##############ECHO OF PROBLEM################# ##############temp/expt_c_linpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 , ( 0.2 * x + 0.3 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(1.0); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; 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=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(c(7.2134752044448170367996234050095)*expt(c(2.0),(c(0.2)*c(x)+c(0.3)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 10.2013944659679 y[1] (numeric) = 10.2013944659679 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] = 1.009999999999999 y[1] (closed_form) = 10.21554640870438 y[1] (numeric) = 10.21554640870438 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] = 1.019999999999998 y[1] (closed_form) = 10.22971798380426 y[1] (numeric) = 10.22971798380426 absolute error = 3.552713678800501e-15 relative error = 3.472934136038916e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 10.24390921850263 y[1] (numeric) = 10.24390921850264 absolute error = 3.552713678800501e-15 relative error = 3.468122962651367e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 10.25812014007239 y[1] (numeric) = 10.2581201400724 absolute error = 7.105427357601002e-15 relative error = 6.926636908690816e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999994 y[1] (closed_form) = 10.27235077582426 y[1] (numeric) = 10.27235077582427 absolute error = 8.881784197001252e-15 relative error = 8.646301504719178e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999993 y[1] (closed_form) = 10.28660115310685 y[1] (numeric) = 10.28660115310686 absolute error = 8.881784197001252e-15 relative error = 8.634323490143966e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999992 y[1] (closed_form) = 10.30087129930672 y[1] (numeric) = 10.30087129930673 absolute error = 1.06581410364015e-14 relative error = 1.034683448294207e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999991 y[1] (closed_form) = 10.3151612418484 y[1] (numeric) = 10.31516124184842 absolute error = 1.4210854715202e-14 relative error = 1.377666754984774e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.08999999999999 y[1] (closed_form) = 10.32947100819449 y[1] (numeric) = 10.32947100819451 absolute error = 1.77635683940025e-14 relative error = 1.71969778315951e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.099999999999989 y[1] (closed_form) = 10.34380062584567 y[1] (numeric) = 10.3438006258457 absolute error = 2.131628207280301e-14 relative error = 2.060778513029418e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999988 y[1] (closed_form) = 10.35815012234078 y[1] (numeric) = 10.3581501223408 absolute error = 2.309263891220326e-14 relative error = 2.229417283921801e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 10.37251952525686 y[1] (numeric) = 10.37251952525688 absolute error = 2.131628207280301e-14 relative error = 2.055072735307784e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 10.3869088622092 y[1] (numeric) = 10.38690886220922 absolute error = 2.486899575160351e-14 relative error = 2.394263402279829e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 10.40131816085141 y[1] (numeric) = 10.40131816085143 absolute error = 2.664535259100376e-14 relative error = 2.561728444313128e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999983 y[1] (closed_form) = 10.41574744887546 y[1] (numeric) = 10.41574744887548 absolute error = 2.486899575160351e-14 relative error = 2.387634288721978e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999982 y[1] (closed_form) = 10.43019675401172 y[1] (numeric) = 10.43019675401175 absolute error = 2.842170943040401e-14 relative error = 2.724944706289676e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999981 y[1] (closed_form) = 10.44466610402907 y[1] (numeric) = 10.4446661040291 absolute error = 3.019806626980426e-14 relative error = 2.891242857266184e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.17999999999998 y[1] (closed_form) = 10.45915552673486 y[1] (numeric) = 10.45915552673489 absolute error = 2.842170943040401e-14 relative error = 2.717400019318452e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.189999999999979 y[1] (closed_form) = 10.47366504997506 y[1] (numeric) = 10.47366504997509 absolute error = 3.019806626980426e-14 relative error = 2.88323773251429e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999978 y[1] (closed_form) = 10.48819470163424 y[1] (numeric) = 10.48819470163427 absolute error = 2.664535259100376e-14 relative error = 2.540508957833511e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999977 y[1] (closed_form) = 10.50274450963567 y[1] (numeric) = 10.5027445096357 absolute error = 3.197442310920451e-14 relative error = 3.044387405584302e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 10.51731450194135 y[1] (numeric) = 10.51731450194138 absolute error = 3.552713678800501e-14 relative error = 3.377966569455273e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 10.53190470655207 y[1] (numeric) = 10.5319047065521 absolute error = 3.730349362740526e-14 relative error = 3.541951305749867e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 10.54651515150746 y[1] (numeric) = 10.5465151515075 absolute error = 3.730349362740526e-14 relative error = 3.537044520537507e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999972 y[1] (closed_form) = 10.56114586488606 y[1] (numeric) = 10.5611458648861 absolute error = 3.907985046680551e-14 relative error = 3.700341891568706e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999971 y[1] (closed_form) = 10.57579687480536 y[1] (numeric) = 10.5757968748054 absolute error = 4.263256414560601e-14 relative error = 4.0311443809184e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.26999999999997 y[1] (closed_form) = 10.59046820942185 y[1] (numeric) = 10.59046820942189 absolute error = 4.618527782440651e-14 relative error = 4.361023224952191e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.279999999999969 y[1] (closed_form) = 10.60515989693107 y[1] (numeric) = 10.60515989693112 absolute error = 4.796163466380676e-14 relative error = 4.522481049784636e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999968 y[1] (closed_form) = 10.61987196556771 y[1] (numeric) = 10.61987196556775 absolute error = 4.796163466380676e-14 relative error = 4.516215903478916e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999967 y[1] (closed_form) = 10.63460444360558 y[1] (numeric) = 10.63460444360563 absolute error = 4.973799150320701e-14 relative error = 4.676994971177671e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999966 y[1] (closed_form) = 10.64935735935775 y[1] (numeric) = 10.6493573593578 absolute error = 5.329070518200751e-14 relative error = 5.004124040891554e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 10.66413074117656 y[1] (numeric) = 10.66413074117662 absolute error = 5.329070518200751e-14 relative error = 4.99719165822305e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 10.67892461745368 y[1] (numeric) = 10.67892461745373 absolute error = 5.329070518200751e-14 relative error = 4.990268879219259e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 10.69373901662015 y[1] (numeric) = 10.6937390166202 absolute error = 5.684341886080801e-14 relative error = 5.315579403280957e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999961 y[1] (closed_form) = 10.70857396714647 y[1] (numeric) = 10.70857396714653 absolute error = 5.861977570020827e-14 relative error = 5.474097286907825e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.35999999999996 y[1] (closed_form) = 10.72342949754264 y[1] (numeric) = 10.7234294975427 absolute error = 5.861977570020827e-14 relative error = 5.466513834370006e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.369999999999959 y[1] (closed_form) = 10.7383056363582 y[1] (numeric) = 10.73830563635826 absolute error = 6.039613253960852e-14 relative error = 5.624363338580789e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999958 y[1] (closed_form) = 10.75320241218229 y[1] (numeric) = 10.75320241218236 absolute error = 6.217248937900877e-14 relative error = 5.781765003193245e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999957 y[1] (closed_form) = 10.76811985364373 y[1] (numeric) = 10.76811985364379 absolute error = 6.217248937900877e-14 relative error = 5.773755328138437e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999956 y[1] (closed_form) = 10.78305798941103 y[1] (numeric) = 10.78305798941109 absolute error = 6.394884621840902e-14 relative error = 5.930492656276804e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999955 y[1] (closed_form) = 10.79801684819249 y[1] (numeric) = 10.79801684819255 absolute error = 6.394884621840902e-14 relative error = 5.922276943762465e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 10.81299645873623 y[1] (numeric) = 10.8129964587363 absolute error = 6.750155989720952e-14 relative error = 6.242632202350576e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 10.82799684983025 y[1] (numeric) = 10.82799684983032 absolute error = 7.105427357601002e-14 relative error = 6.56208849720195e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 10.84301805030249 y[1] (numeric) = 10.84301805030256 absolute error = 7.283063041541027e-14 relative error = 6.716822758897697e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.44999999999995 y[1] (closed_form) = 10.85806008902087 y[1] (numeric) = 10.85806008902094 absolute error = 7.283063041541027e-14 relative error = 6.707517716636416e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.459999999999949 y[1] (closed_form) = 10.87312299489338 y[1] (numeric) = 10.87312299489345 absolute error = 7.815970093361102e-14 relative error = 7.188339630694804e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999948 y[1] (closed_form) = 10.88820679686808 y[1] (numeric) = 10.88820679686816 absolute error = 7.993605777301127e-14 relative error = 7.34152641149361e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999947 y[1] (closed_form) = 10.90331152393323 y[1] (numeric) = 10.90331152393331 absolute error = 8.348877145181177e-14 relative error = 7.657193988133825e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999946 y[1] (closed_form) = 10.91843720511726 y[1] (numeric) = 10.91843720511734 