##############ECHO OF PROBLEM################# ##############temp/arctan_tan_m0d5_0d5postode.ode################# diff ( y , x , 1 ) = arctan ( tan ( x ) ) ; ! #BEGIN FIRST INPUT BLOCK max_terms=30 # Digits:=32; ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-0.5) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_display_interval=0.001 # 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=0 #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=true $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(x)*c(x)/c(2.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -0.5 y[1] (closed_form) 0.125 y[1] (numeric) 0.125 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.49 y[1] (closed_form) 0.12004999999999999 y[1] (numeric) 0.12004999819923452 absolute error 1.8007654672969053e-09 relative error 1.5000128840457355e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.48 y[1] (closed_form) 0.1152 y[1] (numeric) 0.11519999644131002 absolute error 3.5586899815864825e-09 relative error 3.089140609016044e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.47 y[1] (closed_form) 0.11044999999999999 y[1] (numeric) 0.11044999472577674 absolute error 5.274223252582644e-09 relative error 4.775213447336029e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.45999999999999996 y[1] (closed_form) 0.10579999999999998 y[1] (numeric) 0.1057999930522003 absolute error 6.947799682799349e-09 relative error 6.566918414744188e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.44999999999999996 y[1] (closed_form) 0.10124999999999998 y[1] (numeric) 0.10124999142016132 absolute error 8.579838658984151e-09 relative error 8.47391472492262e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.43999999999999995 y[1] (closed_form) 0.09679999999999998 y[1] (numeric) 0.09679998982925479 absolute error 1.0170745190496433e-08 relative error 1.0506968172000449e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.42999999999999994 y[1] (closed_form) 0.09244999999999998 y[1] (numeric) 0.09244998827908972 absolute error 1.1720910256252104e-08 relative error 1.2678107362089894e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.41999999999999993 y[1] (closed_form) 0.08819999999999997 y[1] (numeric) 0.08819998676928871 absolute error 1.3230711262690598e-08 relative error 1.5000806420284128e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.4099999999999999 y[1] (closed_form) 0.08404999999999997 y[1] (numeric) 0.08404998529948755 absolute error 1.4700512418475142e-08 relative error 1.7490199189143543e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3999999999999999 y[1] (closed_form) 0.07999999999999996 y[1] (numeric) 0.07999998386933478 absolute error 1.613066517858197e-08 relative error 2.0163331473227474e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3899999999999999 y[1] (closed_form) 0.07604999999999996 y[1] (numeric) 0.07604998247849148 absolute error 1.7521508480222714e-08 relative error 2.303945888260713e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3799999999999999 y[1] (closed_form) 0.07219999999999996 y[1] (numeric) 0.07219998112663076 absolute error 1.8873369200811396e-08 relative error 2.614040055514045e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3699999999999999 y[1] (closed_form) 0.06844999999999996 y[1] (numeric) 0.06844997981343742 absolute error 2.018656253266471e-08 relative error 2.9490960602870303e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3599999999999999 y[1] (closed_form) 0.06479999999999995 y[1] (numeric) 0.06479997853860786 absolute error 2.1461392094024312e-08 relative error 3.31194322438647e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.34999999999999987 y[1] (closed_form) 0.06124999999999995 y[1] (numeric) 0.0612499773018495 absolute error 2.2698150449473875e-08 relative error 3.705820481546758e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.33999999999999986 y[1] (closed_form) 0.05779999999999995 y[1] (numeric) 0.05779997610288067 absolute error 2.3897119276472534e-08 relative error 4.1344497018118606e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.32999999999999985 y[1] (closed_form) 0.05444999999999995 y[1] (numeric) 0.054449974941430335 absolute error 2.505856961515507e-08 relative error 4.602124814537207e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.31999999999999984 y[1] (closed_form) 0.05119999999999995 y[1] (numeric) 0.05119997381723773 absolute error 2.61827622152766e-08 relative error 5.1138207451712164e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.30999999999999983 y[1] (closed_form) 0.04804999999999995 y[1] (numeric) 0.048049972730052175 absolute error 2.7269947772134984e-08 relative error 5.675327319903229e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2999999999999998 y[1] (closed_form) 0.04499999999999995 y[1] (numeric) 0.044999971679632864 absolute error 2.8320367086165366e-08 relative error 6.293414908036755e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2899999999999998 y[1] (closed_form) 0.04204999999999995 y[1] (numeric) 0.042049970665748615 absolute error 2.933425133355705e-08 relative error 6.97604074519788e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2799999999999998 y[1] (closed_form) 0.03919999999999994 y[1] (numeric) 0.039199969688177655 absolute error 3.0311822288298096e-08 relative error 7.732607726606668e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2699999999999998 y[1] (closed_form) 0.03644999999999995 y[1] (numeric) 0.036449968746707424 absolute error 3.125329252340325e-08 relative error 8.57429150161956e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.2599999999999998 y[1] (closed_form) 0.03379999999999994 y[1] (numeric) 0.03379996784113438 absolute error 3.2158865563569616e-08 relative error 9.514457267328306e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.24999999999999978 y[1] (closed_form) 0.031249999999999944 y[1] (numeric) 0.031249966971263806 absolute error 3.302873613844626e-08 relative error 0.00010569195564302821% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.23999999999999977 y[1] (closed_form) 0.028799999999999944 y[1] (numeric) 0.02879996613690968 absolute error 3.3863090262431506e-08 relative error 0.00011758017452233184% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.22999999999999976 y[1] (closed_form) 0.026449999999999946 y[1] (numeric) 0.02644996533789445 absolute error 3.466210549488147e-08 relative error 0.0001310476578256391% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.21999999999999975 y[1] (closed_form) 0.024199999999999944 y[1] (numeric) 0.024199964574048924 absolute error 3.542595101990731e-08 relative error 0.00014638822735498923% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.20999999999999974 y[1] (closed_form) 0.022049999999999945 y[1] (numeric) 0.022049963845212094 absolute error 3.615478785107262e-08 relative error 0.0001639672918415996% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.19999999999999973 y[1] (closed_form) 0.01999999999999995 y[1] (numeric) 0.019999963151231013 absolute error 3.684876893547684e-08 relative error 0.00018424384467738468% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.18999999999999972 y[1] (closed_form) 0.018049999999999948 y[1] (numeric) 0.018049962491960683 absolute error 3.7508039264777526e-08 relative error 0.0002078007715500146% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.17999999999999972 y[1] (closed_form) 0.01619999999999995 y[1] (numeric) 0.016199961867263885 absolute error 3.8132736066009976e-08 relative error 0.00023538725966672897% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.1699999999999997 y[1] (closed_form) 0.01444999999999995 y[1] (numeric) 0.014449961277011097 absolute error 3.8722988853628904e-08 relative error 0.00026797916161680995% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.1599999999999997 y[1] (closed_form) 0.012799999999999952 y[1] (numeric) 0.012799960721080368 absolute error 3.927891958389884e-08 relative error 0.00030686655924921084% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.1499999999999997 y[1] (closed_form) 0.011249999999999953 y[1] (numeric) 0.011249960199357232 absolute error 3.980064272081363e-08 relative error 0.0003537834908516782% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.13999999999999968 y[1] (closed_form) 0.009799999999999955 y[1] (numeric) 0.009799959711734597 absolute error 4.028826535752705e-08 relative error 0.0004111047485461963% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.12999999999999967 y[1] (closed_form) 0.008449999999999958 y[1] (numeric) 0.008449959258112667 absolute error 4.0741887290945966e-08 relative error 0.0004821525123188896% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.11999999999999966 y[1] (closed_form) 0.00719999999999996 y[1] (numeric) 0.007199958838398851 absolute error 4.116160110933381e-08 relative error 0.0005716889042963061% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.10999999999999965 y[1] (closed_form) 0.006049999999999962 y[1] (numeric) 0.006049958452507693 absolute error 4.1547492268638464e-08 relative error 0.0006867354093989872% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.09999999999999964 y[1] (closed_form) 0.0049999999999999645 y[1] (numeric) 0.004999958100360802 absolute error 4.1899639162748525e-08 relative error 0.0008379927832549765% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.08999999999999964 y[1] (closed_form) 0.004049999999999967 y[1] (numeric) 0.00404995778188678 absolute error 4.2218113186810735e-08 relative error 0.0010424225478224958% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.07999999999999963 y[1] (closed_form) 0.0031999999999999702 y[1] (numeric) 0.0031999574970211745 absolute error 4.2502978795776886e-08 relative error 0.00132821808736804% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.06999999999999962 y[1] (closed_form) 0.0024499999999999735 y[1] (numeric) 0.0024499572457064214 absolute error 4.275429355210872e-08 relative error 0.001745073206208538% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.05999999999999961 y[1] (closed_form) 0.0017999999999999765 y[1] (numeric) 0.0017999570278917985 absolute error 4.297210817803647e-08 relative error 0.0023873393432242793% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.0499999999999996 y[1] (closed_form) 0.00124999999999998 y[1] (numeric) 0.0012499568435333835 absolute error 4.315646659654171e-08 relative error 0.003452517327723392% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.03999999999999959 y[1] (closed_form) 0.0007999999999999837 y[1] (numeric) 0.0007999566925940198 absolute error 4.330740596388341e-08 relative error 0.0054134257454855365% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.029999999999999583 y[1] (closed_form) 0.00044999999999998747 y[1] (numeric) 0.00044995657504328756 absolute error 4.34249566999014e-08 relative error 0.009649990377756134% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.019999999999999574 y[1] (closed_form) 0.00019999999999999147 y[1] (numeric) 0.0001999564908574779 absolute error 4.350914251357641e-08 relative error 0.021754571256789135% Desired digits 8 Estimated correct digits 10 Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.009999999999999565 y[1] (closed_form) 4.9999999999995645e-05 y[1] (numeric) 4.995644001957427e-05 absolute error 4.355998042137346e-08 relative error 0.08711996084275452% Desired digits 8 Estimated correct digits 9 Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.371503159461554e-16 y[1] (closed_form) 9.555019936591174e-32 y[1] (numeric) -4.3577480760924783e-08 absolute error 4.3577480760924783e-08 relative error -1% Desired digits 8 Estimated correct digits 6 Correct digits -16 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.010000000000000439 y[1] (closed_form) 5.0000000000004393e-05 y[1] (numeric) 4.995643835280501e-05 absolute error 4.356164719938329e-08 relative error 0.08712329439875892% Desired digits 8 Estimated correct digits 9 Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.020000000000000448 y[1] (closed_form) 0.00020000000000000895 y[1] (numeric) 0.0001999564875232725 absolute error 4.351247673644817e-08 relative error 0.02175623836822311% Desired digits 8 Estimated correct digits 10 Correct digits 4 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.030000000000000457 y[1] (closed_form) 0.0004500000000000137 y[1] (numeric) 0.00044995657004031194 absolute error 4.3429959701766184e-08 relative error 0.009651102155947748% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.040000000000000466 y[1] (closed_form) 0.0008000000000000186 y[1] (numeric) 0.0007999566859202713 absolute error 4.331407974726264e-08 relative error 0.005414259968407704% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.050000000000000475 y[1] (closed_form) 0.0012500000000000237 y[1] (numeric) 0.0012499568351861897 absolute error 4.3164813833939525e-08 relative error 0.0034531851067150965% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.060000000000000484 y[1] (closed_form) 0.001800000000000029 y[1] (numeric) 0.001799957017867815 absolute error 4.2982132214108154e-08 relative error 0.0023878962341170812% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07000000000000049 y[1] (closed_form) 0.0024500000000000346 y[1] (numeric) 0.0024499572340016275 absolute error 4.276599840707593e-08 relative error 0.0017455509553908296% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.0800000000000005 y[1] (closed_form) 0.00320000000000004 y[1] (numeric) 0.003199957483630873 absolute error 4.251636916705395e-08 relative error 0.0013286365364704193% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09000000000000051 y[1] (closed_form) 0.004050000000000046 y[1] (numeric) 0.004049957766805591 absolute error 4.223319445464252e-08 relative error 0.0010427949248059763% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10000000000000052 y[1] (closed_form) 0.005000000000000052 y[1] (numeric) 0.00499995808358266 absolute error 4.19164173917283e-08 relative error 0.0008383283478345572% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000053 y[1] (closed_form) 0.006050000000000058 y[1] (numeric) 0.006049958434025843 absolute error 4.1565974214646806e-08 relative error 0.000687040896109858% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12000000000000054 y[1] (closed_form) 0.007200000000000064 y[1] (numeric) 0.007199958818205839 absolute error 4.1181794224742774e-08 relative error 0.0005719693642325334% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13000000000000053 y[1] (closed_form) 0.008450000000000069 y[1] (numeric) 0.008449959236200339 absolute error 4.076379972982325e-08 relative error 0.00048241183112216466% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14000000000000054 y[1] (closed_form) 0.009800000000000076 y[1] (numeric) 0.009799959688094086 absolute error 4.031190599038115e-08 relative error 0.000411345979493682% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000055 y[1] (closed_form) 0.011250000000000083 y[1] (numeric) 0.011249960173978953 absolute error 3.9826021130257017e-08 relative error 0.0003540090767133931% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000056 y[1] (closed_form) 0.012800000000000089 y[1] (numeric) 0.012799960693954017 absolute error 3.930604607245425e-08 relative error 0.0003070784849410467% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000057 y[1] (closed_form) 0.014450000000000096 y[1] (numeric) 0.01444996124812563 absolute error 3.87518744662807e-08 relative error 0.00026817906205038367% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000058 y[1] (closed_form) 0.016200000000000103 y[1] (numeric) 0.01619996183660753 absolute error 3.816339257459167e-08 relative error 0.00023557649737402116% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000059 y[1] (closed_form) 0.01805000000000011 y[1] (numeric) 0.018049962459520893 absolute error 3.7540479218278744e-08 relative error 0.0002079804942840915% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2000000000000006 y[1] (closed_form) 0.02000000000000012 y[1] (numeric) 0.019999963116994496 absolute error 3.6883005621879406e-08 relative error 0.00018441502810939594% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2100000000000006 y[1] (closed_form) 0.022050000000000125 y[1] (numeric) 0.022049963809164772 absolute error 3.6190835352861717e-08 relative error 0.00016413077257533564% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2200000000000006 y[1] (closed_form) 0.024200000000000135 y[1] (numeric) 0.024199964536175955 absolute error 3.546382417937699e-08 relative error 0.0001465447280139537% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000000062 y[1] (closed_form) 0.026450000000000144 y[1] (numeric) 0.026449965298180188 absolute error 3.470181995576804e-08 relative error 0.00013119780701613556% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000063 y[1] (closed_form) 0.028800000000000152 y[1] (numeric) 0.028799966095337647 absolute error 3.3904662504607996e-08 relative error 0.00011772452258544382% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2500000000000006 y[1] (closed_form) 0.03125000000000015 y[1] (numeric) 0.031249966927816723 absolute error 3.3072183429350144e-08 relative error 0.00010583098697391995% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000000006 y[1] (closed_form) 0.03380000000000016 y[1] (numeric) 0.03379996779579409 absolute error 3.2204206072694586e-08 relative error 9.527871619140365e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.27000000000000063 y[1] (closed_form) 0.03645000000000017 y[1] (numeric) 0.036449968699454945 absolute error 3.1300545225154686e-08 relative error 8.587255205803715e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.28000000000000064 y[1] (closed_form) 0.03920000000000018 y[1] (numeric) 0.03919996963899312 absolute error 3.0361007062607026e-08 relative error 7.74515486290992e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.29000000000000065 y[1] (closed_form) 0.042050000000000184 y[1] (numeric) 