##############ECHO OF PROBLEM################# ##############temp/lin_coshpostode.ode################# diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(2.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.000000001); 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 */ double exact_soln_y (double x) { return(sinh(c(2.0)*c(x)+c(3.0))/c(2)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 6.122941998282746 y[1] (numeric) = 6.122941998282746 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 6.247041280769291 y[1] (numeric) = 6.247041280769288 absolute error = 2.664535259100376e-15 relative error = 4.265275575019495e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 6.373639463063135 y[1] (numeric) = 6.373639463063134 absolute error = 8.881784197001252e-16 relative error = 1.393518451816024e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 6.502787186125198 y[1] (numeric) = 6.502787186125198 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 6.634536110766698 y[1] (numeric) = 6.634536110766697 absolute error = 8.881784197001252e-16 relative error = 1.33871970077722e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 6.768938938314164 y[1] (numeric) = 6.768938938314164 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 6.906049431690679 y[1] (numeric) = 6.906049431690678 absolute error = 8.881784197001252e-16 relative error = 1.286087550466156e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 7.045922436921756 y[1] (numeric) = 7.045922436921756 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 7.188613905074487 y[1] (numeric) = 7.188613905074487 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 7.334180914638712 y[1] (numeric) = 7.334180914638713 absolute error = 8.881784197001252e-16 relative error = 1.211012422569723e-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) = 7.482681694359175 y[1] (numeric) = 7.482681694359177 absolute error = 1.77635683940025e-15 relative error = 2.373957508762344e-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) = 7.634175646527801 y[1] (numeric) = 7.634175646527801 absolute error = 0 relative error = 0 % 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) = 7.788723370745403 y[1] (numeric) = 7.788723370745403 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 7.946386688162335 y[1] (numeric) = 7.946386688162333 absolute error = 1.77635683940025e-15 relative error = 2.2354271307316e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 8.107228666207765 y[1] (numeric) = 8.107228666207762 absolute error = 3.552713678800501e-15 relative error = 4.382155512165068e-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) = 8.271313643817498 y[1] (numeric) = 8.2713136438175 absolute error = 1.77635683940025e-15 relative error = 2.147611511175146e-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) = 8.438707257170421 y[1] (numeric) = 8.438707257170417 absolute error = 3.552713678800501e-15 relative error = 4.21002123966528e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 8.609476465943798 y[1] (numeric) = 8.609476465943798 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 8.783689580098111 y[1] (numeric) = 8.783689580098109 absolute error = 1.77635683940025e-15 relative error = 2.022335629238402e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 8.96141628720188 y[1] (numeric) = 8.96141628720188 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 9.142727680307679 y[1] (numeric) = 9.142727680307676 absolute error = 3.552713678800501e-15 relative error = 3.88583560948951e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 9.327696286390255 y[1] (numeric) = 9.327696286390259 absolute error = 3.552713678800501e-15 relative error = 3.808779327414586e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 9.516396095358337 y[1] (numeric) = 9.516396095358337 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 9.708902589651528 y[1] (numeric) = 9.708902589651531 absolute error = 3.552713678800501e-15 relative error = 3.659233003931101e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 9.905292774434347 y[1] (numeric) = 9.905292774434347 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 10.10564520839926 y[1] (numeric) = 10.10564520839926 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 10.31004003519128 y[1] (numeric) = 10.31004003519128 absolute error = 3.552713678800501e-15 relative error = 3.445877675231149e-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) = 10.5185590154664 y[1] (numeric) = 10.5185590154664 absolute error = 1.77635683940025e-15 relative error = 1.688783451030042e-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) = 10.73128555959704 y[1] (numeric) = 10.73128555959704 absolute error = 3.552713678800501e-15 relative error = 3.310613308228754e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 10.94830476103722 y[1] (numeric) = 10.94830476103722 absolute error = 