absolute error = 8.171241461241152e-14 relative error = 7.483892893949555e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999945 y[1] (closed_form) = 10.93358386948891 y[1] (numeric) = 10.93358386948899 absolute error = 8.348877145181177e-14 relative error = 7.635993142632241e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 10.94875154615721 y[1] (numeric) = 10.94875154615729 absolute error = 8.348877145181177e-14 relative error = 7.625414742479442e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 10.9639402642716 y[1] (numeric) = 10.96394026427168 absolute error = 8.704148513061227e-14 relative error = 7.938887209578843e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 10.97915005302194 y[1] (numeric) = 10.97915005302202 absolute error = 8.704148513061227e-14 relative error = 7.927889200007308e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 10.99438094163859 y[1] (numeric) = 10.99438094163868 absolute error = 9.237055564881302e-14 relative error = 8.401614983066636e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.549999999999939 y[1] (closed_form) = 11.00963295939246 y[1] (numeric) = 11.00963295939256 absolute error = 9.592326932761353e-14 relative error = 8.712667323371587e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999938 y[1] (closed_form) = 11.02490613559507 y[1] (numeric) = 11.02490613559517 absolute error = 9.769962616701378e-14 relative error = 8.861719543496176e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999937 y[1] (closed_form) = 11.0402004995986 y[1] (numeric) = 11.0402004995987 absolute error = 9.769962616701378e-14 relative error = 8.849443103009398e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999936 y[1] (closed_form) = 11.05551608079595 y[1] (numeric) = 11.05551608079605 absolute error = 1.012523398458143e-13 relative error = 9.15853580292785e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999935 y[1] (closed_form) = 11.07085290862078 y[1] (numeric) = 11.07085290862088 absolute error = 1.012523398458143e-13 relative error = 9.145848172815113e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999934 y[1] (closed_form) = 11.08621101254761 y[1] (numeric) = 11.08621101254771 absolute error = 1.030286966852145e-13 relative error = 9.293409314382027e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 11.10159042209182 y[1] (numeric) = 11.10159042209193 absolute error = 1.06581410364015e-13 relative error = 9.600553282160483e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 11.11699116680976 y[1] (numeric) = 11.11699116680987 absolute error = 1.06581410364015e-13 relative error = 9.587253310249829e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 11.13241327629878 y[1] (numeric) = 11.13241327629888 absolute error = 1.048050535246148e-13 relative error = 9.414405567187099e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 11.14785678019726 y[1] (numeric) = 11.14785678019736 absolute error = 1.06581410364015e-13 relative error = 9.56070861560971e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999928 y[1] (closed_form) = 11.16332170818472 y[1] (numeric) = 11.16332170818483 absolute error = 1.06581410364015e-13 relative error = 9.547463841866322e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999927 y[1] (closed_form) = 11.17880808998187 y[1] (numeric) = 11.17880808998197 absolute error = 1.083577672034153e-13 relative error = 9.693141373499602e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999926 y[1] (closed_form) = 11.1943159553506 y[1] (numeric) = 11.19431595535071 absolute error = 1.083577672034153e-13 relative error = 9.679713136167376e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999925 y[1] (closed_form) = 11.20984533409415 y[1] (numeric) = 11.20984533409425 absolute error = 1.083577672034153e-13 relative error = 9.666303501427528e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999924 y[1] (closed_form) = 11.22539625605704 y[1] (numeric) = 11.22539625605715 absolute error = 1.119104808822158e-13 relative error = 9.969401376083335e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999923 y[1] (closed_form) = 11.24096875112525 y[1] (numeric) = 11.24096875112536 absolute error = 1.13686837721616e-13 relative error = 1.011361567126816e-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) = 11.25656284922618 y[1] (numeric) = 11.25656284922629 absolute error = 1.154631945610163e-13 relative error = 1.025741126377255e-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) = 11.27217858032876 y[1] (numeric) = 11.27217858032887 absolute error = 1.13686837721616e-13 relative error = 1.008561361155266e-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) = 11.2878159744435 y[1] (numeric) = 11.28781597444362 absolute error = 1.13686837721616e-13 relative error = 1.007164166912465e-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) = 11.30347506162254 y[1] (numeric) = 11.30347506162266 absolute error = 1.13686837721616e-13 relative error = 1.005768908250212e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999917 y[1] (closed_form) = 11.3191558719597 y[1] (numeric) = 11.31915587195982 absolute error = 1.13686837721616e-13 relative error = 1.004375582487082e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999916 y[1] (closed_form) = 11.33485843559056 y[1] (numeric) = 11.33485843559068 absolute error = 1.172395514004165e-13 relative error = 1.034327442787407e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999915 y[1] (closed_form) = 11.3505827826925 y[1] (numeric) = 11.35058278269262 absolute error = 1.20792265079217e-13 relative error = 1.064194388885498e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999914 y[1] (closed_form) = 11.36632894348477 y[1] (numeric) = 11.36632894348489 absolute error = 1.225686219186173e-13 relative error = 1.078348361445884e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999913 y[1] (closed_form) = 11.38209694822852 y[1] (numeric) = 11.38209694822864 absolute error = 1.225686219186173e-13 relative error = 1.076854488905874e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999912 y[1] (closed_form) = 11.39788682722691 y[1] (numeric) = 11.39788682722704 absolute error = 1.243449787580175e-13 relative error = 1.090947652340135e-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) = 11.41369861082513 y[1] (numeric) = 11.41369861082525 absolute error = 1.243449787580175e-13 relative error = 1.089436325575346e-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) = 11.42953232941044 y[1] (numeric) = 11.42953232941057 absolute error = 1.261213355974178e-13 relative error = 1.103468908109938e-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) = 11.4453880134123 y[1] (numeric) = 11.44538801341243 absolute error = 1.27897692436818e-13 relative error = 1.117460520228243e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999907 y[1] (closed_form) = 11.46126569330234 y[1] (numeric) = 11.46126569330247 absolute error = 1.27897692436818e-13 relative error = 1.115912464288809e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999906 y[1] (closed_form) = 11.4771653995945 y[1] (numeric) = 11.47716539959463 absolute error = 1.27897692436818e-13 relative error = 1.114366552923746e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999905 y[1] (closed_form) = 11.49308716284501 y[1] (numeric) = 11.49308716284514 absolute error = 1.314504061156185e-13 relative error = 1.143734527138826e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999904 y[1] (closed_form) = 11.50903101365254 y[1] (numeric) = 11.50903101365267 absolute error = 1.332267629550188e-13 relative error = 1.157584533371916e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999903 y[1] (closed_form) = 11.52499698265815 y[1] (numeric) = 11.52499698265828 absolute error = 1.332267629550188e-13 relative error = 1.155980892276911e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999902 y[1] (closed_form) = 11.54098510054545 y[1] (numeric) = 11.54098510054559 absolute error = 1.332267629550188e-13 relative error = 1.154379472760278e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999901 y[1] (closed_form) = 11.55699539804061 y[1] (numeric) = 11.55699539804074 absolute error = 1.35003119794419e-13 relative error = 1.168150675367645e-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) = 11.57302790591241 y[1] (numeric) = 11.57302790591254 absolute error = 1.367794766338193e-13 relative error = 1.181881507120031e-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) = 11.58908265497231 y[1] (numeric) = 11.58908265497245 absolute error = 1.403321903126198e-13 relative error = 1.210899900281668e-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) = 11.60515967607455 y[1] (numeric) = 11.60515967607469 absolute error = 1.4210854715202e-13 relative error = 1.224529012254731e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999896 y[1] (closed_form) = 11.62125900011613 y[1] (numeric) = 11.62125900011628 absolute error = 1.456612608308205e-13 relative error = 1.253403446471376e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999895 y[1] (closed_form) = 11.63738065803694 y[1] (numeric) = 11.63738065803709 absolute error = 1.474376176702208e-13 relative error = 1.266931296677988e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999894 y[1] (closed_form) = 11.65352468081977 y[1] (numeric) = 11.65352468081992 absolute error = 1.49213974509621e-13 relative error = 1.280419260236419e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999893 y[1] (closed_form) = 11.66969109949042 y[1] (numeric) = 11.66969109949057 absolute error = 1.509903313490213e-13 relative error = 1.293867421697346e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999892 y[1] (closed_form) = 11.68587994511769 y[1] (numeric) = 11.68587994511785 absolute error = 1.509903313490213e-13 relative error = 1.292074983297294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999891 y[1] (closed_form) = 11.70209124881353 y[1] (numeric) = 11.70209124881368 absolute error = 1.56319401867222e-13 relative error = 1.3358244996002e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.99999999999989 y[1] (closed_form) = 11.718325041733 y[1] (numeric) = 11.71832504173316 absolute error = 1.580957587066223e-13 relative error = 1.349132731372348e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.009999999999889 