0.04204997061461126 absolute error 2.938538892771625e-08 relative error 6.988201885307044e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30000000000000066 y[1] (closed_form) 0.0450000000000002 y[1] (numeric) 0.044999971626521036 absolute error 2.8373479163401605e-08 relative error 6.305217591866995e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.31000000000000066 y[1] (closed_form) 0.048050000000000204 y[1] (numeric) 0.04804997267494328 absolute error 2.7325056925486813e-08 relative error 5.686796446511279e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000007 y[1] (closed_form) 0.05120000000000022 y[1] (numeric) 0.05119997376010821 absolute error 2.6239892009227717e-08 relative error 5.124978908052267e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000007 y[1] (closed_form) 0.05445000000000023 y[1] (numeric) 0.05444997488225569 absolute error 2.511774453706206e-08 relative error 4.612992568790074e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3400000000000007 y[1] (closed_form) 0.05780000000000023 y[1] (numeric) 0.05779997604163537 absolute error 2.3958364861464965e-08 relative error 4.145045823782849e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3500000000000007 y[1] (closed_form) 0.06125000000000024 y[1] (numeric) 0.061249977238506996 absolute error 2.2761493245759823e-08 relative error 3.716162162573018e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3600000000000007 y[1] (closed_form) 0.06480000000000026 y[1] (numeric) 0.06479997847314056 absolute error 2.1526859697584833e-08 relative error 3.3220462496272756e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3700000000000007 y[1] (closed_form) 0.06845000000000026 y[1] (numeric) 0.06844997974581672 absolute error 2.025418353868158e-08 relative error 2.9589749508665453e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000000007 y[1] (closed_form) 0.07220000000000028 y[1] (numeric) 0.07219998105682686 absolute error 1.894317341877283e-08 relative error 2.6237082297469193e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39000000000000073 y[1] (closed_form) 0.07605000000000028 y[1] (numeric) 0.07604998240647357 absolute error 1.7593526718817643e-08 relative error 2.3134157421193396e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40000000000000074 y[1] (closed_form) 0.0800000000000003 y[1] (numeric) 0.07999998379507076 absolute error 1.6204929537133594e-08 relative error 2.025616192141692e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41000000000000075 y[1] (closed_form) 0.0840500000000003 y[1] (numeric) 0.08404998522294416 absolute error 1.4777056148163048e-08 relative error 1.7581268468962515e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.42000000000000076 y[1] (closed_form) 0.08820000000000032 y[1] (numeric) 0.08819998669043155 absolute error 1.3309568766550761e-08 relative error 1.5090214021032555e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.43000000000000077 y[1] (closed_form) 0.09245000000000034 y[1] (numeric) 0.09244998819788307 absolute error 1.180211726958813e-08 relative error 1.276594620831594e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000008 y[1] (closed_form) 0.09680000000000034 y[1] (numeric) 0.09679998974566163 absolute error 1.0254338711490618e-08 relative error 1.059332511517622e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4500000000000008 y[1] (closed_form) 0.10125000000000035 y[1] (numeric) 0.10124999133414335 absolute error 8.665857004208632e-09 relative error 8.558871115267755e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4600000000000008 y[1] (closed_form) 0.10580000000000037 y[1] (numeric) 0.10579999296371778 absolute error 7.03628258436062e-09 relative error 6.650550646843664e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4700000000000008 y[1] (closed_form) 0.11045000000000038 y[1] (numeric) 0.1104499946347885 absolute error 5.36521188587713e-09 relative error 4.8575933778878336e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4800000000000008 y[1] (closed_form) 0.11520000000000039 y[1] (numeric) 0.1151999963477735 absolute error 3.6522268820338155e-09 relative error 3.170335835098788e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4900000000000008 y[1] (closed_form) 0.1200500000000004 y[1] (numeric) 0.1200499981031056 absolute error 1.896894807895677e-09 relative error 1.5800873035365853e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arctan ( tan ( x ) ) ; Iterations 1000 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.10000000000008%