1.77635683940025e-15 relative error = 1.622494877674525e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 11.16970343036117 y[1] (numeric) = 11.16970343036116 absolute error = 8.881784197001252e-15 relative error = 7.951674144596388e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 11.39557012998862 y[1] (numeric) = 11.39557012998862 absolute error = 1.77635683940025e-15 relative error = 1.55881348553644e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 11.62599520961104 y[1] (numeric) = 11.62599520961103 absolute error = 5.329070518200751e-15 relative error = 4.583754269737947e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 11.86107084233263 y[1] (numeric) = 11.86107084233262 absolute error = 3.552713678800501e-15 relative error = 2.995272286985022e-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) = 12.10089106154088 y[1] (numeric) = 12.10089106154087 absolute error = 5.329070518200751e-15 relative error = 4.403866203818358e-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) = 12.3455517985211 y[1] (numeric) = 12.34555179852109 absolute error = 3.552713678800501e-15 relative error = 2.877727732855237e-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) = 12.59515092083029 y[1] (numeric) = 12.59515092083028 absolute error = 8.881784197001252e-15 relative error = 7.051748925304464e-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) = 12.84978827144539 y[1] (numeric) = 12.84978827144538 absolute error = 5.329070518200751e-15 relative error = 4.147204923246039e-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) = 13.10956570870187 y[1] (numeric) = 13.10956570870186 absolute error = 1.243449787580175e-14 relative error = 9.485057058410393e-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) = 13.37458714703836 y[1] (numeric) = 13.37458714703836 absolute error = 5.329070518200751e-15 relative error = 3.984474780128678e-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) = 13.64495859856389 y[1] (numeric) = 13.64495859856387 absolute error = 1.243449787580175e-14 relative error = 9.112887947575354e-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) = 13.92078821546403 y[1] (numeric) = 13.92078821546403 absolute error = 8.881784197001252e-15 relative error = 6.38023081705592e-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) = 14.20218633326336 y[1] (numeric) = 14.20218633326335 absolute error = 1.77635683940025e-14 relative error = 1.250762944322025e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 14.48926551496099 y[1] (numeric) = 14.48926551496098 absolute error = 1.243449787580175e-14 relative error = 8.581869013969291e-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) = 14.7821405960574 y[1] (numeric) = 14.78214059605739 absolute error = 1.598721155460225e-14 relative error = 1.081522087461829e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 15.08092873049006 y[1] (numeric) = 15.08092873049005 absolute error = 1.06581410364015e-14 relative error = 7.067297529795543e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 15.38574943749666 y[1] (numeric) = 15.38574943749664 absolute error = 2.131628207280301e-14 relative error = 1.3854562079929e-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) = 15.6967246494243 y[1] (numeric) = 15.69672464942428 absolute error = 1.4210854715202e-14 relative error = 9.053388546076846e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 16.01397876050418 y[1] (numeric) = 16.01397876050416 absolute error = 1.77635683940025e-14 relative error = 1.109253899962288e-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) = 16.33763867661081 y[1] (numeric) = 16.3376386766108 absolute error = 1.06581410364015e-14 relative error = 6.523672880377656e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 16.66783386602618 y[1] (numeric) = 16.66783386602617 absolute error = 1.4210854715202e-14 relative error = 8.525915742517566e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 17.0046964112287 y[1] (numeric) = 17.00469641122869 absolute error = 1.06581410364015e-14 relative error = 6.267763198267755e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 17.34836106172804 y[1] (numeric) = 17.34836106172802 absolute error = 1.4210854715202e-14 relative error = 8.191468153468606e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 17.69896528796662 y[1] (numeric) = 17.69896528796661 absolute error = 7.105427357601002e-15 relative error = 4.014600425501668e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 18.05664933630974 y[1] (numeric) = 18.05664933630973 absolute error = 1.77635683940025e-14 relative error = 9.837688079970691e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 18.42155628514591 y[1] (numeric) = 18.4215562851459 absolute error = 7.105427357601002e-15 relative error = 3.857126535682771e-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) = 18.79383210212018 y[1] (numeric) = 18.79383210212016 