y[1] (closed_form) = 11.73458135507442 y[1] (numeric) = 11.73458135507458 absolute error = 1.616484723854228e-13 relative error = 1.377539321549982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999888 y[1] (closed_form) = 11.75086022007936 y[1] (numeric) = 11.75086022007953 absolute error = 1.652011860642233e-13 relative error = 1.405864617314864e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = 11.76716166803276 y[1] (numeric) = 11.76716166803293 absolute error = 1.687538997430238e-13 relative error = 1.434108789390298e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999885 y[1] (closed_form) = 11.78348573026293 y[1] (numeric) = 11.7834857302631 absolute error = 1.70530256582424e-13 relative error = 1.447197039026065e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999884 y[1] (closed_form) = 11.79983243814167 y[1] (numeric) = 11.79983243814184 absolute error = 1.723066134218243e-13 relative error = 1.460246273200135e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999883 y[1] (closed_form) = 11.81620182308427 y[1] (numeric) = 11.81620182308444 absolute error = 1.740829702612245e-13 relative error = 1.473256574893077e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999882 y[1] (closed_form) = 11.83259391654962 y[1] (numeric) = 11.83259391654979 absolute error = 1.740829702612245e-13 relative error = 1.471215622617995e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999881 y[1] (closed_form) = 11.84900875004025 y[1] (numeric) = 11.84900875004043 absolute error = 1.77635683940025e-13 relative error = 1.499160711982946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08999999999988 y[1] (closed_form) = 11.8654463551024 y[1] (numeric) = 11.86544635510258 absolute error = 1.811883976188255e-13 relative error = 1.527025551305203e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.099999999999879 y[1] (closed_form) = 11.88190676332604 y[1] (numeric) = 11.88190676332623 absolute error = 1.811883976188255e-13 relative error = 1.524910111044386e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999878 y[1] (closed_form) = 11.89839000634501 y[1] (numeric) = 11.8983900063452 absolute error = 1.829647544582258e-13 relative error = 1.537726989623443e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999877 y[1] (closed_form) = 11.914896115837 y[1] (numeric) = 11.91489611583718 absolute error = 1.84741111297626e-13 relative error = 1.550505430358495e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 11.93142512352365 y[1] (numeric) = 11.93142512352384 absolute error = 1.900701818158268e-13 relative error = 1.59302162020101e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999874 y[1] (closed_form) = 11.94797706117062 y[1] (numeric) = 11.94797706117081 absolute error = 1.900701818158268e-13 relative error = 1.590814753348752e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999873 y[1] (closed_form) = 11.96455196058761 y[1] (numeric) = 11.96455196058781 absolute error = 1.936228954946273e-13 relative error = 1.618304606243842e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999872 y[1] (closed_form) = 11.9811498536285 y[1] (numeric) = 11.98114985362869 absolute error = 1.936228954946273e-13 relative error = 1.616062714013952e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999871 y[1] (closed_form) = 11.9977707721913 y[1] (numeric) = 11.9977707721915 absolute error = 1.989519660128281e-13 relative error = 1.658241099871348e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17999999999987 y[1] (closed_form) = 12.0144147482183 y[1] (numeric) = 12.0144147482185 absolute error = 1.989519660128281e-13 relative error = 1.655943882263029e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.189999999999869 y[1] (closed_form) = 12.03108181369611 y[1] (numeric) = 12.03108181369631 absolute error = 2.007283228522283e-13 relative error = 1.668414577845531e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999868 y[1] (closed_form) = 12.04777200065569 y[1] (numeric) = 12.04777200065589 absolute error = 2.007283228522283e-13 relative error = 1.666103266573304e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999867 y[1] (closed_form) = 12.06448534117245 y[1] (numeric) = 12.06448534117266 absolute error = 2.042810365310288e-13 relative error = 1.693242859136968e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999866 y[1] (closed_form) = 12.0812218673663 y[1] (numeric) = 12.08122186736651 absolute error = 2.060573933704291e-13 relative error = 1.705600605904189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = 12.0979816114017 y[1] (numeric) = 12.09798161140191 absolute error = 2.096101070492296e-13 relative error = 1.732603948179944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999863 y[1] (closed_form) = 12.11476460548774 y[1] (numeric) = 12.11476460548795 absolute error = 2.131628207280301e-13 relative error = 1.759529199861396e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999862 y[1] (closed_form) = 12.13157088187817 y[1] (numeric) = 12.13157088187839 absolute error = 2.131628207280301e-13 relative error = 1.757091664414599e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999861 y[1] (closed_form) = 12.14840047287152 y[1] (numeric) = 12.14840047287173 absolute error = 2.167155344068306e-13 relative error = 1.783901797531091e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26999999999986 y[1] (closed_form) = 12.16525341081108 y[1] (numeric) = 12.1652534108113 absolute error = 2.184918912462308e-13 relative error = 1.796032387225573e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.279999999999859 y[1] (closed_form) = 12.18212972808506 y[1] (numeric) = 12.18212972808529 absolute error = 2.238209617644316e-13 relative error = 1.837289265180191e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999858 y[1] (closed_form) = 12.19902945712657 y[1] (numeric) = 12.19902945712679 absolute error = 2.255973186038318e-13 relative error = 1.849305466444627e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999857 y[1] (closed_form) = 12.2159526304137 y[1] (numeric) = 12.21595263041393 absolute error = 2.273736754432321e-13 relative error = 1.861284848773451e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999856 y[1] (closed_form) = 12.23289928046963 y[1] (numeric) = 12.23289928046986 absolute error = 2.291500322826323e-13 relative error = 1.87322749111881e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999855 y[1] (closed_form) = 12.24986943986264 y[1] (numeric) = 12.24986943986288 absolute error = 2.344791028008331e-13 relative error = 1.914135525704528e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = 12.26686314120619 y[1] (numeric) = 12.26686314120643 absolute error = 2.362554596402333e-13 relative error = 1.925964746819556e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999852 y[1] (closed_form) = 12.28388041715899 y[1] (numeric) = 12.28388041715922 absolute error = 2.380318164796336e-13 relative error = 1.937757519579351e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999851 y[1] (closed_form) = 12.30092130042504 y[1] (numeric) = 12.30092130042528 absolute error = 2.415845301584341e-13 relative error = 1.963954766136797e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35999999999985 y[1] (closed_form) = 12.31798582375373 y[1] (numeric) = 12.31798582375397 absolute error = 2.433608869978343e-13 relative error = 1.975654871501335e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.369999999999849 y[1] (closed_form) = 12.33507401993987 y[1] (numeric) = 12.33507401994011 absolute error = 2.415845301584341e-13 relative error = 1.95851706903346e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999848 y[1] (closed_form) = 12.35218592182376 y[1] (numeric) = 12.35218592182401 absolute error = 2.451372438372346e-13 relative error = 1.984565690548162e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999847 y[1] (closed_form) = 12.36932156229127 y[1] (numeric) = 12.36932156229152 absolute error = 2.469136006766348e-13 relative error = 1.996177392860154e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999846 y[1] (closed_form) = 12.38648097427389 y[1] (numeric) = 12.38648097427414 absolute error = 2.469136006766348e-13 relative error = 1.993412020649465e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999845 y[1] (closed_form) = 12.40366419074879 y[1] (numeric) = 12.40366419074904 absolute error = 2.486899575160351e-13 relative error = 2.004971705873166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 12.42087124473888 y[1] (numeric) = 12.42087124473913 absolute error = 2.504663143554353e-13 relative error = 2.01649553739256e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 12.4381021693129 y[1] (numeric) = 12.43810216931315 absolute error = 2.540190280342358e-13 relative error = 2.042265166955678e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999841 y[1] (closed_form) = 12.45535699758543 y[1] (numeric) = 12.45535699758569 absolute error = 2.575717417130363e-13 relative error = 2.067959527478567e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44999999999984 y[1] (closed_form) = 12.47263576271704 y[1] (numeric) = 12.4726357627173 absolute error = 2.575717417130363e-13 relative error = 2.06509471304345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.459999999999839 y[1] (closed_form) = 12.48993849791426 y[1] (numeric) = 12.48993849791452 absolute error = 2.593480985524366e-13 relative error = 2.076456169866216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999838 y[1] (closed_form) = 12.50726523642971 y[1] (numeric) = 12.50726523642997 absolute error = 2.629008122312371e-13 relative error = 2.101984784535392e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999837 y[1] (closed_form) = 12.52461601156212 y[1] (numeric) = 12.52461601156239 absolute error = 2.646771690706373e-13 relative error = 2.113255758310675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999836 y[1] (closed_form) = 12.54199085665643 y[1] (numeric) = 12.5419908566567 absolute error = 2.717825964282383e-13 relative error = 2.166981299336498e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999835 y[1] (closed_form) = 12.55938980510383 y[1] (numeric) = 12.5593898051041 absolute error = 2.700062395888381e-13 relative error = 2.149835651084849e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999834 y[1] (closed_form) = 12.57681289034184 y[1] (numeric) = 12.57681289034211 absolute error = 2.717825964282383e-13 relative error = 2.16098147279387e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 12.59426014585435 y[1] (numeric) = 12.59426014585462 absolute error = 2.735589532676386e-13 relative error = 2.172092287276486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999831 y[1] (closed_form) = 12.61173160517172 y[1] (numeric) = 12.61173160517199 absolute error = 2.753353101070388e-13 relative error = 2.183168170135587e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53999999999983 y[1] (closed_form) = 12.62922730187081 y[1] (numeric) = 12.62922730187108 absolute error = 2.788880237858393e-13 relative error = 2.208274640401213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999829 y[1] (closed_form) = 12.64674726957507 y[1] (numeric) = 12.64674726957535 absolute error = 2.824407374646398e-13 relative error = 2.233307359150935e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999828 y[1] (closed_form) = 12.66429154195459 y[1] (numeric) = 12.66429154195487 absolute error = 2.859934511434403e-13 relative error = 2.25826648254262e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999827 y[1] (closed_form) = 12.68186015272617 y[1] (numeric) = 12.68186015272646 absolute error = 2.895461648222408e-13 relative error = 2.283152166443014e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999826 y[1] (closed_form) = 12.69945313565338 y[1] (numeric) = 12.69945313565367 absolute error = 2.913225216616411e-13 relative error = 2.293976902389291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999825 y[1] (closed_form) = 12.71707052454664 y[1] (numeric) = 12.71707052454693 absolute error = 2.913225216616411e-13 relative error = 2.290798978422955e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999824 y[1] (closed_form) = 12.73471235326326 y[1] (numeric) = 12.73471235326355 absolute error = 2.913225216616411e-13 relative error = 2.287625456942417e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999823 y[1] (closed_form) = 12.75237865570752 y[1] (numeric) = 12.75237865570782 absolute error = 2.948752353404416e-13 relative error = 2.312315555407897e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 12.77006946583075 y[1] (numeric) = 12.77006946583105 absolute error = 3.002043058586423e-13 relative error = 2.350843170132377e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.62999999999982 y[1] (closed_form) = 12.78778481763136 y[1] (numeric) = 12.78778481763166 absolute error = 3.019806626980426e-13 relative error = 2.361477511583413e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.639999999999819 y[1] (closed_form) = 12.80552474515494 y[1] (numeric) = 12.80552474515524 absolute error = 3.055333763768431e-13 relative error = 2.385949677637723e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999818 y[1] (closed_form) = 12.82328928249429 y[1] (numeric) = 12.82328928249459 absolute error = 3.073097332162433e-13 relative error = 2.39649692404403e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999817 y[1] (closed_form) = 12.84107846378952 y[1] (numeric) = 12.84107846378983 absolute error = 3.073097332162433e-13 relative error = 2.393176975616372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999816 y[1] (closed_form) = 12.8588923232281 y[1] (numeric) = 12.85889232322841 absolute error = 3.108624468950438e-13 relative error = 2.417490084534783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999815 y[1] (closed_form) = 12.87673089504494 y[1] (numeric) = 12.87673089504525 absolute error = 3.108624468950438e-13 relative error = 2.414141053570251e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999814 y[1] (closed_form) = 12.8945942135224 y[1] (numeric) = 12.89459421352272 absolute error = 3.144151605738443e-13 relative error = 2.438348623984778e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999813 y[1] (closed_form) = 12.91248231299045 y[1] (numeric) = 12.91248231299077 absolute error = 3.144151605738443e-13 relative error = 2.434970696978463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999812 y[1] (closed_form) = 12.93039522782665 y[1] (numeric) = 12.93039522782697 absolute error = 3.179678742526448e-13 relative error = 2.459073126924745e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 12.94833299245626 y[1] (numeric) = 12.94833299245658 absolute error = 3.179678742526448e-13 relative error = 2.455666489561968e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.729999999999809 y[1] (closed_form) = 12.96629564135231 y[1] (numeric) = 12.96629564135263 absolute error = 3.179678742526448e-13 relative error = 2.452264571529411e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999808 y[1] (closed_form) = 12.98428320903562 y[1] (numeric) = 12.98428320903594 absolute error = 3.179678742526448e-13 relative error = 2.448867366289225e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999807 y[1] (closed_form) = 13.00229573007494 y[1] (numeric) = 13.00229573007526 absolute error = 3.161915174132446e-13 relative error = 2.431812996545512e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999806 y[1] (closed_form) = 13.02033323908695 y[1] (numeric) = 13.02033323908726 absolute error = 3.179678742526448e-13 relative error = 2.442087068079852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999805 y[1] (closed_form) = 13.03839577073635 y[1] (numeric) = 13.03839577073667 absolute error = 3.179678742526448e-13 relative error = 2.438703962080202e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999804 y[1] (closed_form) = 13.05648335973594 y[1] (numeric) = 13.05648335973626 absolute error = 3.215205879314453e-13 relative error = 2.462535884072447e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999803 y[1] (closed_form) = 13.07459604084668 y[1] (numeric) = 13.074596040847 absolute error = 3.268496584496461e-13 relative error = 2.499883418413286e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999802 y[1] (closed_form) = 13.09273384887773 y[1] (numeric) = 13.09273384887806 absolute error = 3.268496584496461e-13 relative error = 2.496420245170283e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999801 y[1] (closed_form) = 13.11089681868657 y[1] (numeric) = 13.11089681868689 absolute error = 3.268496584496461e-13 relative error = 2.492961869578572e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 13.12908498517901 y[1] (numeric) = 13.12908498517933 absolute error = 3.286260152890463e-13 relative error = 2.50303822132328e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999798 y[1] (closed_form) = 13.14729838330929 y[1] (numeric) = 13.14729838330962 absolute error = 3.304023721284466e-13 relative error = 2.513081870476887e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999797 y[1] (closed_form) = 13.16553704808015 y[1] (numeric) = 13.16553704808048 absolute error = 3.321787289678468e-13 relative error = 2.523092888309379e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999796 y[1] (closed_form) = 13.18380101454288 y[1] (numeric) = 13.18380101454322 absolute error = 3.339550858072471e-13 relative error = 2.533071345956037e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999795 y[1] (closed_form) = 13.20209031779741 y[1] (numeric) = 13.20209031779774 absolute error = 3.339550858072471e-13 relative error = 2.529562196351972e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999794 y[1] (closed_form) = 13.22040499299232 y[1] (numeric) = 13.22040499299266 absolute error = 3.357314426466473e-13 relative error = 2.539494386326341e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999793 y[1] (closed_form) = 13.238745075325 y[1] (numeric) = 13.23874507532534 absolute error = 3.392841563254478e-13 relative error = 2.562812067118216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999792 y[1] (closed_form) = 13.25711060004165 y[1] (numeric) = 13.25711060004199 absolute error = 3.428368700042483e-13 relative error = 2.586060268692118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999791 y[1] (closed_form) = 13.27550160243735 y[1] (numeric) = 13.27550160243769 absolute error = 3.428368700042483e-13 relative error = 2.582477711737117e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.90999999999979 y[1] (closed_form) = 13.29391811785616 y[1] (numeric) = 13.29391811785651 absolute error = 3.481659405224491e-13 relative error = 2.618986648148515e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 13.31236018169117 y[1] (numeric) = 13.31236018169152 absolute error = 3.481659405224491e-13 relative error = 2.615358477163882e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999787 y[1] (closed_form) = 13.33082782938456 y[1] (numeric) = 13.33082782938491 absolute error = 3.517186542012496e-13 relative error = 2.638385692942276e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999786 y[1] (closed_form) = 13.34932109642769 y[1] (numeric) = 13.34932109642804 absolute error = 3.534950110406498e-13 relative error = 2.648037368246734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999785 y[1] (closed_form) = 13.36784001836114 y[1] (numeric) = 13.3678400183615 absolute error = 3.588240815588506e-13 relative error = 2.68423381089237e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999784 y[1] (closed_form) = 13.38638463077482 y[1] (numeric) = 13.38638463077518 absolute error = 3.570477247194503e-13 relative error = 2.667245373322162e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999783 y[1] (closed_form) = 13.40495496930798 y[1] (numeric) = 13.40495496930834 absolute error = 3.606004383982508e-13 relative error = 2.690053336425841e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999782 y[1] (closed_form) = 13.42355106964933 y[1] (numeric) = 13.4235510696497 absolute error = 3.641531520770513e-13 relative error = 2.712792987396622e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999781 y[1] (closed_form) = 13.44217296753709 y[1] (numeric) = 13.44217296753746 absolute error = 3.641531520770513e-13 relative error = 2.709034863310291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99999999999978 y[1] (closed_form) = 13.46082069875905 y[1] (numeric) = 13.46082069875942 absolute error = 3.677058657558518e-13 relative error = 2.731674940070709e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.009999999999779 y[1] (closed_form) = 13.47949429915265 y[1] (numeric) = 13.47949429915302 absolute error = 3.712585794346523e-13 relative error = 2.754247089655214e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 13.49819380460505 y[1] (numeric) = 13.49819380460542 absolute error = 3.712585794346523e-13 relative error = 2.750431537795772e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999776 y[1] (closed_form) = 13.51691925105319 y[1] (numeric) = 13.51691925105356 absolute error = 3.730349362740526e-13 relative error = 2.75976300032263e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999775 y[1] (closed_form) = 13.53567067448386 y[1] (numeric) = 13.53567067448423 absolute error = 3.730349362740526e-13 relative error = 2.755939807085157e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999774 y[1] (closed_form) = 13.55444811093378 y[1] (numeric) = 13.55444811093415 absolute error = 3.694822225952521e-13 relative error = 2.725911225387385e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999773 y[1] (closed_form) = 13.57325159648965 y[1] (numeric) = 13.57325159649003 absolute error = 3.712585794346523e-13 relative error = 2.735222115315891e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999772 y[1] (closed_form) = 13.59208116728826 y[1] (numeric) = 13.59208116728864 absolute error = 3.730349362740526e-13 relative error = 2.744501976428943e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999771 y[1] (closed_form) = 13.6109368595165 y[1] (numeric) = 13.61093685951688 absolute error = 3.730349362740526e-13 relative error = 2.740699924805204e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08999999999977 y[1] (closed_form) = 13.62981870941148 y[1] (numeric) = 13.62981870941186 absolute error = 3.765876499528531e-13 relative error = 2.762968884485726e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.099999999999769 y[1] (closed_form) = 13.64872675326056 y[1] (numeric) = 13.64872675326094 absolute error = 3.801403636316536e-13 relative error = 2.785170884462474e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999768 y[1] (closed_form) = 13.66766102740147 y[1] (numeric) = 13.66766102740185 absolute error = 3.819167204710538e-13 relative error = 2.794309280171436e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 13.68662156822231 y[1] (numeric) = 13.6866215682227 absolute error = 3.872457909892546e-13 relative error = 2.82937457618003e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999765 y[1] (closed_form) = 13.7056084121617 y[1] (numeric) = 13.70560841216209 absolute error = 3.872457909892546e-13 relative error = 2.825454947666761e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999764 y[1] (closed_form) = 13.72462159570878 y[1] (numeric) = 13.72462159570917 absolute error = 3.872457909892546e-13 relative error = 2.821540749147743e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999763 y[1] (closed_form) = 13.74366115540333 y[1] (numeric) = 13.74366115540372 absolute error = 3.907985046680551e-13 relative error = 2.843481807716223e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999762 y[1] (closed_form) = 13.76272712783581 y[1] (numeric) = 13.7627271278362 absolute error = 3.907985046680551e-13 relative error = 2.839542635976887e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999761 y[1] (closed_form) = 13.78181954964744 y[1] (numeric) = 13.78181954964783 absolute error = 3.907985046680551e-13 relative error = 2.835608921305695e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17999999999976 y[1] (closed_form) = 13.80093845753027 y[1] (numeric) = 13.80093845753066 absolute error = 3.907985046680551e-13 relative error = 2.831680656142785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.189999999999759 y[1] (closed_form) = 13.82008388822725 y[1] (numeric) = 13.82008388822764 absolute error = 3.907985046680551e-13 relative error = 2.827757832938771e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999758 y[1] (closed_form) = 13.83925587853231 y[1] (numeric) = 13.8392558785327 absolute error = 3.907985046680551e-13 relative error = 2.82384044415472e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 13.85845446529043 y[1] (numeric) = 13.85845446529082 absolute error = 3.890221478286549e-13 relative error = 2.807110625524592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 13.87767968539767 y[1] (numeric) = 13.87767968539806 absolute error = 3.907985046680551e-13 relative error = 2.816021939742996e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999754 y[1] (closed_form) = 13.8969315758013 y[1] (numeric) = 13.8969315758017 absolute error = 3.961275751862559e-13 relative error = 2.850467911031756e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999753 y[1] (closed_form) = 13.91621017349986 y[1] (numeric) = 13.91621017350025 absolute error = 3.961275751862559e-13 relative error = 2.846519061206674e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999752 y[1] (closed_form) = 13.93551551554317 y[1] (numeric) = 13.93551551554357 absolute error = 3.979039320256561e-13 relative error = 2.855322658008944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999751 y[1] (closed_form) = 13.9548476390325 y[1] (numeric) = 13.9548476390329 absolute error = 4.014566457044566e-13 relative error = 2.87682571740561e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26999999999975 y[1] (closed_form) = 13.97420658112055 y[1] (numeric) = 13.97420658112095 absolute error = 4.014566457044566e-13 relative error = 2.872840353217857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.279999999999749 y[1] (closed_form) = 13.99359237901158 y[1] (numeric) = 13.99359237901198 absolute error = 4.032330025438569e-13 relative error = 2.881554583143709e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999748 y[1] (closed_form) = 14.01300506996144 y[1] (numeric) = 14.01300506996185 absolute error = 4.050093593832571e-13 relative error = 2.890239155421725e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999747 y[1] (closed_form) = 14.03244469127771 y[1] (numeric) = 14.03244469127811 absolute error = 4.085620730620576e-13 relative error = 2.911553061855372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 14.05191128031966 y[1] (numeric) = 14.05191128032008 absolute error = 4.103384299014579e-13 relative error = 2.920160978216218e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999744 y[1] (closed_form) = 14.07140487449845 y[1] (numeric) = 14.07140487449886 absolute error = 4.103384299014579e-13 relative error = 2.916115580222643e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999743 y[1] (closed_form) = 14.0909255112771 y[1] (numeric) = 14.09092551127751 absolute error = 4.103384299014579e-13 relative error = 2.912075786456043e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999742 y[1] (closed_form) = 14.1104732281706 y[1] (numeric) = 14.11047322817102 absolute error = 4.103384299014579e-13 relative error = 2.908041589152694e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999741 y[1] (closed_form) = 14.13004806274601 y[1] (numeric) = 14.13004806274643 absolute error = 4.121147867408581e-13 relative error = 2.916584465323951e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35999999999974 y[1] (closed_form) = 14.14965005262249 y[1] (numeric) = 14.1496500526229 absolute error = 4.138911435802584e-13 relative error = 2.925098091055248e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.369999999999739 y[1] (closed_form) = 14.16927923547137 y[1] (numeric) = 14.16927923547179 absolute error = 4.121147867408581e-13 relative error = 2.90850917602901e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999738 y[1] (closed_form) = 14.18893564901627 y[1] (numeric) = 14.18893564901669 absolute error = 4.174438572590589e-13 relative error = 2.942037849667748e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999737 y[1] (closed_form) = 14.20861933103313 y[1] (numeric) = 14.20861933103354 absolute error = 4.156675004196586e-13 relative error = 2.925460178328494e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999736 y[1] (closed_form) = 14.22833031935028 y[1] (numeric) = 14.22833031935069 absolute error = 4.174438572590589e-13 relative error = 2.933892086349321e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 14.24806865184855 y[1] (numeric) = 14.24806865184897 absolute error = 4.227729277772596e-13 relative error = 2.967229721499194e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999733 y[1] (closed_form) = 14.26783436646131 y[1] (numeric) = 14.26783436646173 absolute error = 4.245492846166599e-13 relative error = 2.975569197905933e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999732 y[1] (closed_form) = 14.28762750117456 y[1] (numeric) = 14.28762750117498 absolute error = 4.245492846166599e-13 relative error = 2.97144704102734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999731 y[1] (closed_form) = 14.30744809402698 y[1] (numeric) = 14.3074480940274 absolute error = 4.245492846166599e-13 relative error = 2.967330594712408e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44999999999973 y[1] (closed_form) = 14.32729618311004 y[1] (numeric) = 14.32729618311046 absolute error = 4.263256414560601e-13 relative error = 2.975618260468719e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.459999999999729 y[1] (closed_form) = 14.34717180656803 y[1] (numeric) = 14.34717180656846 absolute error = 4.263256414560601e-13 relative error = 2.971496035622095e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999728 y[1] (closed_form) = 14.36707500259819 y[1] (numeric) = 14.36707500259862 absolute error = 4.263256414560601e-13 relative error = 2.96737952143329e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999727 y[1] (closed_form) = 14.38700580945072 y[1] (numeric) = 14.38700580945114 absolute error = 4.281019982954604e-13 relative error = 2.975615662949433e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999726 y[1] (closed_form) = 14.40696426542888 y[1] (numeric) = 14.40696426542931 absolute error = 4.298783551348606e-13 relative error = 2.983823290007055e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999725 y[1] (closed_form) = 14.42695040888908 y[1] (numeric) = 14.42695040888952 absolute error = 4.316547119742609e-13 relative error = 2.992002465803856e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 14.44696427824095 y[1] (numeric) = 14.44696427824139 absolute error = 4.352074256530614e-13 relative error = 3.01244896347215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999722 y[1] (closed_form) = 14.46700591194739 y[1] (numeric) = 14.46700591194782 absolute error = 4.334310688136611e-13 relative error = 2.995997039413095e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999721 y[1] (closed_form) = 14.48707534852464 y[1] (numeric) = 14.48707534852508 absolute error = 4.387601393318619e-13 relative error = 3.028631582126375e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.53999999999972 y[1] (closed_form) = 14.50717262654242 y[1] (numeric) = 14.50717262654286 absolute error = 4.405364961712621e-13 relative error = 3.036680595950542e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.549999999999719 y[1] (closed_form) = 14.5272977846239 y[1] (numeric) = 14.52729778462434 absolute error = 4.405364961712621e-13 relative error = 3.032473779380624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999718 y[1] (closed_form) = 14.54745086144587 y[1] (numeric) = 14.54745086144632 absolute error = 4.440892098500626e-13 relative error = 3.052694345419666e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999717 y[1] (closed_form) = 14.56763189573877 y[1] (numeric) = 14.56763189573922 absolute error = 4.458655666894629e-13 relative error = 3.060659205837598e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999716 y[1] (closed_form) = 14.58784092628675 y[1] (numeric) = 14.5878409262872 absolute error = 4.494182803682634e-13 relative error = 3.080773108503179e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999715 y[1] (closed_form) = 14.60807799192778 y[1] (numeric) = 14.60807799192824 absolute error = 4.547473508864641e-13 relative error = 3.11298550800284e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999714 y[1] (closed_form) = 14.6283431315537 y[1] (numeric) = 14.62834313155416 absolute error = 4.583000645652646e-13 relative error = 3.132959491336377e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 14.64863638411031 y[1] (numeric) = 14.64863638411077 absolute error = 4.565237077258644e-13 relative error = 3.116492864967728e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999711 y[1] (closed_form) = 14.66895778859743 y[1] (numeric) = 14.66895778859789 absolute error = 4.600764214046649e-13 relative error = 3.13639474620545e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.62999999999971 y[1] (closed_form) = 14.68930738406898 y[1] (numeric) = 14.68930738406944 absolute error = 4.618527782440651e-13 relative error = 3.144142648583684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.639999999999709 y[1] (closed_form) = 14.70968520963308 y[1] (numeric) = 14.70968520963354 absolute error = 4.654054919228656e-13 relative error = 3.163939168583166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999708 y[1] (closed_form) = 14.73009130445207 y[1] (numeric) = 14.73009130445254 absolute error = 4.671818487622659e-13 relative error = 3.171615430659709e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999707 y[1] (closed_form) = 14.75052570774265 y[1] (numeric) = 14.75052570774312 absolute error = 4.671818487622659e-13 relative error = 3.167221684289117e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999706 y[1] (closed_form) = 14.7709884587759 y[1] (numeric) = 14.77098845877637 absolute error = 4.725109192804666e-13 relative error = 3.198911979378965e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999705 y[1] (closed_form) = 14.79147959687739 y[1] (numeric) = 14.79147959687787 absolute error = 4.742872761198669e-13 relative error = 3.206489743054461e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999704 y[1] (closed_form) = 14.81199916142724 y[1] (numeric) = 14.81199916142772 absolute error = 4.778399897986674e-13 relative error = 3.226033060027692e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999703 y[1] (closed_form) = 14.83254719186021 y[1] (numeric) = 14.83254719186069 absolute error = 4.760636329592671e-13 relative error = 3.209587852992106e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 14.85312372766576 y[1] (numeric) = 14.85312372766624 absolute error = 4.796163466380676e-13 relative error = 3.229060468571493e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7199999999997 y[1] (closed_form) = 14.87372880838812 y[1] (numeric) = 14.8737288083886 absolute error = 4.796163466380676e-13 relative error = 3.224587141642554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.729999999999699 y[1] (closed_form) = 14.8943624736264 y[1] (numeric) = 14.89436247362687 absolute error = 4.778399897986674e-13 relative error = 3.208193641351106e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999698 y[1] (closed_form) = 14.91502476303462 y[1] (numeric) = 14.9150247630351 absolute error = 4.813927034774679e-13 relative error = 3.227568918762717e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999697 y[1] (closed_form) = 14.93571571632183 y[1] (numeric) = 14.93571571632232 absolute error = 4.849454171562684e-13 relative error = 3.246884356712263e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999696 y[1] (closed_form) = 14.95643537325217 y[1] (numeric) = 14.95643537325265 absolute error = 4.867217739956686e-13 relative error = 3.25426321077891e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999695 y[1] (closed_form) = 14.97718377364491 y[1] (numeric) = 14.9771837736454 absolute error = 4.920508445138694e-13 relative error = 3.285336228428489e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999694 y[1] (closed_form) = 14.99796095737461 y[1] (numeric) = 14.9979609573751 absolute error = 4.973799150320701e-13 relative error = 3.316316907649402e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999693 y[1] (closed_form) = 15.01876696437109 y[1] (numeric) = 15.01876696437159 absolute error = 5.009326287108706e-13 relative error = 3.335377863570487e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999692 y[1] (closed_form) = 15.03960183461962 y[1] (numeric) = 15.03960183462012 absolute error = 5.027089855502709e-13 relative error = 3.342568447477688e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 15.06046560816089 y[1] (numeric) = 15.0604656081614 absolute error = 5.062616992290714e-13 relative error = 3.361527541052521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.819999999999689 y[1] (closed_form) = 15.08135832509117 y[1] (numeric) = 15.08135832509167 absolute error = 5.080380560684716e-13 relative error = 3.368649196692305e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999688 y[1] (closed_form) = 15.10228002556233 y[1] (numeric) = 15.10228002556284 absolute error = 5.115907697472721e-13 relative error = 3.387506845862655e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999687 y[1] (closed_form) = 15.12323074978196 y[1] (numeric) = 15.12323074978247 absolute error = 5.133671265866724e-13 relative error = 3.394559899802322e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999686 y[1] (closed_form) = 15.14421053801342 y[1] (numeric) = 15.14421053801394 absolute error = 5.151434834260726e-13 relative error = 3.401586910938758e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999685 y[1] (closed_form) = 15.16521943057593 y[1] (numeric) = 15.16521943057645 absolute error = 5.186961971048731e-13 relative error = 3.420301298503364e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999684 y[1] (closed_form) = 15.18625746784464 y[1] (numeric) = 15.18625746784516 absolute error = 5.222489107836736e-13 relative error = 3.438957306561427e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999683 y[1] (closed_form) = 15.2073246902507 y[1] (numeric) = 15.20732469025122 absolute error = 5.240252676230739e-13 relative error = 3.445874131687492e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999682 y[1] (closed_form) = 15.22842113828137 y[1] (numeric) = 15.22842113828189 absolute error = 5.258016244624741e-13 relative error = 3.452765192713961e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 15.24954685248005 y[1] (numeric) = 15.24954685248058 absolute error = 5.240252676230739e-13 relative error = 3.436333372344445e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 15.27070187344642 y[1] (numeric) = 15.27070187344694 absolute error = 5.275779813018744e-13 relative error = 3.454837804274456e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999678 y[1] (closed_form) = 15.29188624183644 y[1] (numeric) = 15.29188624183697 absolute error = 5.329070518200751e-13 relative error = 3.484900707422978e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999677 y[1] (closed_form) = 15.3130999983625 y[1] (numeric) = 15.31309999836304 absolute error = 5.364597654988756e-13 relative error = 3.503273442714027e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999676 y[1] (closed_form) = 15.33434318379346 y[1] (numeric) = 15.334343183794 absolute error = 5.364597654988756e-13 relative error = 3.498420239256471e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999675 y[1] (closed_form) = 15.35561583895475 y[1] (numeric) = 15.35561583895528 absolute error = 5.346834086594754e-13 relative error = 3.482005634076029e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999674 y[1] (closed_form) = 15.37691800472839 y[1] (numeric) = 15.37691800472893 absolute error = 5.417888360170764e-13 relative error = 3.523390290892341e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999673 y[1] (closed_form) = 15.39824972205317 y[1] (numeric) = 15.39824972205372 absolute error = 5.453415496958769e-13 relative error = 3.541581410482296e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999672 y[1] (closed_form) = 15.41961103192464 y[1] (numeric) = 15.41961103192519 absolute error = 5.506706202140776e-13 relative error = 3.571235481063521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999671 y[1] (closed_form) = 15.44100197539523 y[1] (numeric) = 15.44100197539579 absolute error = 5.542233338928781e-13 relative error = 3.589296437990334e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 15.46242259357433 y[1] (numeric) = 15.46242259357488 absolute error = 5.577760475716786e-13 relative error = 3.607300500268774e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999673 y[1] (closed_form) = 15.48387292762833 y[1] (numeric) = 15.48387292762889 absolute error = 5.542233338928781e-13 relative error = 3.579358578330625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999676 y[1] (closed_form) = 15.50535301878077 y[1] (numeric) = 15.50535301878132 absolute error = 5.471179065352771e-13 relative error = 3.528574330894521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02999999999968 y[1] (closed_form) = 15.52686290831235 y[1] (numeric) = 15.52686290831288 absolute error = 5.346834086594754e-13 relative error = 3.443602302775735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999683 y[1] (closed_form) = 15.54840263756101 y[1] (numeric) = 15.54840263756154 absolute error = 5.293543381412746e-13 relative error = 3.404557693035864e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999686 y[1] (closed_form) = 15.56997224792211 y[1] (numeric) = 15.56997224792263 absolute error = 5.222489107836736e-13 relative error = 3.354205790915077e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05999999999969 y[1] (closed_form) = 15.59157178084836 y[1] (numeric) = 15.59157178084888 absolute error = 5.151434834260726e-13 relative error = 3.303986863331125e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999693 y[1] (closed_form) = 15.61320127785003 y[1] (numeric) = 15.61320127785054 absolute error = 5.098144129078719e-13 relative error = 3.265277913448344e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999696 y[1] (closed_form) = 15.63486078049496 y[1] (numeric) = 15.63486078049545 absolute error = 4.973799150320701e-13 relative error = 3.181223817819787e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.0899999999997 y[1] (closed_form) = 15.65655033040863 y[1] (numeric) = 15.65655033040911 absolute error = 4.884981308350689e-13 relative error = 3.120087889899303e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999703 y[1] (closed_form) = 15.67826996927429 y[1] (numeric) = 15.67826996927477 absolute error = 4.813927034774679e-13 relative error = 3.070445300539435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999706 y[1] (closed_form) = 15.70001973883302 y[1] (numeric) = 15.70001973883349 absolute error = 4.725109192804666e-13 relative error = 3.009619905838337e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11999999999971 y[1] (closed_form) = 15.72179968088378 y[1] (numeric) = 15.72179968088425 absolute error = 4.654054919228656e-13 relative error = 2.960255831835553e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999713 y[1] (closed_form) = 15.74360983728355 y[1] (numeric) = 15.74360983728401 absolute error = 4.600764214046649e-13 relative error = 2.922305787298701e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999716 y[1] (closed_form) = 15.76545024994736 y[1] (numeric) = 15.76545024994781 absolute error = 4.511946372076636e-13 relative error = 2.861920402236341e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14999999999972 y[1] (closed_form) = 15.78732096084837 y[1] (numeric) = 15.78732096084881 absolute error = 4.440892098500626e-13 relative error = 2.812948510715516e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999723 y[1] (closed_form) = 15.80922201201798 y[1] (numeric) = 15.80922201201842 absolute error = 4.369837824924616e-13 relative error = 2.76410681158296e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999726 y[1] (closed_form) = 15.83115344554592 y[1] (numeric) = 15.83115344554634 absolute error = 4.281019982954604e-13 relative error = 2.7041743974499e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17999999999973 y[1] (closed_form) = 15.85311530358027 y[1] (numeric) = 15.85311530358069 absolute error = 4.174438572590589e-13 relative error = 2.633197635071659e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999733 y[1] (closed_form) = 15.87510762832761 y[1] (numeric) = 15.87510762832803 absolute error = 4.121147867408581e-13 relative error = 2.595981056566058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999736 y[1] (closed_form) = 15.89713046205307 y[1] (numeric) = 15.89713046205347 absolute error = 4.032330025438569e-13 relative error = 2.536514394886462e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.20999999999974 y[1] (closed_form) = 15.91918384708039 y[1] (numeric) = 15.91918384708078 absolute error = 3.943512183468556e-13 relative error = 2.477207513494358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999743 y[1] (closed_form) = 15.94126782579204 y[1] (numeric) = 15.94126782579243 absolute error = 3.854694341498544e-13 relative error = 2.418060083817093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999746 y[1] (closed_form) = 15.96338244062929 y[1] (numeric) = 15.96338244062967 absolute error = 3.783640067922533e-13 relative error = 2.370199474951236e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23999999999975 y[1] (closed_form) = 15.98552773409228 y[1] (numeric) = 15.98552773409265 absolute error = 3.730349362740526e-13 relative error = 2.333579112802653e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999753 y[1] (closed_form) = 16.00770374874011 y[1] (numeric) = 16.00770374874047 absolute error = 3.623767952376511e-13 relative error = 2.26376500293599e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999756 y[1] (closed_form) = 16.0299105271909 y[1] (numeric) = 16.02991052719126 absolute error = 3.552713678800501e-13 relative error = 2.21630287503737e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26999999999976 y[1] (closed_form) = 16.05214811212194 y[1] (numeric) = 16.05214811212229 absolute error = 3.552713678800501e-13 relative error = 2.213232555534193e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999763 y[1] (closed_form) = 16.07441654626967 y[1] (numeric) = 16.07441654627002 absolute error = 3.481659405224491e-13 relative error = 2.16596315965973e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999766 y[1] (closed_form) = 16.09671587242986 y[1] (numeric) = 16.09671587243021 absolute error = 3.410605131648481e-13 relative error = 2.11882048405296e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29999999999977 y[1] (closed_form) = 16.11904613345763 y[1] (numeric) = 16.11904613345797 absolute error = 3.375077994860476e-13 relative error = 2.093844739270873e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999773 y[1] (closed_form) = 16.14140737226754 y[1] (numeric) = 16.14140737226787 absolute error = 3.268496584496461e-13 relative error = 2.024914252589924e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999776 y[1] (closed_form) = 16.1637996318337 y[1] (numeric) = 16.16379963183403 absolute error = 3.232969447708456e-13 relative error = 2.000129623817721e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32999999999978 y[1] (closed_form) = 16.18622295518984 y[1] (numeric) = 16.18622295519016 absolute error = 3.197442310920451e-13 relative error = 1.97540977890413e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999783 y[1] (closed_form) = 16.20867738542936 y[1] (numeric) = 16.20867738542968 absolute error = 3.126388037344441e-13 relative error = 1.928835995066986e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999786 y[1] (closed_form) = 16.23116296570549 y[1] (numeric) = 16.23116296570579 absolute error = 3.019806626980426e-13 relative error = 1.860499234319141e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35999999999979 y[1] (closed_form) = 16.25367973923127 y[1] (numeric) = 16.25367973923157 absolute error = 2.984279490192421e-13 relative error = 1.836063917876583e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999793 y[1] (closed_form) = 16.27622774927973 y[1] (numeric) = 16.27622774928002 absolute error = 2.877698079828406e-13 relative error = 1.768037486422953e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 16.29880703918391 y[1] (numeric) = 16.29880703918419 absolute error = 2.842170943040401e-13 relative error = 1.743790779415663e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3899999999998 y[1] (closed_form) = 16.32141765233697 y[1] (numeric) = 16.32141765233725 absolute error = 2.806643806252396e-13 relative error = 1.719607858849522e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999803 y[1] (closed_form) = 16.34405963219225 y[1] (numeric) = 16.34405963219253 absolute error = 2.806643806252396e-13 relative error = 1.71722562778972e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 16.36673302226341 y[1] (numeric) = 16.36673302226369 absolute error = 2.771116669464391e-13 relative error = 1.693139776701242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41999999999981 y[1] (closed_form) = 16.38943786612444 y[1] (numeric) = 16.38943786612471 absolute error = 2.664535259100376e-13 relative error = 1.625763666127769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999813 y[1] (closed_form) = 16.41217420740979 y[1] (numeric) = 16.41217420741005 absolute error = 2.522426711948356e-13 relative error = 1.536924163776867e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 16.43494208981445 y[1] (numeric) = 16.43494208981469 absolute error = 2.486899575160351e-13 relative error = 1.513178179496967e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44999999999982 y[1] (closed_form) = 16.457741557094 y[1] (numeric) = 16.45774155709424 absolute error = 2.415845301584341e-13 relative error = 1.467908153256305e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999823 y[1] (closed_form) = 16.48057265306475 y[1] (numeric) = 16.48057265306499 absolute error = 2.344791028008331e-13 relative error = 1.42276065120364e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 16.50343542160379 y[1] (numeric) = 16.50343542160402 absolute error = 2.344791028008331e-13 relative error = 1.420789652643405e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47999999999983 y[1] (closed_form) = 16.52632990664906 y[1] (numeric) = 16.52632990664928 absolute error = 2.167155344068306e-13 relative error = 1.311334916045934e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999833 y[1] (closed_form) = 16.54925615219947 y[1] (numeric) = 16.54925615219967 absolute error = 2.096101070492296e-13 relative error = 1.266583253781902e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 16.57221420231495 y[1] (numeric) = 16.57221420231515 absolute error = 1.989519660128281e-13 relative error = 1.2005152937562e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.50999999999984 y[1] (closed_form) = 16.59520410111658 y[1] (numeric) = 16.59520410111677 absolute error = 1.882938249764265e-13 relative error = 1.134627955336551e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999843 y[1] (closed_form) = 16.61822589278662 y[1] (numeric) = 16.61822589278681 absolute error = 1.84741111297626e-13 relative error = 1.111677699469807e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 16.64127962156865 y[1] (numeric) = 16.64127962156882 absolute error = 1.70530256582424e-13 relative error = 1.02474245046277e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53999999999985 y[1] (closed_form) = 16.66436533176759 y[1] (numeric) = 16.66436533176775 absolute error = 1.598721155460225e-13 relative error = 9.593651625079016e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999853 y[1] (closed_form) = 16.68748306774986 y[1] (numeric) = 16.68748306775001 absolute error = 1.49213974509621e-13 relative error = 8.941670466650013e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999857 y[1] (closed_form) = 16.7106328739434 y[1] (numeric) = 16.71063287394354 absolute error = 1.4210854715202e-13 relative error = 8.50407930232298e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56999999999986 y[1] (closed_form) = 16.7338147948378 y[1] (numeric) = 16.73381479483794 absolute error = 1.385558334732195e-13 relative error = 8.279990855161283e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999863 y[1] (closed_form) = 16.75702887498436 y[1] (numeric) = 16.75702887498449 absolute error = 1.314504061156185e-13 relative error = 7.844493620933813e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999867 y[1] (closed_form) = 16.78027515899619 y[1] (numeric) = 16.78027515899631 absolute error = 1.243449787580175e-13 relative error = 7.410187114324767e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59999999999987 y[1] (closed_form) = 16.80355369154828 y[1] (numeric) = 16.80355369154839 absolute error = 1.172395514004165e-13 relative error = 6.977068872007996e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999873 y[1] (closed_form) = 16.8268645173776 y[1] (numeric) = 16.82686451737771 absolute error = 1.101341240428155e-13 relative error = 6.545136435197227e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999877 y[1] (closed_form) = 16.85020768128319 y[1] (numeric) = 16.85020768128329 absolute error = 9.947598300641403e-14 relative error = 5.903546406547235e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.62999999999988 y[1] (closed_form) = 16.87358322812623 y[1] (numeric) = 16.87358322812633 absolute error = 9.947598300641403e-14 relative error = 5.895368023586095e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999883 y[1] (closed_form) = 16.89699120283014 y[1] (numeric) = 16.89699120283023 absolute error = 8.881784197001252e-14 relative error = 5.256429437871524e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999887 y[1] (closed_form) = 16.92043165038064 y[1] (numeric) = 16.92043165038072 absolute error = 8.171241461241152e-14 relative error = 4.829215725744994e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65999999999989 y[1] (closed_form) = 16.94390461582589 y[1] (numeric) = 16.94390461582597 absolute error = 8.171241461241152e-14 relative error = 4.822525649494673e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999893 y[1] (closed_form) = 16.96741014427651 y[1] (numeric) = 16.96741014427658 absolute error = 7.460698725481052e-14 relative error = 4.397075724604745e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999897 y[1] (closed_form) = 16.99094828090572 y[1] (numeric) = 16.99094828090578 absolute error = 6.750155989720952e-14 relative error = 3.97279532497119e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6899999999999 y[1] (closed_form) = 17.0145190709494 y[1] (numeric) = 17.01451907094946 absolute error = 6.039613253960852e-14 relative error = 3.549682026730271e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999903 y[1] (closed_form) = 17.03812255970619 y[1] (numeric) = 17.03812255970625 absolute error = 5.684341886080801e-14 relative error = 3.336248971188774e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999907 y[1] (closed_form) = 17.06175879253757 y[1] (numeric) = 17.06175879253762 absolute error = 4.618527782440651e-14 relative error = 2.706947061319781e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71999999999991 y[1] (closed_form) = 17.08542781486794 y[1] (numeric) = 17.08542781486798 absolute error = 3.907985046680551e-14 relative error = 2.287320568747934e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999913 y[1] (closed_form) = 17.10912967218471 y[1] (numeric) = 17.10912967218474 absolute error = 2.842170943040401e-14 relative error = 1.661201357109988e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999917 y[1] (closed_form) = 17.13286441003843 y[1] (numeric) = 17.13286441003844 absolute error = 1.77635683940025e-14 relative error = 1.036812524098103e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74999999999992 y[1] (closed_form) = 17.15663207404278 y[1] (numeric) = 17.15663207404279 absolute error = 1.4210854715202e-14 relative error = 8.283009540492738e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999923 y[1] (closed_form) = 17.18043270987477 y[1] (numeric) = 17.18043270987478 absolute error = 7.105427357601002e-15 relative error = 4.135767403295394e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999927 y[1] (closed_form) = 17.20426636327475 y[1] (numeric) = 17.20426636327475 absolute error = 3.552713678800501e-15 relative error = 2.065018992256673e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77999999999993 y[1] (closed_form) = 17.22813308004653 y[1] (numeric) = 17.22813308004652 absolute error = 1.06581410364015e-14 relative error = 6.18647475433404e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999933 y[1] (closed_form) = 17.25203290605747 y[1] (numeric) = 17.25203290605745 absolute error = 1.77635683940025e-14 relative error = 1.029650736856955e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999937 y[1] (closed_form) = 17.27596588723853 y[1] (numeric) = 17.27596588723851 absolute error = 2.131628207280301e-14 relative error = 1.233869192144503e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.80999999999994 y[1] (closed_form) = 17.29993206958443 y[1] (numeric) = 17.2999320695844 absolute error = 2.842170943040401e-14 relative error = 1.642879828434305e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999943 y[1] (closed_form) = 17.32393149915367 y[1] (numeric) = 17.32393149915363 absolute error = 3.552713678800501e-14 relative error = 2.050754864145048e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999947 y[1] (closed_form) = 17.34796422206865 y[1] (numeric) = 17.3479642220686 absolute error = 4.618527782440651e-14 relative error = 2.662288049087248e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83999999999995 y[1] (closed_form) = 17.37203028451574 y[1] (numeric) = 17.3720302845157 absolute error = 4.973799150320701e-14 relative error = 2.863107575142792e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999953 y[1] (closed_form) = 17.39612973274543 y[1] (numeric) = 17.39612973274537 absolute error = 6.039613253960852e-14 relative error = 3.471814332697375e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999957 y[1] (closed_form) = 17.4202626130723 y[1] (numeric) = 17.42026261307223 absolute error = 7.105427357601002e-14 relative error = 4.078829071307475e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86999999999996 y[1] (closed_form) = 17.44442897187524 y[1] (numeric) = 17.44442897187516 absolute error = 7.815970093361102e-14 relative error = 4.48049638423957e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999963 y[1] (closed_form) = 17.46862885559745 y[1] (numeric) = 17.46862885559737 absolute error = 8.526512829121202e-14 relative error = 4.881042982597378e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999967 y[1] (closed_form) = 17.49286231074657 y[1] (numeric) = 17.49286231074648 absolute error = 9.237055564881302e-14 relative error = 5.280471200648853e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89999999999997 y[1] (closed_form) = 17.51712938389475 y[1] (numeric) = 17.51712938389466 absolute error = 9.592326932761353e-14 relative error = 5.475969676618669e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999973 y[1] (closed_form) = 17.54143012167875 y[1] (numeric) = 17.54143012167865 absolute error = 1.06581410364015e-13 relative error = 6.075981811328787e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999977 y[1] (closed_form) = 17.56576457080003 y[1] (numeric) = 17.56576457079992 absolute error = 1.172395514004165e-13 relative error = 6.674321002531622e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92999999999998 y[1] (closed_form) = 17.59013277802485 y[1] (numeric) = 17.59013277802471 absolute error = 1.314504061156185e-13 relative error = 7.472962698714704e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 17.6145347901843 y[1] (numeric) = 17.61453479018417 absolute error = 1.35003119794419e-13 relative error = 7.664302316383032e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999987 y[1] (closed_form) = 17.63897065417449 y[1] (numeric) = 17.63897065417435 absolute error = 1.385558334732195e-13 relative error = 7.855097453797765e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95999999999999 y[1] (closed_form) = 17.66344041695657 y[1] (numeric) = 17.66344041695642 absolute error = 1.527666881884215e-13 relative error = 8.64875044624763e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 17.68794412555681 y[1] (numeric) = 17.68794412555666 absolute error = 1.56319401867222e-13 relative error = 8.837624133002575e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999997 y[1] (closed_form) = 17.71248182706677 y[1] (numeric) = 17.7124818270666 absolute error = 1.63424829224823e-13 relative error = 9.226534757827702e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 17.73705356864328 y[1] (numeric) = 17.73705356864312 absolute error = 1.669775429036235e-13 relative error = 9.414051903119766e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 Finished! diff ( y , x , 1 ) = expt ( 2.0 , ( 0.2 * x + 0.3 ) ) ; Iterations = 4000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %