986745 y[1] (numeric) 1.6462356546988877 absolute error 2.1316282072803006e-13 relative error 1.2948499816513037e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7899999999998037 y[1] (closed_form) 1.6556065327414258 y[1] (numeric) 1.6556065327416418 absolute error 2.1604940059205546e-13 relative error 1.3049561977404825e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.7999999999998026 y[1] (closed_form) 1.6650118498439093 y[1] (numeric) 1.6650118498441278 absolute error 2.184918912462308e-13 relative error 1.3122542717441554e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8099999999998015 y[1] (closed_form) 1.6744506654822522 y[1] (numeric) 1.6744506654824736 absolute error 2.2137847111025621e-13 relative error 1.3220961099292696e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8199999999998004 y[1] (closed_form) 1.6839220357827571 y[1] (numeric) 1.6839220357829812 absolute error 2.240430063693566e-13 relative error 1.3304832504624364e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8299999999997993 y[1] (closed_form) 1.693425013616286 y[1] (numeric) 1.6934250136165128 absolute error 2.2670754162845697e-13 relative error 1.3387515821815227e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8399999999997982 y[1] (closed_form) 1.702958648692975 y[1] (numeric) 1.7029586486932045 absolute error 2.2937207688755734e-13 relative error 1.346903385256013e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.849999999999797 y[1] (closed_form) 1.7125219876572613 y[1] (numeric) 1.712521987657493 absolute error 2.318145675417327e-13 relative error 1.3536443281458604e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.859999999999796 y[1] (closed_form) 1.7221140741832173 y[1] (numeric) 1.7221140741834517 absolute error 2.3447910280083306e-13 relative error 1.361577065747194e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.869999999999795 y[1] (closed_form) 1.7317339490701844 y[1] (numeric) 1.731733949070421 absolute error 2.3669954885008337e-13 relative error 1.3668355290786664e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.879999999999794 y[1] (closed_form) 1.7413806503386902 y[1] (numeric) 1.7413806503389293 absolute error 2.391420395042587e-13 relative error 1.373289863176938e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8899999999997927 y[1] (closed_form) 1.7510532133266465 y[1] (numeric) 1.7510532133268886 absolute error 2.4202861936828413e-13 relative error 1.382188830849285e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.8999999999997916 y[1] (closed_form) 1.7607506707858154 y[1] (numeric) 1.76075067078606 absolute error 2.446931546273845e-13 relative error 1.3897092796118544e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9099999999997905 y[1] (closed_form) 1.7704720529785318 y[1] (numeric) 1.770472052978779 absolute error 2.4713564528155985e-13 relative error 1.3958743085822465e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9199999999997894 y[1] (closed_form) 1.7802163877746777 y[1] (numeric) 1.7802163877749273 absolute error 2.495781359357352e-13 relative error 1.4019539290260951e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9299999999997883 y[1] (closed_form) 1.7899827007488938 y[1] (numeric) 1.7899827007491462 absolute error 2.524647157997606e-13 relative error 1.4104310376526784e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9399999999997872 y[1] (closed_form) 1.7997700152780212 y[1] (numeric) 1.7997700152782767 absolute error 2.5557334026871104e-13 relative error 1.4200333270316824e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.949999999999786 y[1] (closed_form) 1.8095773526387628 y[1] (numeric) 1.809577352639021 absolute error 2.582378755278114e-13 relative error 1.4270618227579145e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.959999999999785 y[1] (closed_form) 1.8194037321055556 y[1] (numeric) 1.8194037321058167 absolute error 2.611244553918368e-13 relative error 1.4352199612652397e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.969999999999784 y[1] (closed_form) 1.8292481710486417 y[1] (numeric) 1.8292481710489055 absolute error 2.637889906509372e-13 relative error 1.4420623446610666e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.979999999999783 y[1] (closed_form) 1.8391096850323299 y[1] (numeric) 1.8391096850325965 absolute error 2.666755705149626e-13 relative error 1.4500253719792394e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9899999999997817 y[1] (closed_form) 1.8489872879134401 y[1] (numeric) 1.8489872879137093 absolute error 2.6911806116913795e-13 relative error 1.455488974577183e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 2.9999999999997806 y[1] (closed_form) 1.8588799919399155 y[1] (numeric) 1.8588799919401873 absolute error 2.717825964282383e-13 relative error 1.4620771518693238e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0099999999997795 y[1] (closed_form) 1.8687868078495975 y[1] (numeric) 1.8687868078498715 absolute error 2.7400304247748863e-13 relative error 1.4662081374214238e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0199999999997784 y[1] (closed_form) 1.8787067449691504 y[1] (numeric) 1.878706744969427 absolute error 2.76667577736589e-13 relative error 1.472649089473153e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0299999999997773 y[1] (closed_form) 1.888638811313129 y[1] (numeric) 1.8886388113134085 absolute error 2.795541576006144e-13 relative error 1.48018856716307e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.039999999999776 y[1] (closed_form) 1.8985820136831755 y[1] (numeric) 1.898582013683458 absolute error 2.824407374646398e-13 relative error 1.4876404360152752e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.049999999999775 y[1] (closed_form) 1.908535357767339 y[1] (numeric) 1.9085353577676238 absolute error 2.8488322811881517e-13 relative error 1.492679855049057e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.059999999999774 y[1] (closed_form) 1.9184978482395056 y[1] (numeric) 1.9184978482397934 absolute error 2.877698079828406e-13 relative error 1.4999746194498485e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.069999999999773 y[1] (closed_form) 1.9284684888589299 y[1] (numeric) 1.9284684888592207 absolute error 2.90878432451791e-13 relative error 1.5083390479660007e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.079999999999772 y[1] (closed_form) 1.938446282569859 y[1] (numeric) 1.9384462825701527 absolute error 2.937650123158164e-13 relative error 1.515466355489423e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0899999999997707 y[1] (closed_form) 1.9484302316012365 y[1] (numeric) 1.948430231601533 absolute error 2.964295475749168e-13 relative error 1.5213762482596487e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.0999999999997696 y[1] (closed_form) 1.9584193375664791 y[1] (numeric) 1.9584193375667782 absolute error 2.9909408283401717e-13 relative error 1.527221862533638e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1099999999997685 y[1] (closed_form) 1.9684126015633148 y[1] (numeric) 1.9684126015636167 absolute error 3.019806626980426e-13 relative error 1.5341329478291763e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1199999999997674 y[1] (closed_form) 1.9784090242736714 y[1] (numeric) 1.978409024273976 absolute error 3.0464519795714295e-13 relative error 1.5398494154614293e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1299999999997663 y[1] (closed_form) 1.9884076060636082 y[1] (numeric) 1.9884076060639153 absolute error 3.070876886113183e-13 relative error 1.5443900318770692e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.139999999999765 y[1] (closed_form) 1.9984073470832782 y[1] (numeric) 1.9984073470835884 absolute error 3.1019631308026874e-13 relative error 1.5522176373751198e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.149999999999764 y[1] (closed_form) 2.008407247366913 y[1] (numeric) 2.0084072473672263 absolute error 3.135269821541442e-13 relative error 1.5610727483939737e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.159999999999763 y[1] (closed_form) 2.0184063069328166 y[1] (numeric) 2.0184063069331324 absolute error 3.157474282033945e-13 relative error 1.5643402773706468e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.169999999999762 y[1] (closed_form) 2.0284035258833657 y[1] (numeric) 2.0284035258836837 absolute error 3.1796787425264483e-13 relative error 1.5675770141159188e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.179999999999761 y[1] (closed_form) 2.038397904504996 y[1] (numeric) 2.038397904505317 absolute error 3.2107649872159527e-13 relative error 1.5751414285306842e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1899999999997597 y[1] (closed_form) 2.0483884433681743 y[1] (numeric) 2.0483884433684976 absolute error 3.232969447708456e-13 relative error 1.578299007776313e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.1999999999997586 y[1] (closed_form) 2.058374143427339 y[1] (numeric) 2.058374143427665 absolute error 3.2596148002994596e-13 relative error 1.583587129049323e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2099999999997575 y[1] (closed_form) 2.068354006120806 y[1] (numeric) 2.068354006121135 absolute error 3.290701044988964e-13 relative error 1.5909757397674238e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2199999999997564 y[1] (closed_form) 2.078327033470622 y[1] (numeric) 2.0783270334709543 absolute error 3.3217872896784684e-13 relative error 1.5982986489529407e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2299999999997553 y[1] (closed_form) 2.0882922281823637 y[1] (numeric) 2.088292228182698 absolute error 3.3439917501709715e-13 relative error 1.6013045037674447e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.239999999999754 y[1] (closed_form) 2.098248593744864 y[1] (numeric) 2.098248593745201 absolute error 3.3706371027619753e-13 relative error 1.606405033612441e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.249999999999753 y[1] (closed_form) 2.108195134529863 y[1] (numeric) 2.108195134530203 absolute error 3.397282455352979e-13 relative error 1.611464897015137e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.259999999999752 y[1] (closed_form) 2.1181308558915712 y[1] (numeric) 2.1181308558919136 absolute error 3.423927807943983e-13 relative error 1.616485496361258e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.269999999999751 y[1] (closed_form) 2.1280547642661327 y[1] (numeric) 2.1280547642664778 absolute error 3.4505731605349865e-13 relative error 1.6214682152340796e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.27999999999975 y[1] (closed_form) 2.1379658672709794 y[1] (numeric) 2.1379658672713266 absolute error 3.4727776210274897e-13 relative error 1.6243372610341715e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2899999999997487 y[1] (closed_form) 2.14786317380407 y[1] (numeric) 2.14786317380442 absolute error 3.4994229736184934e-13 relative error 1.629257867213526e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.2999999999997476 y[1] (closed_form) 2.1577456941429993 y[1] (numeric) 2.157745694143351 absolute error 3.517186542012496e-13 relative error 1.630028298311322e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3099999999997465 y[1] (closed_form) 2.1676124400439685 y[1] (numeric) 2.1676124400443233 absolute error 3.5482727867020003e-13 relative error 1.6369498168362728e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3199999999997454 y[1] (closed_form) 2.1774624248406096 y[1] (numeric) 2.177462424840967 absolute error 3.574918139293004e-13 relative error 1.6417817816326675e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3299999999997443 y[1] (closed_form) 2.187294663542652 y[1] (numeric) 2.1872946635430113 absolute error 3.5926817076870066e-13 relative error 1.6425229611579263e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.339999999999743 y[1] (closed_form) 2.1971081729344184 y[1] (numeric) 2.19710817293478 absolute error 3.6148861681795097e-13 relative error 1.6452927592324836e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.349999999999742 y[1] (closed_form) 2.2069019716731475 y[1] (numeric) 2.206901971673512 absolute error 3.645972412869014e-13 relative error 1.652077192221114e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.359999999999741 y[1] (closed_form) 2.2166750803871267 y[1] (numeric) 2.216675080387495 absolute error 3.681499549657019e-13 relative error 1.6608205605911675e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.36999999999974 y[1] (closed_form) 2.2264265217736297 y[1] (numeric) 2.226426521774 absolute error 3.703704010149522e-13 relative error 1.663519534073397e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3799999999997388 y[1] (closed_form) 2.236155320696643 y[1] (numeric) 2.2361553206970166 absolute error 3.7347902548390266e-13 relative error 1.6701837391489894e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3899999999997377 y[1] (closed_form) 2.2458605042843827 y[1] (numeric) 2.2458605042847593 absolute error 3.765876499528531e-13 relative error 1.676807839286743e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.3999999999997366 y[1] (closed_form) 2.2555411020265765 y[1] (numeric) 2.2555411020269562 absolute error 3.7969627442180354e-13 relative error 1.6833932845677298e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 3.4099999999997355 y[1] (closed_form) 2.265196145871518 y[1] (numeric) 2.2651961458719008 absolute error 3.82804898890754e-13 relative error 1.689941507221983e-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) 2.2748246703228685 y[1] (numeric) 2.2748246703232535 absolute error 3.850253449400043e-13 relative error 1.6925495400283187e-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) 2.2844257125362066 y[1] (numeric) 2.2844257125365943 absolute error 3.8768988019910466e-13 relative error 1.6970999672766118e-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) 2.2939983124153116 y[1] (numeric) 2.293998312415702 absolute error 3.9035441545820504e-13 relative error 1.7016334028912496e-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) 2.303541512708173 y[1] (numeric) 2.303541512708566 absolute error 3.930189507173054e-13 relative error 1.7061509356315018e-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) 2.313054359102714 y[1] (numeric) 2.3130543591031096 absolute error 3.956834859764058e-13 relative error 1.71065364036624e-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) 2.3225359003222223 y[1] (numeric) 2.322535900322621 absolute error 3.9879211044535623e-13 relative error 1.7170546659366122e-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) 2.3319851882204774 y[1] (numeric) 2.331985188220879 absolute error 4.014566457044566e-13 relative error 1.7215231371636865e-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) 2.341401277876564 y[1] (numeric) 2.341401277876968 absolute error 4.04121180963557e-13 relative error 1.725980013686752e-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) 2.3507832276893628 y[1] (numeric) 2.3507832276897696 absolute error 4.0678571622265736e-13 relative error 1.73042631677484e-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) 2.360130099471711 y[1] (numeric) 2.3601300994721206 absolute error 4.0945025148175773e-13 relative error 1.7348630551061935e-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) 2.36944095854422 y[1] (numeric) 2.3694409585446317 absolute error 4.1167069753100805e-13 relative error 1.737416988790207e-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) 2.378714873828741 y[1] (numeric) 2.3787148738291557 absolute error 4.147793219999585e-13 relative error 1.743711810791078e-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) 2.387950917941473 y[1] (numeric) 2.387950917941891 absolute error 4.178879464689089e-13 relative error 1.749985493123737e-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) 2.397148167285703 y[1] (numeric) 2.3971481672861237 absolute error 4.205524817280093e-13 relative error 1.7543866810878108e-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) 2.40630570214416 y[1] (numeric) 2.4063057021445835 absolute error 4.2366110619695974e-13 relative error 1.7606287755518877e-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) 2.4154226067709894 y[1] (numeric) 2.4154226067714157 absolute error 4.263256414560601e-13 relative error 1.765014702855602e-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) 2.424497969483326 y[1] (numeric) 2.4244979694837547 absolute error 4.285460875053104e-13 relative error 1.767566287533893e-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) 2.4335308827524615 y[1] (numeric) 2.4335308827528923 absolute error 4.3076653355456074e-13 relative error 1.7701297181293188e-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) 2.4425204432945966 y[1] (numeric) 2.44252044329503 absolute error 4.334310688136611e-13 relative error 1.7745238120874317e-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) 2.451465752161168 y[1] (numeric) 2.451465752161604 absolute error 4.360956040727615e-13 relative error 1.7789177910737995e-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) 2.460365914828743 y[1] (numeric) 2.460365914829182 absolute error 4.3920422854171193e-13 relative error 1.7851175140031288e-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) 2.469220041288472 y[1] (numeric) 2.469220041288914 absolute error 4.418687638008123e-13 relative error 1.789507441265701e-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) 2.4780272461350883 y[1] (numeric) 2.478027246135533 absolute error 4.445332990599127e-13 relative error 1.7938999651970704e-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) 2.4867866486554453 y[1] (numeric) 2.486786648655893 absolute error 4.476419235288631e-13 relative error 1.8000817391025238e-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) 2.4954973729165912 y[1] (numeric) 2.4954973729170415 absolute error 4.503064587879635e-13 relative error 1.8044757877732072e-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) 2.5041585478533586 y[1] (numeric) 2.50415854785381 absolute error 4.516387264175137e-13 relative error 1.803554838030013e-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) 2.5127693073554713 y[1] (numeric) 2.512769307355925 absolute error 4.53859172466764e-13 relative error 1.806211064176129e-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) 2.5213287903541546 y[1] (numeric) 2.521328790354611 absolute error 4.565237077258644e-13 relative error 1.8106472645391855e-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) 2.529836140908242 y[1] (numeric) 2.529836140908701 absolute error 4.591882429849647e-13 relative error 1.8150908494022487e-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) 2.5382905082897667 y[1] (numeric) 2.5382905082902285 absolute error 4.618527782440651e-13 relative error 1.8195426281416834e-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) 2.5466910470690367 y[1] (numeric) 2.5466910470695003 absolute error 4.636291350834654e-13 relative error 1.820515824316624e-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) 2.5550369171991747 y[1] (numeric) 2.5550369171996405 absolute error 4.658495811327157e-13 relative error 1.8232596875483854e-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) 2.5633272841001213 y[1] (numeric) 2.5633272841005894 absolute error 4.68070027181966e-13 relative error 1.8260252215365707e-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) 2.571561318742096 y[1] (numeric) 2.5715613187425665 absolute error 4.707345624410664e-13 relative error 1.8305399097826327e-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) 2.579738197728496 y[1] (numeric) 2.579738197728969 absolute error 4.729550084903167e-13 relative error 1.8333449840249747e-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) 2.5878571033782367 y[1] (numeric) 2.587857103378712 absolute error 4.75175454539567e-13 relative error 1.8361734653712684e-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) 2.5959172238075188 y[1] (numeric) 2.595917223807996 absolute error 4.773959005888173e-13 relative error 1.839025898863619e-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) 2.6039177530110162 y[1] (numeric) 2.603917753011496 absolute error 4.796163466380676e-13 relative error 1.841902825400179e-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) 2.611857890942476 y[1] (numeric) 2.6118578909429577 absolute error 4.818367926873179e-13 relative error 1.8448047819073708e-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) 2.619736843594721 y[1] (numeric) 2.6197368435952058 absolute error 4.849454171562684e-13 relative error 1.8511226360081323e-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) 2.6275538230790523 y[1] (numeric) 2.6275538230795394 absolute error 4.871658632055187e-13 relative error 1.854066161943134e-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) 2.6353080477040356 y[1] (numeric) 2.635308047704525 absolute error 4.89386309254769e-13 relative error 1.8570364465783723e-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) 2.64299874205367 y[1] (numeric) 2.642998742054162 absolute error 4.920508445138694e-13 relative error 1.8617142592036753e-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) 2.65062513706493 y[1] (numeric) 2.650625137065424 absolute error 4.942712905631197e-13 relative error 1.864734788980506e-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) 2.6581864701046687 y[1] (numeric) 2.658186470105165 absolute error 4.9649173661237e-13 relative error 1.8677837021449445e-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) 2.665681985045884 y[1] (numeric) 2.6656819850463833 absolute error 4.991562718714704e-13 relative error 1.8725274607836556e-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) 2.6731109323433278 y[1] (numeric) 2.673110932343829 absolute error 5.013767179207207e-13 relative error 1.8756300453314862e-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) 2.680472569108461 y[1] (numeric) 2.680472569108965 absolute error 5.03597163969971e-13 relative error 1.8787626098985596e-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) 2.6877661591837425 y[1] (numeric) 2.687766159184248 absolute error 5.053735208093713e-13 relative error 1.8802733976040905e-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) 2.694990973216242 y[1] (numeric) 2.6949909732167496 absolute error 5.075939668586216e-13 relative error 1.8834718628124064e-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) 2.702146288730577 y[1] (numeric) 2.7021462887310874 absolute error 5.102585021177219e-13 relative error 1.88834521745095e-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) 2.7092313902011593 y[1] (numeric) 2.709231390201671 absolute error 5.115907697472721e-13 relative error 1.8883243845380323e-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) 2.7162455691237453 y[1] (numeric) 2.7162455691242586 absolute error 5.133671265866724e-13 relative error 1.889987902501332e-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) 2.7231881240862883 y[1] (numeric) 2.723188124086804 absolute error 5.155875726359227e-13 relative error 1.893323373716305e-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) 2.7300583608390774 y[1] (numeric) 2.730058360839595 absolute error 5.17808018685173e-13 relative error 1.89669212245714e-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) 2.7368555923641624 y[1] (numeric) 2.7368555923646825 absolute error 5.200284647344233e-13 relative error 1.9000946421334932e-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) 2.743579138944056 y[1] (numeric) 2.7435791389445776 absolute error 5.218048215738236e-13 relative error 1.9019127757862124e-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) 2.7502283282297015 y[1] (numeric) 2.7502283282302256 absolute error 5.240252676230739e-13 relative error 1.9053882262945944e-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) 2.7568024953077126 y[1] (numeric) 2.756802495308239 absolute error 5.262457136723242e-13 relative error 1.908898858616221e-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) 2.7633009827668626 y[1] (numeric) 2.7633009827673876 absolute error 5.24913446042774e-13 relative error 1.899588388367249e-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) 2.769723140763818 y[1] (numeric) 2.7697231407643415 absolute error 5.235811784132238e-13 relative error 1.8903737009210016e-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) 2.776068327088131 y[1] (numeric) 2.7760683270886535 absolute error 5.226929999935237e-13 relative error 1.8828535122612994e-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) 2.782335907226456 y[1] (numeric) 2.7823359072269787 absolute error 5.226929999935237e-13 relative error 1.8786121353498437e-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) 2.788525254426003 y[1] (numeric) 2.788525254426525 absolute error 5.222489107836736e-13 relative error 1.8728498512062955e-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) 2.794635749757209 y[1] (numeric) 2.7946357497577305 absolute error 5.213607323639735e-13 relative error 1.8655766942409866e-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) 2.800666782175634 y[1] (numeric) 2.800666782176155 absolute error 5.209166431541234e-13 relative error 1.8599736550931677e-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) 2.8066177485830615 y[1] (numeric) 2.8066177485835815 absolute error 5.200284647344233e-13 relative error 1.8528653037876746e-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) 2.81248805388781 y[1] (numeric) 2.8124880538883295 absolute error 5.195843755245733e-13 relative error 1.8474189599004052e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.099999999999704 y[1] (closed_form) 2.81827711106424 y[1] (numeric) 2.8182771110647598 absolute error 5.195843755245733e-13 relative error 1.8436241542208295e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.109999999999707 y[1] (closed_form) 2.82398434121146 y[1] (numeric) 2.823984341211979 absolute error 5.191402863147232e-13 relative error 1.8383256547804278e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.119999999999711 y[1] (closed_form) 2.8296091736112094 y[1] (numeric) 2.829609173611729 absolute error 5.195843755245733e-13 relative error 1.8362407797168266e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.129999999999714 y[1] (closed_form) 2.835151045784936 y[1] (numeric) 2.835151045785456 absolute error 5.200284647344233e-13 relative error 1.8342178470792865e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.139999999999717 y[1] (closed_form) 2.8406094035500415 y[1] (numeric) 2.8406094035505607 absolute error 5.191402863147232e-13 relative error 1.827566597737547e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.149999999999721 y[1] (closed_form) 2.8459837010752973 y[1] (numeric) 2.8459837010758164 absolute error 5.191402863147232e-13 relative error 1.8241154582810034e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.159999999999724 y[1] (closed_form) 2.8512734009354297 y[1] (numeric) 2.8512734009359484 absolute error 5.186961971048731e-13 relative error 1.819173836275056e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.169999999999727 y[1] (closed_form) 2.8564779741648603 y[1] (numeric) 2.8564779741653785 absolute error 5.182521078950231e-13 relative error 1.814304582714463e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.179999999999731 y[1] (closed_form) 2.861596900310604 y[1] (numeric) 2.8615969003111217 absolute error 5.17808018685173e-13 relative error 1.80950719728893e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.189999999999734 y[1] (closed_form) 2.8666296674843115 y[1] (numeric) 2.8666296674848284 absolute error 5.169198402654729e-13 relative error 1.8032320188715198e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.199999999999737 y[1] (closed_form) 2.8715757724134594 y[1] (numeric) 2.8715757724139763 absolute error 5.169198402654729e-13 relative error 1.8001260674762545e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.209999999999741 y[1] (closed_form) 2.8764347204916767 y[1] (numeric) 2.8764347204921936 absolute error 5.169198402654729e-13 relative error 1.797085247869329e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.219999999999744 y[1] (closed_form) 2.881206025828204 y[1] (numeric) 2.881206025828722 absolute error 5.17808018685173e-13 relative error 1.797191919089954e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.229999999999747 y[1] (closed_form) 2.8858892112964853 y[1] (numeric) 2.885889211297003 absolute error 5.17808018685173e-13 relative error 1.7942754581786173e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.239999999999751 y[1] (closed_form) 2.890483808581875 y[1] (numeric) 2.890483808582394 absolute error 5.191402863147232e-13 relative error 1.7960325007647183e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.249999999999754 y[1] (closed_form) 2.894989358228474 y[1] (numeric) 2.894989358228994 absolute error 5.200284647344233e-13 relative error 1.796305272267541e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.259999999999757 y[1] (closed_form) 2.8994054096850714 y[1] (numeric) 2.8994054096855915 absolute error 5.200284647344233e-13 relative error 1.7935693401044868e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.269999999999761 y[1] (closed_form) 2.903731521350203 y[1] (numeric) 2.9037315213507227 absolute error 5.195843755245733e-13 relative error 1.7893678244845868e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.279999999999764 y[1] (closed_form) 2.9079672606163065 y[1] (numeric) 2.907967260616827 absolute error 5.204725539442734e-13 relative error 1.789815727959626e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.289999999999767 y[1] (closed_form) 2.9121122039129848 y[1] (numeric) 2.912112203913506 absolute error 5.213607323639735e-13 relative error 1.790318146613392e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.299999999999771 y[1] (closed_form) 2.916165936749363 y[1] (numeric) 2.916165936749885 absolute error 5.222489107836736e-13 relative error 1.790875149463621e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.309999999999774 y[1] (closed_form) 2.920128053755535 y[1] (numeric) 2.9201280537560583 absolute error 5.231370892033738e-13 relative error 1.7914868100752452e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.319999999999777 y[1] (closed_form) 2.9239981587231028 y[1] (numeric) 2.9239981587236272 absolute error 5.24469356832924e-13 relative error 1.7936719804979545e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.329999999999781 y[1] (closed_form) 2.9277758646447936 y[1] (numeric) 2.927775864645319 absolute error 5.253575352526241e-13 relative error 1.7943912360120574e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.339999999999784 y[1] (closed_form) 2.931460793753164 y[1] (numeric) 2.9314607937536907 absolute error 5.266898028821743e-13 relative error 1.7966803581495308e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.349999999999787 y[1] (closed_form) 2.935052577558374 y[1] (numeric) 2.9350525775589014 absolute error 5.275779813018744e-13 relative error 1.797507769829318e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.359999999999791 y[1] (closed_form) 2.9385508568850356 y[1] (numeric) 2.9385508568855645 absolute error 5.289102489314246e-13 relative error 1.799901634141148e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.369999999999794 y[1] (closed_form) 2.9419552819081316 y[1] (numeric) 2.9419552819086627 absolute error 5.311306949806749e-13 relative error 1.8053663094300577e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.379999999999797 y[1] (closed_form) 2.9452655121879974 y[1] (numeric) 2.94526551218853 absolute error 5.324629626102251e-13 relative error 1.8078606509559323e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.389999999999801 y[1] (closed_form) 2.9484812167043626 y[1] (numeric) 2.948481216704897 absolute error 5.342393194496253e-13 relative error 1.811913592743746e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.399999999999804 y[1] (closed_form) 2.9516020738894557 y[1] (numeric) 2.9516020738899913 absolute error 5.355715870791755e-13 relative error 1.814511487903345e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.409999999999807 y[1] (closed_form) 2.954627771660159 y[1] (numeric) 2.954627771660696 absolute error 5.369038547087257e-13 relative error 1.8171624184221615e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.419999999999811 y[1] (closed_form) 2.9575580074492165 y[1] (numeric) 2.957558007449755 absolute error 5.38680211548126e-13 relative error 1.8213682037388593e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.429999999999814 y[1] (closed_form) 2.9603924882354917 y[1] (numeric) 2.9603924882360317 absolute error 5.400124791776761e-13 relative error 1.8241246095700792e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.439999999999817 y[1] (closed_form) 2.9631309305732674 y[1] (numeric) 2.9631309305738096 absolute error 5.422329252269265e-13 relative error 1.8299323854785666e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.449999999999821 y[1] (closed_form) 2.9657730606205925 y[1] (numeric) 2.9657730606211365 absolute error 5.440092820663267e-13 relative error 1.834291670153926e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.459999999999824 y[1] (closed_form) 2.9683186141666633 y[1] (numeric) 2.9683186141672095 absolute error 5.46229728115577e-13 relative error 1.840199113089238e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.4699999999998274 y[1] (closed_form) 2.970767336658247 y[1] (numeric) 2.9707673366587946 absolute error 5.475619957451272e-13 relative error 1.843166878093752e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.479999999999831 y[1] (closed_form) 2.9731189832251346 y[1] (numeric) 2.9731189832256844 absolute error 5.497824417943775e-13 relative error 1.8491773955107337e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.489999999999834 y[1] (closed_form) 2.97537331870463 y[1] (numeric) 2.9753733187051816 absolute error 5.515587986337778e-13 relative error 1.853746537170356e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.4999999999998375 y[1] (closed_form) 2.977530117665063 y[1] (numeric) 2.9775301176656166 absolute error 5.537792446830281e-13 relative error 1.8598611023195762e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.509999999999841 y[1] (closed_form) 2.9795891644283348 y[1] (numeric) 2.9795891644288908 absolute error 5.559996907322784e-13 relative error 1.8660280328914163e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.519999999999844 y[1] (closed_form) 2.981550253091486 y[1] (numeric) 2.9815502530920432 absolute error 5.573319583618286e-13 relative error 1.8692690414456262e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.5299999999998475 y[1] (closed_form) 2.983413187547283 y[1] (numeric) 2.9834131875478427 absolute error 5.595524044110789e-13 relative error 1.8755444493797954e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.539999999999851 y[1] (closed_form) 2.985177781503834 y[1] (numeric) 2.9851777815043956 absolute error 5.617728504603292e-13 relative error 1.8818740174909336e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.549999999999854 y[1] (closed_form) 2.986843858503213 y[1] (numeric) 2.986843858503776 absolute error 5.631051180898794e-13 relative error 1.8852847512828018e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.5599999999998575 y[1] (closed_form) 2.988411251939109 y[1] (numeric) 2.9884112519396746 absolute error 5.657696533489798e-13 relative error 1.8932121640951036e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.569999999999861 y[1] (closed_form) 2.989879805073484 y[1] (numeric) 2.989879805074052 absolute error 5.679900993982301e-13 relative error 1.8997088058002058e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.579999999999864 y[1] (closed_form) 2.991249371052249 y[1] (numeric) 2.9912493710528185 absolute error 5.693223670277803e-13 relative error 1.9032928933889133e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.5899999999998675 y[1] (closed_form) 2.992519812919947 y[1] (numeric) 2.9925198129205195 absolute error 5.724309914967307e-13 relative error 1.912872853925007e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.599999999999871 y[1] (closed_form) 2.99369100363345 y[1] (numeric) 2.9936910036340247 absolute error 5.74651437545981e-13 relative error 1.919541585449284e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.609999999999874 y[1] (closed_form) 2.9947628260746626 y[1] (numeric) 2.9947628260752404 absolute error 5.777600620149315e-13 relative error 1.929234786088958e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.6199999999998775 y[1] (closed_form) 2.995735173062234 y[1] (numeric) 2.995735173062815 absolute error 5.808686864838819e-13 relative error 1.9389854340499635e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.629999999999881 y[1] (closed_form) 2.9966079473622758 y[1] (numeric) 2.9966079473628593 absolute error 5.835332217429823e-13 relative error 1.9473125346831893e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.639999999999884 y[1] (closed_form) 2.9973810616980847 y[1] (numeric) 2.9973810616986714 absolute error 5.866418462119327e-13 relative error 1.9571813998170348e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.649999999999888 y[1] (closed_form) 2.9980544387588726 y[1] (numeric) 2.9980544387594614 absolute error 5.88862292261183e-13 relative error 1.9641480976741663e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.659999999999891 y[1] (closed_form) 2.9986280112074932 y[1] (numeric) 2.998628011208085 absolute error 5.919709167301335e-13 relative error 1.9741392213959794e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.669999999999894 y[1] (closed_form) 2.9991017216871803 y[1] (numeric) 2.999101721687776 absolute error 5.95523630408934e-13 relative error 1.9856733304594786e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.679999999999898 y[1] (closed_form) 2.9994755228272805 y[1] (numeric) 2.9994755228278795 absolute error 5.990763440877345e-13 relative error 1.9972703211895196e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.689999999999901 y[1] (closed_form) 2.9997493772479915 y[1] (numeric) 2.9997493772485937 absolute error 6.021849685566849e-13 relative error 2.0074509328147176e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.699999999999904 y[1] (closed_form) 2.9999232575640997 y[1] (numeric) 2.999923257564705 absolute error 6.052935930256353e-13 relative error 2.0176969244110805e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.709999999999908 y[1] (closed_form) 2.9999971463877175 y[1] (numeric) 2.999997146388327 absolute error 6.092903959142859e-13 relative error 2.0309699182478544e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.719999999999911 y[1] (closed_form) 2.999971036330025 y[1] (numeric) 2.999971036330637 absolute error 6.119549311733863e-13 relative error 2.039869464613276e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.729999999999914 y[1] (closed_form) 2.999844930002006 y[1] (numeric) 2.9998449300026215 absolute error 6.155076448521868e-13 relative error 2.0517982069552347e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.739999999999918 y[1] (closed_form) 2.999618840014188 y[1] (numeric) 2.9996188400148065 absolute error 6.186162693211372e-13 relative error 2.0623162552153168e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] 4.749999999999921 y[1] (closed_form) 2.9992927889753807 y[1] (numeric) 2.9992927889760037 absolute error 6.230571614196379e-13 relative error 2.0773469122782337e-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) 2.998866809490418 y[1] (numeric) 2.9988668094910444 absolute error 6.266098750984384e-13 relative error 2.089488846638424e-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) 2.998340944156892 y[1] (numeric) 2.9983409441575217 absolute error 6.297184995673888e-13 relative error 2.1002231277085812e-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) 2.997715245560898 y[1] (numeric) 2.997715245561531 absolute error 6.328271240363392e-13 relative error 2.1110314762999842e-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) 2.9969897762717745 y[1] (numeric) 2.9969897762724114 absolute error 6.368239269249898e-13 relative error 2.124878543019898e-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) 2.996164608835846 y[1] (numeric) 2.996164608836487 absolute error 6.408207298136404e-13 relative error 2.1388034820377578e-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) 2.9952398257691684 y[1] (numeric) 2.995239825769813 absolute error 6.448175327022909e-13 relative error 2.1528076889025197e-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) 2.9942155195492774 y[1] (numeric) 2.9942155195499267 absolute error 6.492584248007915e-13 relative error 2.1683757249996658e-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) 2.9930917926059415 y[1] (numeric) 2.9930917926065947 absolute error 6.532552276894421e-13 relative error 2.182543246094982e-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) 2.991868757310919 y[1] (numeric) 2.9918687573115763 absolute error 6.572520305780927e-13 relative error 2.1967943245238755e-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) 2.9905465359667196 y[1] (numeric) 2.9905465359673813 absolute error 6.616929226765933e-13 relative error 2.212615368858306e-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) 2.989125260794376 y[1] (numeric) 2.9891252607950425 absolute error 6.66577903984944e-13 relative error 2.2300099387865644e-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) 2.9876050739202213 y[1] (numeric) 2.987605073920892 absolute error 6.705747068735946e-13 relative error 2.244522586761081e-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) 2.9859861273616763 y[1] (numeric) 2.985986127362351 absolute error 6.745715097622451e-13 relative error 2.2591247279446516e-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) 2.9842685830120472 y[1] (numeric) 2.984268583012727 absolute error 6.799005802804459e-13 relative error 2.278282136369296e-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) 2.982452612624338 y[1] (numeric) 2.9824526126250226 absolute error 6.847855615887966e-13 relative error 2.2960484223292853e-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) 2.980538397794074 y[1] (numeric) 2.9805383977947635 absolute error 6.896705428971472e-13 relative error 2.3139126253417143e-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) 2.978526129941143 y[1] (numeric) 2.9785261299418373 absolute error 6.941114349956479e-13 relative error 2.3303855823798457e-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) 2.976416010290654 y[1] (numeric) 2.9764160102913526 absolute error 6.985523270941485e-13 relative error 2.3469579678343863e-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) 2.9742082498528126 y[1] (numeric) 2.974208249853517 absolute error 7.043254868221993e-13 relative error 2.368110863982221e-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) 2.9719030694018236 y[1] (numeric) 2.9719030694025332 absolute error 7.096545573404001e-13 relative error 2.3878792166772698e-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) 2.969500699453811 y[1] (numeric) 2.9695006994545254 absolute error 7.145395386487507e-13 relative error 2.4062615603363155e-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) 2.9670013802437674 y[1] (numeric) 2.9670013802444877 absolute error 7.203126983768016e-13 relative error 2.4277464215996457e-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) 2.964405361701531 y[1] (numeric) 2.964405361702257 absolute error 7.260858581048524e-13 relative error 2.4493474053362536e-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) 2.9617129034267933 y[1] (numeric) 2.9617129034275242 absolute error 7.309708394132031e-13 relative error 2.4680678487352615e-11% Desired digits 8 Estimated correct digits 12 Correct digits 13 h 0.001 Finished! diff ( y , x , 2 ) = sin ( x ) ; Iterations 4900 Total Elapsed Time 2 Seconds Elapsed Time(since restart) 2 Seconds Time to Timeout 2 Minutes 58.0 Seconds Percent Done 100.0204081632654%