absolute error = 2.131628207280301e-14 relative error = 1.134216904619376e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 19.17362570252305 y[1] (numeric) = 19.17362570252304 absolute error = 1.77635683940025e-14 relative error = 9.264584940585858e-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) = 19.5610890088587 y[1] (numeric) = 19.56108900885868 absolute error = 2.486899575160351e-14 relative error = 1.27135026788851e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 19.95637701161587 y[1] (numeric) = 19.95637701161586 absolute error = 1.06581410364015e-14 relative error = 5.34071942527333e-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) = 20.35964783126629 y[1] (numeric) = 20.35964783126627 absolute error = 2.486899575160351e-14 relative error = 1.221484573687577e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 20.77106278151478 y[1] (numeric) = 20.77106278151476 absolute error = 1.4210854715202e-14 relative error = 6.841659892265582e-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) = 21.19078643382709 y[1] (numeric) = 21.19078643382706 absolute error = 2.486899575160351e-14 relative error = 1.173575875971495e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 21.6189866832605 y[1] (numeric) = 21.61898668326048 absolute error = 1.4210854715202e-14 relative error = 6.573321369500365e-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) = 22.05583481562423 y[1] (numeric) = 22.05583481562421 absolute error = 2.486899575160351e-14 relative error = 1.12754724359771e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 22.50150557599591 y[1] (numeric) = 22.50150557599589 absolute error = 2.131628207280301e-14 relative error = 9.473269244500121e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 22.95617723862209 y[1] (numeric) = 22.95617723862205 absolute error = 3.197442310920451e-14 relative error = 1.392846151031187e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 23.42003167823013 y[1] (numeric) = 23.42003167823011 absolute error = 2.486899575160351e-14 relative error = 1.061868578714189e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 23.89325444278074 y[1] (numeric) = 23.89325444278072 absolute error = 2.842170943040401e-14 relative error = 1.189528596804087e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 24.37603482768942 y[1] (numeric) = 24.37603482768941 absolute error = 1.4210854715202e-14 relative error = 5.829846739084691e-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) = 24.86856595154733 y[1] (numeric) = 24.8685659515473 absolute error = 2.486899575160351e-14 relative error = 1.000017282864521e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 25.37104483337113 y[1] (numeric) = 25.37104483337112 absolute error = 1.77635683940025e-14 relative error = 7.001512358149974e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = 25.88367247141342 y[1] (numeric) = 25.88367247141338 absolute error = 3.197442310920451e-14 relative error = 1.235312459795567e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 26.40665392356447 y[1] (numeric) = 26.40665392356445 absolute error = 2.486899575160351e-14 relative error = 9.41770048700157e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 26.94019838937839 y[1] (numeric) = 26.94019838937836 absolute error = 3.907985046680551e-14 relative error = 1.450614798820983e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 27.48451929375548 y[1] (numeric) = 27.48451929375545 absolute error = 2.842170943040401e-14 relative error = 1.034098836753585e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 28.03983437231524 y[1] (numeric) = 28.03983437231519 absolute error = 4.263256414560601e-14 relative error = 1.520428529624223e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 28.60636575849333 y[1] (numeric) = 28.6063657584933 absolute error = 2.842170943040401e-14 relative error = 9.935449217964886e-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) = 29.18434007239815 y[1] (numeric) = 29.18434007239811 absolute error = 3.907985046680551e-14 relative error = 1.339069184701774e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 29.77398851146162 y[1] (numeric) = 29.77398851146159 absolute error = 3.197442310920451e-14 relative error = 1.073904596184546e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 30.37554694292151 y[1] (numeric) = 30.37554694292147 absolute error = 4.618527782440651e-14 relative error = 1.52047559542526e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 30.98925599817124 y[1] (numeric) = 30.98925599817121 absolute error = 2.842170943040401e-14 relative error = 9.171472019877228e-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) = 31.61536116901585 y[1] (numeric) = 31.61536116901581 absolute error = 4.263256414560601e-14 relative error = 1.348476264993215e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 32.25411290587181 y[1] (numeric) = 32.25411290587177 absolute error = 3.552713678800501e-14 relative error = 1.101476171168774e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 32.90576671795072 y[1] (numeric) = 32.90576671795066 absolute error = 5.684341886080801e-14 relative error = 1.727460701585745e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 33.57058327546618 y[1] (numeric) = 33.57058327546613 absolute error = 4.263256414560601e-14 relative error = 1.269938141848207e-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) = 34.24882851390561 y[1] (numeric) = 34.24882851390555 absolute error = 6.394884621840902e-14 relative error = 1.867183462711569e-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) = 34.9407737404077 y[1] (numeric) = 34.94077374040766 absolute error = 3.552713678800501e-14 relative error = 1.016781627446309e-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) = 35.64669574228918 y[1] (numeric) = 35.64669574228914 absolute error = 4.263256414560601e-14 relative error = 1.19597520212874e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 36.36687689776317 y[1] (numeric) = 36.36687689776315 absolute error = 2.131628207280301e-14 relative error = 5.861455228264079e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 37.10160528889444 y[1] (numeric) = 37.1016052888944 absolute error = 3.552713678800501e-14 relative error = 9.575633321353696e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 37.85117481683584 y[1] (numeric) = 37.85117481683589 absolute error = 4.973799150320701e-14 relative error = 1.314040891567889e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 38.61588531939304 y[1] (numeric) = 38.61588531939317 absolute error = 1.35003119794419e-13 relative error = 3.496051396408617e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 39.39604269096332 y[1] (numeric) = 39.39604269096355 absolute error = 2.273736754432321e-13 relative error = 5.77148515212131e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 40.19195900489756 y[1] (numeric) = 40.19195900489787 absolute error = 3.197442310920451e-13 relative error = 7.955427876831854e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 41.00395263833368 y[1] (numeric) = 41.00395263833409 absolute error = 4.121147867408581e-13 relative error = 1.005061122706452e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 41.83234839955179 y[1] (numeric) = 41.83234839955229 absolute error = 5.044853423896711e-13 relative error = 1.205969451131929e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 42.6774776579018 y[1] (numeric) = 42.6774776579024 absolute error = 6.039613253960852e-13 relative error = 1.415175775469619e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 43.53967847635559 y[1] (numeric) = 43.53967847635629 absolute error = 6.963318810448982e-13 relative error = 1.599304141446622e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 44.4192957467367 y[1] (numeric) = 44.41929574673751 absolute error = 8.100187187665142e-13 relative error = 1.823573978716272e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 45.31668132768169 y[1] (numeric) = 45.31668132768259 absolute error = 9.023892744153272e-13 relative error = 1.991296026048807e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 46.23219418538822 y[1] (numeric) = 46.23219418538922 absolute error = 1.001865257421741e-12 relative error = 2.167029437115453e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 47.16620053720636 y[1] (numeric) = 47.16620053720747 absolute error = 1.108446667785756e-12 relative error = 2.35008683158902e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 48.11907399813045 y[1] (numeric) = 48.11907399813165 absolute error = 1.20792265079217e-12 relative error = 2.510278254396794e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 49.09119573024999 y[1] (numeric) = 49.0911957302513 absolute error = 1.314504061156185e-12 relative error = 2.677677823085063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 50.08295459521963 y[1] (numeric) = 50.08295459522103 absolute error = 1.406874616804998e-12 relative error = 2.809088697293596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 51.09474730980898 y[1] (numeric) = 51.09474730981049 absolute error = 1.513456027169013e-12 relative error = 2.962057954787978e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 52.12697860459464 y[1] (numeric) = 52.12697860459626 absolute error = 1.620037437533028e-12 relative error = 3.107867520620566e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 53.18006138585778 y[1] (numeric) = 53.18006138585952 absolute error = 1.740829702612245e-12 relative error = 3.273463131193726e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 54.2544169007522 y[1] (numeric) = 54.25441690075405 absolute error = 1.854516540333861e-12 relative error = 3.418185368624153e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 55.35047490580878 y[1] (numeric) = 55.35047490581076 absolute error = 1.975308805413079e-12 relative error = 3.568729642834155e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 56.46867383884386 y[1] (numeric) = 56.46867383884595 absolute error = 2.096101070492296e-12 relative error = 3.711971484356735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 57.60946099434015 y[1] (numeric) = 57.60946099434237 absolute error = 2.223998762929114e-12 relative error = 3.860474867396539e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 58.77329270237057 y[1] (numeric) = 58.77329270237291 absolute error = 2.344791028008331e-12 relative error = 3.98955192094207e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 59.96063451113628 y[1] (numeric) = 59.96063451113876 absolute error = 2.47979414780275e-12 relative error = 4.13570364626843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 61.17196137319222 y[1] (numeric) = 61.17196137319484 absolute error = 2.62190269495477e-12 relative error = 4.286118404736623e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 62.40775783543447 y[1] (numeric) = 62.40775783543722 absolute error = 2.749800387391588e-12 relative error = 4.406183594422103e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 63.66851823292541 y[1] (numeric) = 63.6685182329283 absolute error = 2.891908934543608e-12 relative error = 4.542133247021432e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 64.95474688663441 y[1] (numeric) = 64.95474688663745 absolute error = 3.041122909053229e-12 relative error = 4.68191018334796e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 66.26695830517291 y[1] (numeric) = 66.26695830517609 absolute error = 3.183231456205249e-12 relative error = 4.803648058729082e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 67.6056773906047 y[1] (numeric) = 67.60567739060801 absolute error = 3.311129148642067e-12 relative error = 4.897708707970466e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 68.97143964841376 y[1] (numeric) = 68.97143964841723 absolute error = 3.467448550509289e-12 relative error = 5.027368673446321e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 70.36479140171363 y[1] (numeric) = 70.36479140171726 absolute error = 3.623767952376511e-12 relative error = 5.149973275254049e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 71.78629000978394 y[1] (numeric) = 71.78629000978769 absolute error = 3.751665644813329e-12 relative error = 5.226158984260093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 73.23650409102142 y[1] (numeric) = 73.23650409102534 absolute error = 3.922195901395753e-12 relative error = 5.355520378909788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 74.71601375039506 y[1] (numeric) = 74.71601375039913 absolute error = 4.064304448547773e-12 relative error = 5.439669817136468e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 76.22541081149565 y[1] (numeric) = 76.2254108114999 absolute error = 4.249045559845399e-12 relative error = 5.574316379026448e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 77.7652990532732 y[1] (numeric) = 77.76529905327762 absolute error = 4.419575816427823e-12 relative error = 5.68322358459676e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 79.33629445155651 y[1] (numeric) = 79.3362944515611 absolute error = 4.590106073010247e-12 relative error = 5.785632042359892e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 80.93902542545182 y[1] (numeric) = 80.93902542545658 absolute error = 4.760636329592671e-12 relative error = 5.881756426604634e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 82.5741330887187 y[1] (numeric) = 82.57413308872364 absolute error = 4.945377440890297e-12 relative error = 5.989015271376717e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 84.24227150622417 y[1] (numeric) = 84.2422715062293 absolute error = 5.130118552187923e-12 relative error = 6.08972011374229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 85.94410795557738 y[1] (numeric) = 85.94410795558269 absolute error = 5.314859663485549e-12 relative error = 6.184088461576312e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 87.68032319404954 y[1] (numeric) = 87.68032319405505 absolute error = 5.513811629498377e-12 relative error = 6.28853935368771e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 89.45161173088587 y[1] (numeric) = 89.45161173089159 absolute error = 5.712763595511205e-12 relative error = 6.386428913878028e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 91.25868210511862 y[1] (numeric) = 91.25868210512451 absolute error = 5.88329385209363e-12 relative error = 6.446831924788053e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 93.10225716899205 y[1] (numeric) = 93.10225716899814 absolute error = 6.082245818106458e-12 relative error = 6.532866122747629e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 94.98307437711306 y[1] (numeric) = 94.98307437711935 absolute error = 6.295408638834488e-12 relative error = 6.627926796557153e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 96.90188608144277 y[1] (numeric) = 96.90188608144929 absolute error = 6.52278231427772e-12 relative error = 6.731326476757678e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 98.85945983224742 y[1] (numeric) = 98.85945983225416 absolute error = 6.73594513500575e-12 relative error = 6.813657637251747e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 100.8565786851287 y[1] (numeric) = 100.8565786851357 absolute error = 6.977529665164184e-12 relative error = 6.918269245428034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 102.8940415142563 y[1] (numeric) = 102.8940415142635 absolute error = 7.190692485892214e-12 relative error = 6.988444014900436e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 104.9726633319284 y[1] (numeric) = 104.9726633319358 absolute error = 7.403855306620244e-12 relative error = 7.053127044332398e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 107.0932756145875 y[1] (numeric) = 107.0932756145952 absolute error = 7.631228982063476e-12 relative error = 7.125777914877786e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 109.2567266354218 y[1] (numeric) = 109.2567266354297 absolute error = 7.844391802791506e-12 relative error = 7.179779263355943e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 111.4638818036861 y[1] (numeric) = 111.4638818036942 absolute error = 8.08597633294994e-12 relative error = 7.254346611749296e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 113.7156240108767 y[1] (numeric) = 113.715624010885 absolute error = 8.327560863108374e-12 relative error = 7.323145729132049e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 116.0128539839001 y[1] (numeric) = 116.0128539839087 absolute error = 8.597567102697212e-12 relative error = 7.410874577648398e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 118.3564906453758 y[1] (numeric) = 118.3564906453847 absolute error = 8.839151632855646e-12 relative error = 7.468244102758879e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 120.7474714812173 y[1] (numeric) = 120.7474714812264 absolute error = 9.094947017729282e-12 relative error = 7.532204944882872e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 123.1867529156389 y[1] (numeric) = 123.1867529156483 absolute error = 9.350742402602918e-12 relative error = 7.590704504571621e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 125.6753106937388 y[1] (numeric) = 125.6753106937484 absolute error = 9.634959496906959e-12 relative error = 7.666549176382486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 128.2141402718092 y[1] (numeric) = 128.2141402718191 absolute error = 9.890754881780595e-12 relative error = 7.714246541615893e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 130.8042572155331 y[1] (numeric) = 130.8042572155433 absolute error = 1.017497197608463e-11 relative error = 7.778777382848323e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 133.4466976062232 y[1] (numeric) = 133.4466976062336 absolute error = 1.048761077981908e-11 relative error = 7.859026089027773e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 136.1425184552687 y[1] (numeric) = 136.1425184552795 absolute error = 1.077182787412312e-11 relative error = 7.912170272993982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 138.8927981269542 y[1] (numeric) = 138.8927981269653 absolute error = 1.105604496842716e-11 relative error = 7.960128327403586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 141.6986367698191 y[1] (numeric) = 141.6986367698304 absolute error = 1.13402620627312e-11 relative error = 8.003084801128166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 144.5611567567323 y[1] (numeric) = 144.5611567567439 absolute error = 1.165290086646564e-11 relative error = 8.060879649763153e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 147.4815031338559 y[1] (numeric) = 147.4815031338678 absolute error = 1.199396137963049e-11 relative error = 8.132519078507518e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 150.4608440786793 y[1] (numeric) = 150.4608440786915 absolute error = 1.224975676450413e-11 relative error = 8.141491455476921e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 153.5003713673055 y[1] (numeric) = 153.5003713673181 absolute error = 1.253397385880817e-11 relative error = 8.165435527720042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 156.6013008511775 y[1] (numeric) = 156.6013008511904 absolute error = 1.293187779083382e-11 relative error = 8.257835484472342e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 159.7648729434352 y[1] (numeric) = 159.7648729434484 absolute error = 1.324451659456827e-11 relative error = 8.290005400159203e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 162.9923531150969 y[1] (numeric) = 162.9923531151105 absolute error = 1.361399881716352e-11 relative error = 8.352538359606358e-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) = 166.285032401265 y[1] (numeric) = 166.285032401279 absolute error = 1.398348103975877e-11 relative error = 8.409344387662633e-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) = 169.644227917557 y[1] (numeric) = 169.6442279175713 absolute error = 1.432454155292362e-11 relative error = 8.443872054335384e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 173.0712833869691 y[1] (numeric) = 173.0712833869838 absolute error = 1.469402377551887e-11 relative error = 8.490157054341931e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 176.5675696773839 y[1] (numeric) = 176.567569677399 absolute error = 1.506350599811412e-11 relative error = 8.53129825915227e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 180.1344853499353 y[1] (numeric) = 180.1344853499508 absolute error = 1.546140993013978e-11 relative error = 8.583259279922957e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 183.7734572184518 y[1] (numeric) = 183.7734572184677 absolute error = 1.588773557159584e-11 relative error = 8.645283063217375e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 187.4859409202011 y[1] (numeric) = 187.4859409202174 absolute error = 1.62856395036215e-11 relative error = 8.686325717912412e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 191.2734214981643 y[1] (numeric) = 191.2734214981811 absolute error = 1.676880856393836e-11 relative error = 8.766930832624489e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 195.1374139950731 y[1] (numeric) = 195.1374139950903 absolute error = 1.719513420539442e-11 relative error = 8.811807973343633e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = 199.0794640594468 y[1] (numeric) = 199.0794640594644 absolute error = 1.762145984685048e-11 relative error = 8.85147040660536e-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) = 203.1011485638724 y[1] (numeric) = 203.1011485638905 absolute error = 1.804778548830654e-11 relative error = 8.886107053516131e-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) = 207.2040762357751 y[1] (numeric) = 207.2040762357935 absolute error = 1.84741111297626e-11 relative error = 8.915901397973046e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 211.3898883009298 y[1] (numeric) = 211.3898883009488 absolute error = 1.895728019007947e-11 relative error = 8.967921948609159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 215.6602591399744 y[1] (numeric) = 215.6602591399938 absolute error = 1.944044925039634e-11 relative error = 9.014386483593395e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 220.0168969581834 y[1] (numeric) = 220.0168969582033 absolute error = 1.995204002014361e-11 relative error = 9.068412606480726e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 224.4615444687734 y[1] (numeric) = 224.4615444687938 absolute error = 2.040678737103008e-11 relative error = 9.091440326371375e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 228.9959795900113 y[1] (numeric) = 228.9959795900322 absolute error = 2.088995643134695e-11 relative error = 9.122411873233671e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 233.6220161564057 y[1] (numeric) = 233.6220161564272 absolute error = 2.142996891052462e-11 relative error = 9.172923538241209e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 238.3415046442644 y[1] (numeric) = 238.3415046442864 absolute error = 2.19984030991327e-11 relative error = 9.229782757294549e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 243.1563329119099 y[1] (numeric) = 243.1563329119323 absolute error = 2.248157215944957e-11 relative error = 9.245727590238887e-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) = 248.0684269548478 y[1] (numeric) = 248.0684269548707 absolute error = 2.299316292919684e-11 relative error = 9.268879240880561e-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) = 253.0797516761907 y[1] (numeric) = 253.0797516762142 absolute error = 2.356159711780492e-11 relative error = 9.309949516605899e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 258.1923116726457 y[1] (numeric) = 258.1923116726699 absolute error = 2.415845301584341e-11 relative error = 9.356767000278918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 263.4081520363799 y[1] (numeric) = 263.4081520364045 absolute error = 2.467004378559068e-11 relative error = 9.365710056757638e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 268.729359173084 y[1] (numeric) = 268.7293591731094 absolute error = 2.535216481192037e-11 relative error = 9.434088217949968e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 274.1580616365634 y[1] (numeric) = 274.1580616365893 absolute error = 2.586375558166765e-11 relative error = 9.43388475512124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; Iterations = 1901 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %