##############ECHO OF PROBLEM################# ##############temp/lin_sin_cospostode.ode################# diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(-0.5)*cos(c(2.0)*c(x) + c(3.0)) + c(2.0)/c(3.0)*sin(c(1.5)*c(x)-c(2.0))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = -0.14170274741949 y[1] (numeric) = -0.14170274741949 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = -0.1450699809230483 y[1] (numeric) = -0.1450699809230482 absolute error = 5.551115123125783e-17 relative error = 3.826508480807167e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = -0.1484918009250558 y[1] (numeric) = -0.1484918009250557 absolute error = 1.110223024625157e-16 relative error = 7.476662130224209e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = -0.1519672830296706 y[1] (numeric) = -0.1519672830296705 absolute error = 5.551115123125783e-17 relative error = 3.652835671242451e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = -0.1554954559396129 y[1] (numeric) = -0.1554954559396128 absolute error = 1.665334536937735e-16 relative error = 1.070985982757253e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = -0.1590753017504311 y[1] (numeric) = -0.1590753017504309 absolute error = 1.387778780781446e-16 relative error = 8.724036764416731e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = -0.1627057562691551 y[1] (numeric) = -0.1627057562691549 absolute error = 1.387778780781446e-16 relative error = 8.529377279594956e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = -0.1663857093572293 y[1] (numeric) = -0.1663857093572293 absolute error = 2.775557561562891e-17 relative error = 1.668146604828773e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = -0.170114005297606 y[1] (numeric) = -0.170114005297606 absolute error = 2.775557561562891e-17 relative error = 1.631586744846311e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = -0.1738894431858688 y[1] (numeric) = -0.1738894431858688 absolute error = 2.775557561562891e-17 relative error = 1.596162199792729e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = -0.1777107773452486 y[1] (numeric) = -0.1777107773452485 absolute error = 1.387778780781446e-16 relative error = 7.809198752675142e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = -0.1815767177653774 y[1] (numeric) = -0.1815767177653773 absolute error = 1.110223024625157e-16 relative error = 6.114346807720804e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = -0.1854859305646203 y[1] (numeric) = -0.1854859305646202 absolute error = 8.326672684688674e-17 relative error = 4.489112818067782e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = -0.1894370384758114 y[1] (numeric) = -0.1894370384758114 absolute error = 8.326672684688674e-17 relative error = 4.395482927564811e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = -0.1934286213552113 y[1] (numeric) = -0.1934286213552111 absolute error = 1.387778780781446e-16 relative error = 7.17462995423483e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = -0.1974592167144896 y[1] (numeric) = -0.1974592167144895 absolute error = 1.110223024625157e-16 relative error = 5.62254344516342e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = -0.2015273202755321 y[1] (numeric) = -0.201527320275532 absolute error = 1.387778780781446e-16 relative error = 6.886305930550991e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = -0.2056313865478526 y[1] (numeric) = -0.2056313865478525 absolute error = 8.326672684688674e-17 relative error = 4.0493199138892e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = -0.2097698294283877 y[1] (numeric) = -0.2097698294283876 absolute error = 1.665334536937735e-16 relative error = 7.938865858239424e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = -0.2139410228234359 y[1] (numeric) = -0.2139410228234357 absolute error = 1.110223024625157e-16 relative error = 5.189388224723112e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = -0.2181433012924979 y[1] (numeric) = -0.2181433012924976 absolute error = 2.498001805406602e-16 relative error = 1.145119648692376e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = -0.2223749607137592 y[1] (numeric) = -0.222374960713759 absolute error = 1.665334536937735e-16 relative error = 7.488858150182438e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = -0.2266342589709517 y[1] (numeric) = -0.2266342589709515 absolute error = 1.942890293094024e-16 relative error = 8.572800519726582e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = -0.2309194166613155 y[1] (numeric) = -0.2309194166613154 absolute error = 1.665334536937735e-16 relative error = 7.21175620922447e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = -0.2352286178243783 y[1] (numeric) = -0.2352286178243779 absolute error = 3.33066907387547e-16 relative error = 1.415928514430225e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = -0.2395600106912533 y[1] (numeric) = -0.2395600106912531 absolute error = 1.387778780781446e-16 relative error = 5.793031886987287e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = -0.2439117084541566 y[1] (numeric) = -0.2439117084541565 absolute error = 1.387778780781446e-16 relative error = 5.68967676696127e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = -0.2482817900558217 y[1] (numeric) = -0.2482817900558217 absolute error = 2.775557561562891e-17 relative error = 1.117906214925733e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = -0.2526683009984959 y[1] (numeric) = -0.2526683009984956 absolute error = 2.775557561562891e-16 relative error = 1.098498525772497e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = -0.2570692541721781 y[1] (numeric) = -0.257069254172178 absolute error = 1.110223024625157e-16 relative error = 4.318770162539776e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = -0.2614826307017653 y[1] (numeric) = -0.261482630701765 absolute error = 2.220446049250313e-16 relative error = 8.491753518354529e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = -0.2659063808127455 y[1] (numeric) = -0.2659063808127455 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = -0.270338424715091 y[1] (numeric) = -0.2703384247150908 absolute error = 1.665334536937735e-16 relative error = 6.16018436407191e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = -0.2747766535049705 y[1] (numeric) = -0.2747766535049706 absolute error = 5.551115123125783e-17 relative error = 2.0202280842704e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = -0.2792189300839172 y[1] (numeric) = -0.2792189300839171 absolute error = 1.110223024625157e-16 relative error = 3.976173908737088e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = -0.2836630900950547 y[1] (numeric) = -0.2836630900950548 absolute error = 1.110223024625157e-16 relative error = 3.913879046629309e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = -0.2881069428760011 y[1] (numeric) = -0.2881069428760011 absolute error = 5.551115123125783e-17 relative error = 1.926755068000891e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = -0.2925482724280383 y[1] (numeric) = -0.2925482724280384 absolute error = 1.110223024625157e-16 relative error = 3.795007967097983e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = -0.2969848384011486 y[1] (numeric) = -0.2969848384011486 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = -0.3014143770944935 y[1] (numeric) = -0.3014143770944936 absolute error = 1.665334536937735e-16 relative error = 5.525066697185622e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = -0.3058346024719183 y[1] (numeric) = -0.3058346024719183 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = -0.3102432071920454 y[1] (numeric) = -0.3102432071920456 absolute error = 1.665334536937735e-16 relative error = 5.367835615194845e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = -0.3146378636525244 y[1] (numeric) = -0.3146378636525244 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = -0.3190162250479869 y[1] (numeric) = -0.3190162250479871 absolute error = 2.220446049250313e-16 relative error = 6.960291906520775e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = -0.3233759264412623 y[1] (numeric) = -0.3233759264412622 absolute error = 5.551115123125783e-17 relative error = 1.716613597126898e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = -0.3277145858473876 y[1] (numeric) = -0.3277145858473878 absolute error = 2.220446049250313e-16 relative error = 6.775548434955367e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = -0.3320298053299564 y[1] (numeric) = -0.3320298053299564 absolute error = 5.551115123125783e-17 relative error = 1.671872534939847e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = -0.336319172109325 y[1] (numeric) = -0.3363191721093251 absolute error = 1.110223024625157e-16 relative error = 3.3010994219035e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = -0.340580259682211 y[1] (numeric) = -0.3405802596822108 absolute error = 1.110223024625157e-16 relative error = 3.259798514632307e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = -0.3448106289521886 y[1] (numeric) = -0.3448106289521887 absolute error = 1.665334536937735e-16 relative error = 4.829707663010151e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = -0.3490078293706074 y[1] (numeric) = -0.3490078293706072 absolute error = 1.665334536937735e-16 relative error = 4.771625152194896e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = -0.3531694000874246 y[1] (numeric) = -0.3531694000874246 absolute error = 5.551115123125783e-17 relative error = 1.571799573165637e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = -0.3572928711114689 y[1] (numeric) = -0.3572928711114686 absolute error = 3.33066907387547e-16 relative error = 9.321957819965463e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = -0.3613757644796157 y[1] (numeric) = -0.3613757644796156 absolute error = 1.110223024625157e-16 relative error = 3.072212178433956e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = -0.3654155954343813 y[1] (numeric) = -0.365415595434381 absolute error = 3.33066907387547e-16 relative error = 9.114742543804667e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = -0.369409873609408 y[1] (numeric) = -0.3694098736094079 absolute error = 1.665334536937735e-16 relative error = 4.508094276599007e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = -0.3733561042223368 y[1] (numeric) = -0.3733561042223364 absolute error = 4.440892098500626e-16 relative error = 1.189452120449606e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = -0.3772517892745328 y[1] (numeric) = -0.3772517892745327 absolute error = 1.665334536937735e-16 relative error = 4.414384727346757e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = -0.3810944287571522 y[1] (numeric) = -0.3810944287571517 absolute error = 4.440892098500626e-16 relative error = 1.165299664176023e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = -0.3848815218630061 y[1] (numeric) = -0.3848815218630059 absolute error = 1.665334536937735e-16 relative error = 4.326875784726527e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = -0.3886105682037062 y[1] (numeric) = -0.3886105682037058 absolute error = 4.440892098500626e-16 relative error = 1.142761536061147e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = -0.3922790690315385 y[1] (numeric) = -0.3922790690315384 absolute error = 1.665334536937735e-16 relative error = 4.245280129396465e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = -0.3958845284655446 y[1] (numeric) = -0.3958845284655441 absolute error = 4.996003610813204e-16 relative error = 1.261985061699128e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = -0.3994244547212508 y[1] (numeric) = -0.3994244547212505 absolute error = 2.775557561562891e-16 relative error = 6.948892409454222e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = -0.40289636134352 y[1] (numeric) = -0.4028963613435195 absolute error = 4.996003610813204e-16 relative error = 1.240022023071457e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = -0.4062977684419616 y[1] (numeric) = -0.4062977684419615 absolute error = 1.110223024625157e-16 relative error = 2.732535373951355e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = -0.4096262039283677 y[1] (numeric) = -0.4096262039283674 absolute error = 2.775557561562891e-16 relative error = 6.775830098135664e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = -0.4128792047556107 y[1] (numeric) = -0.4128792047556106 absolute error = 1.110223024625157e-16 relative error = 2.688977821690763e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = -0.4160543181574645 y[1] (numeric) = -0.4160543181574642 absolute error = 3.33066907387547e-16 relative error = 8.005370761744883e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = -0.4191491028887819 y[1] (numeric) = -0.4191491028887818 absolute error = 5.551115123125783e-17 relative error = 1.324377192952917e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = -0.4221611304654882 y[1] (numeric) = -0.4221611304654878 absolute error = 3.885780586188048e-16 relative error = 9.204496354042504e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = -0.4250879864038214 y[1] (numeric) = -0.4250879864038213 absolute error = 5.551115123125783e-17 relative error = 1.305874383815774e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = -0.4279272714582777 y[1] (numeric) = -0.4279272714582773 absolute error = 4.440892098500626e-16 relative error = 1.037767956075126e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = -0.4306766028576903 y[1] (numeric) = -0.4306766028576902 absolute error = 5.551115123125783e-17 relative error = 1.288928882203534e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = -0.4333336155389014 y[1] (numeric) = -0.4333336155389012 absolute error = 2.775557561562891e-16 relative error = 6.405128663076735e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = -0.4358959633774544 y[1] (numeric) = -0.4358959633774543 absolute error = 5.551115123125783e-17 relative error = 1.273495418520065e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = -0.4383613204147654 y[1] (numeric) = -0.4383613204147651 absolute error = 3.33066907387547e-16 relative error = 7.597999455618215e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = -0.4407273820812036 y[1] (numeric) = -0.4407273820812036 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = -0.44299186641454 y[1] (numeric) = -0.4429918664145396 absolute error = 3.33066907387547e-16 relative error = 7.518578390237798e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = -0.4451525152731952 y[1] (numeric) = -0.4451525152731952 absolute error = 5.551115123125783e-17 relative error = 1.247014210336203e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = -0.4472070955437499 y[1] (numeric) = -0.4472070955437496 absolute error = 3.33066907387547e-16 relative error = 7.447710707330744e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = -0.4491534003421486 y[1] (numeric) = -0.4491534003421485 absolute error = 5.551115123125783e-17 relative error = 1.235906289231507e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = -0.4509892502080651 y[1] (numeric) = -0.4509892502080648 absolute error = 3.33066907387547e-16 relative error = 7.3852515826904e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = -0.4527124942918647 y[1] (numeric) = -0.4527124942918648 absolute error = 1.110223024625157e-16 relative error = 2.452379906946844e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = -0.4543210115336336 y[1] (numeric) = -0.4543210115336334 absolute error = 2.775557561562891e-16 relative error = 6.10924322472683e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = -0.455812711833716 y[1] (numeric) = -0.4558127118337161 absolute error = 5.551115123125783e-17 relative error = 1.217850002645576e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = -0.457185537214235 y[1] (numeric) = -0.4571855372142348 absolute error = 2.775557561562891e-16 relative error = 6.070965364467069e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = -0.4584374629710423 y[1] (numeric) = -0.4584374629710422 absolute error = 5.551115123125783e-17 relative error = 1.210877288943645e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = -0.4595664988155791 y[1] (numeric) = -0.4595664988155788 absolute error = 3.33066907387547e-16 relative error = 7.247414862613919e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = -0.4605706900061 y[1] (numeric) = -0.4605706900060999 absolute error = 1.110223024625157e-16 relative error = 2.410537727901123e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = -0.4614481184677488 y[1] (numeric) = -0.4614481184677484 absolute error = 4.440892098500626e-16 relative error = 9.623816677911118e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = -0.462196903900944 y[1] (numeric) = -0.4621969039009437 absolute error = 3.33066907387547e-16 relative error = 7.206169158132837e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = -0.4628152048775733 y[1] (numeric) = -0.462815204877573 absolute error = 2.220446049250313e-16 relative error = 4.79769468645197e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = -0.4633012199244638 y[1] (numeric) = -0.4633012199244637 absolute error = 1.110223024625157e-16 relative error = 2.396330889882324e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = -0.463653188593628 y[1] (numeric) = -0.4636531885936279 absolute error = 1.110223024625157e-16 relative error = 2.394511785830118e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = -0.4638693925187736 y[1] (numeric) = -0.4638693925187736 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = -0.4639481564575767 y[1] (numeric) = -0.4639481564575768 absolute error = 5.551115123125783e-17 relative error = 1.196494704389105e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = -0.4638878493192214 y[1] (numeric) = -0.4638878493192214 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = -0.4636868851767149 y[1] (numeric) = -0.463686885176715 absolute error = 5.551115123125783e-17 relative error = 1.197168887148966e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = -0.4633437242634911 y[1] (numeric) = -0.4633437242634911 absolute error = 5.551115123125783e-17 relative error = 1.198055532520607e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = -0.4628568739538236 y[1] (numeric) = -0.4628568739538235 absolute error = 1.110223024625157e-16 relative error = 2.398631384992495e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = -0.4622248897265733 y[1] (numeric) = -0.4622248897265732 absolute error = 5.551115123125783e-17 relative error = 1.20095547567971e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = -0.4614463761118036 y[1] (numeric) = -0.4614463761118033 absolute error = 2.220446049250313e-16 relative error = 4.81192650803768e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = -0.4605199876197991 y[1] (numeric) = -0.4605199876197989 absolute error = 2.220446049250313e-16 relative error = 4.821606247161398e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = -0.459444429652037 y[1] (numeric) = -0.4594444296520366 absolute error = 4.440892098500626e-16 relative error = 9.665787224504957e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = -0.458218459393658 y[1] (numeric) = -0.4582184593936575 absolute error = 4.996003610813204e-16 relative error = 1.090310420366786e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = -0.4568408866869995 y[1] (numeric) = -0.4568408866869988 absolute error = 6.661338147750939e-16 relative error = 1.45813090331271e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = -0.4553105748857544 y[1] (numeric) = -0.4553105748857535 absolute error = 8.881784197001252e-16 relative error = 1.950708963706773e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = -0.453626441689331 y[1] (numeric) = -0.45362644168933 absolute error = 1.054711873393899e-15 relative error = 2.32506700770372e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = -0.4517874599569917 y[1] (numeric) = -0.4517874599569905 absolute error = 1.165734175856414e-15 relative error = 2.580271209757322e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = -0.4497926585013626 y[1] (numeric) = -0.4497926585013612 absolute error = 1.443289932012704e-15 relative error = 3.208789438274771e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = -0.4476411228609086 y[1] (numeric) = -0.4476411228609069 absolute error = 1.720845688168993e-15 relative error = 3.844252907710838e-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) = -0.4453319960509778 y[1] (numeric) = -0.445331996050976 absolute error = 1.887379141862766e-15 relative error = 4.238139542182626e-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) = -0.4428644792930306 y[1] (numeric) = -0.4428644792930285 absolute error = 2.109423746787797e-15 relative error = 4.763136005297125e-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) = -0.4402378327216728 y[1] (numeric) = -0.4402378327216704 absolute error = 2.442490654175344e-15 relative error = 5.548116205904403e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = -0.437451376069123 y[1] (numeric) = -0.4374513760691203 absolute error = 2.775557561562891e-15 relative error = 6.344836737064731e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = -0.4345044893267545 y[1] (numeric) = -0.4345044893267515 absolute error = 2.997602166487923e-15 relative error = 6.898898032406005e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = -0.4313966133833573 y[1] (numeric) = -0.4313966133833539 absolute error = 3.33066907387547e-15 relative error = 7.720665787692905e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = -0.4281272506397792 y[1] (numeric) = -0.4281272506397755 absolute error = 3.719247132494274e-15 relative error = 8.687246903663232e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = -0.4246959655996105 y[1] (numeric) = -0.4246959655996063 absolute error = 4.218847493575595e-15 relative error = 9.933806382217877e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = -0.4211023854355892 y[1] (numeric) = -0.4211023854355846 absolute error = 4.6074255521944e-15 relative error = 1.09413427982092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = -0.4173462005314109 y[1] (numeric) = -0.417346200531406 absolute error = 4.940492459581947e-15 relative error = 1.183787573312317e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = -0.413427164998639 y[1] (numeric) = -0.4134271649986336 absolute error = 5.384581669432009e-15 relative error = 1.302425705250823e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = -0.4093450971684195 y[1] (numeric) = -0.4093450971684137 absolute error = 5.88418203051333e-15 relative error = 1.437462442134091e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = -0.4050998800577161 y[1] (numeric) = -0.4050998800577097 absolute error = 6.38378239159465e-15 relative error = 1.57585393278446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = -0.4006914618097889 y[1] (numeric) = -0.400691461809782 absolute error = 6.827871601444713e-15 relative error = 1.704022234615509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = -0.396119856108654 y[1] (numeric) = -0.3961198561086468 absolute error = 7.216449660063518e-15 relative error = 1.821784378838125e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = -0.3913851425672686 y[1] (numeric) = -0.3913851425672608 absolute error = 7.827072323607354e-15 relative error = 1.999838898397144e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = -0.3864874670891963 y[1] (numeric) = -0.3864874670891879 absolute error = 8.43769498715119e-15 relative error = 2.18317428264857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = -0.381427042203523 y[1] (numeric) = -0.381427042203514 absolute error = 9.048317650695026e-15 relative error = 2.372227621414162e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = -0.3762041473727972 y[1] (numeric) = -0.3762041473727876 absolute error = 9.603429163007604e-15 relative error = 2.55271751523014e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = -0.3708191292737856 y[1] (numeric) = -0.3708191292737754 absolute error = 1.02695629777827e-14 relative error = 2.76942643112686e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = -0.365272402050842 y[1] (numeric) = -0.3652724020508312 absolute error = 1.082467449009528e-14 relative error = 2.963452598477067e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = -0.3595644475417011 y[1] (numeric) = -0.3595644475416896 absolute error = 1.149080830487037e-14 relative error = 3.19575764050969e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = -0.3536958154755175 y[1] (numeric) = -0.3536958154755054 absolute error = 1.215694211964546e-14 relative error = 3.437117881448884e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = -0.347667123642984 y[1] (numeric) = -0.3476671236429712 absolute error = 1.27675647831893e-14 relative error = 3.672353212292857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = -0.3414790580383722 y[1] (numeric) = -0.3414790580383588 absolute error = 1.337818744673314e-14 relative error = 3.917718270509526e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = -0.3351323729733531 y[1] (numeric) = -0.3351323729733389 absolute error = 1.415534356397075e-14 relative error = 4.223806682231877e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = -0.3286278911624612 y[1] (numeric) = -0.3286278911624463 absolute error = 1.48769885299771e-14 relative error = 4.52700118585567e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = -0.3219665037800852 y[1] (numeric) = -0.3219665037800695 absolute error = 1.565414464721471e-14 relative error = 4.862041381145368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = -0.315149170488872 y[1] (numeric) = -0.3151491704888556 absolute error = 1.643130076445232e-14 relative error = 5.213816916910625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = -0.3081769194394485 y[1] (numeric) = -0.3081769194394314 absolute error = 1.715294573045867e-14 relative error = 5.565941071011623e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = -0.301050847241373 y[1] (numeric) = -0.3010508472413551 absolute error = 1.793010184769628e-14 relative error = 5.955838361524521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = -0.2937721189052438 y[1] (numeric) = -0.293772118905225 absolute error = 1.876276911616515e-14 relative error = 6.386844737371785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = -0.2863419677559008 y[1] (numeric) = -0.2863419677558813 absolute error = 1.953992523340276e-14 relative error = 6.823982312666106e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = -0.2787616953166709 y[1] (numeric) = -0.2787616953166507 absolute error = 2.020605904817785e-14 relative error = 7.248506300416898e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = -0.2710326711646175 y[1] (numeric) = -0.2710326711645965 absolute error = 2.103872631664672e-14 relative error = 7.762431822792462e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = -0.2631563327567674 y[1] (numeric) = -0.2631563327567453 absolute error = 2.203792703880936e-14 relative error = 8.374461981570013e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = -0.2551341852273017 y[1] (numeric) = -0.2551341852272788 absolute error = 2.287059430727822e-14 relative error = 8.964143431779859e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = -0.2469678011557071 y[1] (numeric) = -0.2469678011556835 absolute error = 2.364775042451583e-14 relative error = 9.575236250982576e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = -0.2386588203058966 y[1] (numeric) = -0.2386588203058721 absolute error = 2.453592884421596e-14 relative error = 1.028075510168343e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = -0.2302089493363224 y[1] (numeric) = -0.2302089493362969 absolute error = 2.550737399076297e-14 relative error = 1.108009660975348e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = -0.2216199614811133 y[1] (numeric) = -0.2216199614810868 absolute error = 2.645106356169435e-14 relative error = 1.193532540341523e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = -0.2128936962022835 y[1] (numeric) = -0.2128936962022562 absolute error = 2.736699755701011e-14 relative error = 1.285477120515913e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = -0.2040320588130702 y[1] (numeric) = -0.2040320588130418 absolute error = 2.833844270355712e-14 relative error = 1.388921077815531e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = -0.1950370200724683 y[1] (numeric) = -0.1950370200724389 absolute error = 2.930988785010413e-14 relative error = 1.502785873123661e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = -0.1859106157510472 y[1] (numeric) = -0.1859106157510168 absolute error = 3.03368441478824e-14 relative error = 1.63179730352281e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = -0.1766549461681409 y[1] (numeric) = -0.1766549461681096 absolute error = 3.136380044566067e-14 relative error = 1.775427245371804e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = -0.1672721757005192 y[1] (numeric) = -0.1672721757004868 absolute error = 3.239075674343894e-14 relative error = 1.93641032095085e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = -0.1577645322626567 y[1] (numeric) = -0.1577645322626233 absolute error = 3.347322419244847e-14 relative error = 2.121720497780835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = -0.1481343067587311 y[1] (numeric) = -0.1481343067586965 absolute error = 3.4555691641458e-14 relative error = 2.332727131044631e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = -0.138383852506491 y[1] (numeric) = -0.1383838525064554 absolute error = 3.56104035148519e-14 relative error = 2.573306268748485e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = -0.1285155846331497 y[1] (numeric) = -0.128515584633113 absolute error = 3.669287096386142e-14 relative error = 2.855130066022884e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = -0.1185319794434676 y[1] (numeric) = -0.1185319794434299 absolute error = 3.774758283725532e-14 relative error = 3.184590607065545e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = -0.1084355737602032 y[1] (numeric) = -0.1084355737601644 absolute error = 3.883005028626485e-14 relative error = 3.580932800903002e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = -0.09822896423712107 y[1] (numeric) = -0.09822896423708108 absolute error = 3.999578446212126e-14 relative error = 4.071689523832597e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = -0.08791480664475804 y[1] (numeric) = -0.0879148066447169 absolute error = 4.113376306236205e-14 relative error = 4.678820853075797e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = -0.07749581512916021 y[1] (numeric) = -0.07749581512911792 absolute error = 4.228561945041065e-14 relative error = 5.456503603444178e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = -0.06697476144381515 y[1] (numeric) = -0.06697476144377175 absolute error = 4.339584247503581e-14 relative error = 6.479432183038144e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = -0.05635447415501516 y[1] (numeric) = -0.05635447415497055 absolute error = 4.460321001431566e-14 relative error = 7.914759330665548e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = -0.04563783782089814 y[1] (numeric) = -0.04563783782085238 absolute error = 4.576200529626817e-14 relative error = 1.002720713366337e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = -0.034827792144426 y[1] (numeric) = -0.03482779214437898 absolute error = 4.701794509287538e-14 relative error = 1.350012222936743e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = -0.02392733110056816 y[1] (numeric) = -0.02392733110052004 absolute error = 4.812122922359663e-14 relative error = 2.011140691844816e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = -0.01293950203797423 y[1] (numeric) = -0.0129395020379249 absolute error = 4.932859676287649e-14 relative error = 3.812248463511911e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = -0.001867404755424074 y[1] (numeric) = -0.001867404755373474 absolute error = 5.059949854946399e-14 relative error = 2.709616027403402e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y[1] (closed_form) = 0.009285809446638593 y[1] (numeric) = 0.009285809446690435 absolute error = 5.184221107956688e-14 relative error = 5.582950132401591e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y[1] (closed_form) = 0.0205169387391767 y[1] (numeric) = 0.02051693873922977 absolute error = 5.306172168317858e-14 relative error = 2.586239709428884e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 0.03182273176190986 y[1] (numeric) = 0.03182273176196414 absolute error = 5.427602811636234e-14 relative error = 1.705574132429696e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 0.04319988864460844 y[1] (numeric) = 0.04319988864466397 absolute error = 5.552502901906564e-14 relative error = 1.285304910756881e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 0.05464506205198627 y[1] (numeric) = 0.05464506205204307 absolute error = 5.679484660348066e-14 relative error = 1.039340874925702e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 0.06615485825183565 y[1] (numeric) = 0.0661548582518937 absolute error = 5.805078640008787e-14 relative error = 8.774984624576245e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 0.07772583820603818 y[1] (numeric) = 0.07772583820609757 absolute error = 5.939693181744587e-14 relative error = 7.641851562924875e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 0.08935451868407612 y[1] (numeric) = 0.0893545186841367 absolute error = 6.05765437811101e-14 relative error = 6.779348674607707e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 0.1010373733986555 y[1] (numeric) = 0.1010373733987174 absolute error = 6.186717804723685e-14 relative error = 6.123197383915774e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 0.1127708341630478 y[1] (numeric) = 0.112770834163111 absolute error = 6.321332346459485e-14 relative error = 5.605467400657775e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y[1] (closed_form) = 0.1245512920697416 y[1] (numeric) = 0.1245512920698061 absolute error = 6.453171330633722e-14 relative error = 5.181135597549896e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y[1] (closed_form) = 0.1363750986899899 y[1] (numeric) = 0.1363750986900558 absolute error = 6.583622536027178e-14 relative error = 4.827584067230027e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 0.1482385672938282 y[1] (numeric) = 0.1482385672938953 absolute error = 6.711298183859071e-14 relative error = 4.527363092059844e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 0.1601379740901286 y[1] (numeric) = 0.160137974090197 absolute error = 6.838973831690964e-14 relative error = 4.27067587844084e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 0.1720695594862475 y[1] (numeric) = 0.1720695594863172 absolute error = 6.972200594645983e-14 relative error = 4.05196631842556e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 0.1840295293668144 y[1] (numeric) = 0.1840295293668855 absolute error = 7.108202915162565e-14 relative error = 3.86253387682921e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = 0.1960140563912003 y[1] (numeric) = 0.1960140563912725 absolute error = 7.222000775186643e-14 relative error = 3.684430039432041e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = 0.2080192813091971 y[1] (numeric) = 0.2080192813092705 absolute error = 7.346900865456973e-14 relative error = 3.531836481319555e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = 0.2200413142944302 y[1] (numeric) = 0.2200413142945051 absolute error = 7.488454301096681e-14 relative error = 3.403203768850708e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = 0.2320762362950184 y[1] (numeric) = 0.2320762362950946 absolute error = 7.616129948928574e-14 relative error = 3.281736239141196e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = 0.2441201004009846 y[1] (numeric) = 0.244120100401062 absolute error = 7.743805596760467e-14 relative error = 3.172129449414742e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = 0.2561689332279193 y[1] (numeric) = 0.2561689332279982 absolute error = 7.882583474838611e-14 relative error = 3.077103603279363e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = 0.2682187363163854 y[1] (numeric) = 0.2682187363164656 absolute error = 8.01581023779363e-14 relative error = 2.988534786152427e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = 0.2802654875465457 y[1] (numeric) = 0.2802654875466272 absolute error = 8.154588115871775e-14 relative error = 2.909594109234547e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = 0.292305142567492 y[1] (numeric) = 0.2923051425675748 absolute error = 8.287814878826794e-14 relative error = 2.835329822126949e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 0.3043336362407422 y[1] (numeric) = 0.3043336362408263 absolute error = 8.409939411535561e-14 relative error = 2.763394646552609e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 0.3163468840973677 y[1] (numeric) = 0.3163468840974531 absolute error = 8.54316617449058e-14 relative error = 2.700569091700331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 0.3283407838082071 y[1] (numeric) = 0.3283407838082939 absolute error = 8.676392937445598e-14 relative error = 2.642496261601701e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 0.3403112166666142 y[1] (numeric) = 0.3403112166667022 absolute error = 8.798517470154366e-14 relative error = 2.585432697851341e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = 0.3522540490831815 y[1] (numeric) = 0.3522540490832708 absolute error = 8.931744233109384e-14 relative error = 2.535597321409423e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 0.3641651340918792 y[1] (numeric) = 0.3641651340919699 absolute error = 9.070522111187529e-14 relative error = 2.49077170273501e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 0.376040312867037 y[1] (numeric) = 0.376040312867129 absolute error = 9.192646643896296e-14 relative error = 2.44459073385217e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 0.3878754162505952 y[1] (numeric) = 0.3878754162506885 absolute error = 9.331424521974441e-14 relative error = 2.405778796753047e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = 0.3996662662890449 y[1] (numeric) = 0.3996662662891395 absolute error = 9.459100169806334e-14 relative error = 2.366749702854672e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = 0.4114086777794719 y[1] (numeric) = 0.4114086777795677 absolute error = 9.586775817638227e-14 relative error = 2.330231795153588e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = 0.4230984598241135 y[1] (numeric) = 0.4230984598242107 absolute error = 9.720002580593246e-14 relative error = 2.297338209322235e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = 0.4347314173928348 y[1] (numeric) = 0.4347314173929333 absolute error = 9.842127113302013e-14 relative error = 2.263955794206703e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = 0.4463033528929224 y[1] (numeric) = 0.4463033528930221 absolute error = 9.96425164601078e-14 relative error = 2.232618594824093e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = 0.457810067745595 y[1] (numeric) = 0.457810067745696 absolute error = 1.010302952408892e-13 relative error = 2.206816808079279e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = 0.4692473639686215 y[1] (numeric) = 0.4692473639687237 absolute error = 1.021960294167457e-13 relative error = 2.177871145666776e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = 0.480611045764436 y[1] (numeric) = 0.4806110457645393 absolute error = 1.033062524413708e-13 relative error = 2.149477282134809e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = 0.4918969211131337 y[1] (numeric) = 0.4918969211132383 absolute error = 1.04638520070921e-13 relative error = 2.127244867362256e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = 0.5031008033697326 y[1] (numeric) = 0.5031008033698386 absolute error = 1.060262988517024e-13 relative error = 2.107456361459692e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = 0.5142185128650774 y[1] (numeric) = 0.5142185128651847 absolute error = 1.073585664812526e-13 relative error = 2.087800493278269e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = 0.5252458785097613 y[1] (numeric) = 0.5252458785098698 absolute error = 1.084687895058778e-13 relative error = 2.065105009745678e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = 0.5361787394004431 y[1] (numeric) = 0.5361787394005526 absolute error = 1.094679902280404e-13 relative error = 2.041632429335932e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = 0.5470129464279267 y[1] (numeric) = 0.5470129464280374 absolute error = 1.106892355551281e-13 relative error = 2.023521312940484e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = 0.5577443638863762 y[1] (numeric) = 0.5577443638864881 absolute error = 1.119104808822158e-13 relative error = 2.006483402224289e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = 0.5683688710830306 y[1] (numeric) = 0.5683688710831438 absolute error = 1.13242748511766e-13 relative error = 1.992416444200773e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 0.5788823639477879 y[1] (numeric) = 0.5788823639479022 absolute error = 1.142419492339286e-13 relative error = 1.973491616756744e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 0.5892807566420207 y[1] (numeric) = 0.5892807566421362 absolute error = 1.154631945610163e-13 relative error = 1.95939190716113e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 0.5995599831659888 y[1] (numeric) = 0.5995599831661055 absolute error = 1.16684439888104e-13 relative error = 1.946167909204837e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 0.6097159989642108 y[1] (numeric) = 0.6097159989643285 absolute error = 1.176836406102666e-13 relative error = 1.930138635203739e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 0.6197447825281581 y[1] (numeric) = 0.6197447825282769 absolute error = 1.187938636348917e-13 relative error = 1.916819100118755e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 0.6296423369956335 y[1] (numeric) = 0.6296423369957537 absolute error = 1.201261312644419e-13 relative error = 1.907847109481696e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 0.6394046917461966 y[1] (numeric) = 0.639404691746318 absolute error = 1.213473765915296e-13 relative error = 1.897818051039526e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 0.6490279039919977 y[1] (numeric) = 0.6490279039921203 absolute error = 1.225686219186173e-13 relative error = 1.888495412365637e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 0.6585080603633856 y[1] (numeric) = 0.6585080603635094 absolute error = 1.23789867245705e-13 relative error = 1.879853485428771e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 0.6678412784886503 y[1] (numeric) = 0.6678412784887752 absolute error = 1.249000902703301e-13 relative error = 1.870206204578784e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 0.677023708567268 y[1] (numeric) = 0.6770237085673937 absolute error = 1.256772463875677e-13 relative error = 1.856319724068875e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 0.6860515349360127 y[1] (numeric) = 0.6860515349361395 absolute error = 1.267874694121929e-13 relative error = 1.848075005385976e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 0.6949209776273033 y[1] (numeric) = 0.694920977627431 absolute error = 1.27675647831893e-13 relative error = 1.837268580779085e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 0.703628293919155 y[1] (numeric) = 0.7036282939192838 absolute error = 1.287858708565182e-13 relative error = 1.830311145380338e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 0.7121697798761061 y[1] (numeric) = 0.7121697798762359 absolute error = 1.297850715786808e-13 relative error = 1.822389481357368e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 0.7205417718804952 y[1] (numeric) = 0.720541771880626 absolute error = 1.307842723008434e-13 relative error = 1.815082447746479e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 0.7287406481534646 y[1] (numeric) = 0.7287406481535964 absolute error = 1.317834730230061e-13 relative error = 1.808372750400688e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 0.7367628302650686 y[1] (numeric) = 0.7367628302652012 absolute error = 1.325606291402437e-13 relative error = 1.799230684487052e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 0.7446047846328676 y[1] (numeric) = 0.7446047846330014 absolute error = 1.337818744673314e-13 relative error = 1.796682981741696e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 0.7522630240083984 y[1] (numeric) = 0.7522630240085328 absolute error = 1.344480082821065e-13 relative error = 1.787247332265602e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 0.7597341089509022 y[1] (numeric) = 0.7597341089510377 absolute error = 1.354472090042691e-13 relative error = 1.782823851245862e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 0.7670146492877105 y[1] (numeric) = 0.7670146492878467 absolute error = 1.362243651215067e-13 relative error = 1.77603342058736e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 0.7741013055606799 y[1] (numeric) = 0.7741013055608168 absolute error = 1.368904989362818e-13 relative error = 1.76837964169473e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 0.780990790458081 y[1] (numeric) = 0.7809907904582186 absolute error = 1.376676550535194e-13 relative error = 1.762730838000946e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 0.7876798702313442 y[1] (numeric) = 0.7876798702314826 absolute error = 1.383337888682945e-13 relative error = 1.756218409233505e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 0.7941653660960752 y[1] (numeric) = 0.7941653660962141 absolute error = 1.388889003806071e-13 relative error = 1.748866247634939e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 0.8004441556167523 y[1] (numeric) = 0.8004441556168919 absolute error = 1.395550341953822e-13 relative error = 1.743469962471689e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 0.8065131740745309 y[1] (numeric) = 0.8065131740746712 absolute error = 1.402211680101573e-13 relative error = 1.738609765067511e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 0.8123694158175768 y[1] (numeric) = 0.8123694158177176 absolute error = 1.407762795224698e-13 relative error = 1.732909644078503e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 0.8180099355933625 y[1] (numeric) = 0.8180099355935038 absolute error = 1.412203687323199e-13 relative error = 1.726389406626002e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 0.8234318498623641 y[1] (numeric) = 0.8234318498625059 absolute error = 1.41886502547095e-13 relative error = 1.723111664563512e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 0.8286323380926028 y[1] (numeric) = 0.8286323380927452 absolute error = 1.423305917569451e-13 relative error = 1.717656736455283e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 0.833608644034481 y[1] (numeric) = 0.8336086440346238 absolute error = 1.427746809667951e-13 relative error = 1.712730332015241e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 0.8383580769753696 y[1] (numeric) = 0.838358076975513 absolute error = 1.434408147815702e-13 relative error = 1.71097313571638e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 0.8428780129734134 y[1] (numeric) = 0.8428780129735572 absolute error = 1.438849039914203e-13 relative error = 1.707066761462181e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 0.8471658960700206 y[1] (numeric) = 0.8471658960701648 absolute error = 1.442179708988078e-13 relative error = 1.702358080841439e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 0.8512192394805197 y[1] (numeric) = 0.8512192394806642 absolute error = 1.445510378061954e-13 relative error = 1.698164598516496e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 0.8550356267624664 y[1] (numeric) = 0.8550356267626117 absolute error = 1.45328193923433e-13 relative error = 1.699674134909538e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 0.8586127129610969 y[1] (numeric) = 0.8586127129612428 absolute error = 1.458833054357456e-13 relative error = 1.699058297572114e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 0.8619482257314255 y[1] (numeric) = 0.8619482257315717 absolute error = 1.462163723431331e-13 relative error = 1.696347506476482e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 0.8650399664364994 y[1] (numeric) = 0.8650399664366456 absolute error = 1.462163723431331e-13 relative error = 1.690284588184591e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 0.8678858112213276 y[1] (numeric) = 0.8678858112214741 absolute error = 1.465494392505207e-13 relative error = 1.688579734288889e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 0.8704837120620117 y[1] (numeric) = 0.8704837120621588 absolute error = 1.471045507628332e-13 relative error = 1.68991732670529e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 0.8728316977896118 y[1] (numeric) = 0.8728316977897591 absolute error = 1.473265953677583e-13 relative error = 1.687915273252026e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 0.874927875088293 y[1] (numeric) = 0.8749278750884402 absolute error = 1.472155730652958e-13 relative error = 1.682602386516026e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 0.8767704294673067 y[1] (numeric) = 0.8767704294674542 absolute error = 1.475486399726833e-13 relative error = 1.682865149345062e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 0.8783576262063708 y[1] (numeric) = 0.8783576262065187 absolute error = 1.478817068800709e-13 relative error = 1.68361613160658e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 0.8796878112740176 y[1] (numeric) = 0.8796878112741652 absolute error = 1.475486399726833e-13 relative error = 1.677284123773346e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 0.8807594122184927 y[1] (numeric) = 0.8807594122186403 absolute error = 1.475486399726833e-13 relative error = 1.675243408424461e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 0.8815709390308006 y[1] (numeric) = 0.8815709390309485 absolute error = 1.478817068800709e-13 relative error = 1.677479376108428e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 0.882120984979496 y[1] (numeric) = 0.8821209849796442 absolute error = 1.482147737874584e-13 relative error = 1.680209135835302e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 0.8824082274168312 y[1] (numeric) = 0.8824082274169794 absolute error = 1.482147737874584e-13 relative error = 1.679662192422474e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 0.8824314285558862 y[1] (numeric) = 0.8824314285560343 absolute error = 1.481037514849959e-13 relative error = 1.678359889417925e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 0.8821894362183135 y[1] (numeric) = 0.8821894362184618 absolute error = 1.483257960899209e-13 relative error = 1.681337250259422e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 0.8816811845523423 y[1] (numeric) = 0.8816811845524908 absolute error = 1.484368183923834e-13 relative error = 1.683565681031852e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 0.8809056947206951 y[1] (numeric) = 0.8809056947208432 absolute error = 1.481037514849959e-13 relative error = 1.68126681860031e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 0.8798620755580822 y[1] (numeric) = 0.8798620755582298 absolute error = 1.476596622751458e-13 relative error = 1.678213738005331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 0.8785495241979563 y[1] (numeric) = 0.8785495241981039 absolute error = 1.476596622751458e-13 relative error = 1.68072098621813e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 0.8769673266682121 y[1] (numeric) = 0.8769673266683596 absolute error = 1.475486399726833e-13 relative error = 1.682487311508541e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 0.8751148584555275 y[1] (numeric) = 0.8751148584556747 absolute error = 1.472155730652958e-13 relative error = 1.682242869525876e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 0.8729915850380651 y[1] (numeric) = 0.8729915850382116 absolute error = 1.465494392505207e-13 relative error = 1.678703916076472e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 0.870597062386251 y[1] (numeric) = 0.8705970623863973 absolute error = 1.463273946455956e-13 relative error = 1.680770599484009e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 0.8679309374313727 y[1] (numeric) = 0.8679309374315191 absolute error = 1.463273946455956e-13 relative error = 1.685933619080905e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 0.8649929485017351 y[1] (numeric) = 0.8649929485018809 absolute error = 1.457722831332831e-13 relative error = 1.685242444875152e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 0.8617829257261387 y[1] (numeric) = 0.8617829257262837 absolute error = 1.449951270160454e-13 relative error = 1.682501737823043e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = 0.858300791404452 y[1] (numeric) = 0.8583007914045969 absolute error = 1.448841047135829e-13 relative error = 1.688034150318173e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = 0.8545465603450613 y[1] (numeric) = 0.8545465603452059 absolute error = 1.446620601086579e-13 relative error = 1.692851704303206e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = 0.8505203401689895 y[1] (numeric) = 0.8505203401691335 absolute error = 1.439959262938828e-13 relative error = 1.69303330553238e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 0.8462223315804982 y[1] (numeric) = 0.8462223315806414 absolute error = 1.432187701766452e-13 relative error = 1.692448483475424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = 0.8416528286039923 y[1] (numeric) = 0.8416528286041354 absolute error = 1.431077478741827e-13 relative error = 1.700318029127858e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = 0.8368122187870618 y[1] (numeric) = 0.8368122187872047 absolute error = 1.428857032692576e-13 relative error = 1.707500202092733e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = 0.8317009833695039 y[1] (numeric) = 0.8317009833696458 absolute error = 1.41886502547095e-13 relative error = 1.705979737720935e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = 0.8263196974181882 y[1] (numeric) = 0.8263196974183292 absolute error = 1.409983241273949e-13 relative error = 1.706341075590235e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = 0.8206690299276379 y[1] (numeric) = 0.8206690299277786 absolute error = 1.406652572200073e-13 relative error = 1.714031504666509e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = 0.8147497438862117 y[1] (numeric) = 0.8147497438863519 absolute error = 1.402211680101573e-13 relative error = 1.721033594209274e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = 0.8085626963077817 y[1] (numeric) = 0.8085626963079208 absolute error = 1.391109449855321e-13 relative error = 1.720471963655607e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = 0.8021088382288222 y[1] (numeric) = 0.8021088382289604 absolute error = 1.38222766565832e-13 relative error = 1.723242033725109e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = 0.7953892146708348 y[1] (numeric) = 0.7953892146709726 absolute error = 1.377786773559819e-13 relative error = 1.732217068256331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 0.7884049645680458 y[1] (numeric) = 0.7884049645681829 absolute error = 1.371125435412068e-13 relative error = 1.739113142397937e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = 0.7811573206603266 y[1] (numeric) = 0.7811573206604628 absolute error = 1.362243651215067e-13 relative error = 1.743878749114887e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = 0.7736476093513014 y[1] (numeric) = 0.7736476093514366 absolute error = 1.352251643993441e-13 relative error = 1.747890935935671e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = 0.7658772505316229 y[1] (numeric) = 0.7658772505317575 absolute error = 1.34559030584569e-13 relative error = 1.756926850760572e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = 0.7578477573674057 y[1] (numeric) = 0.75784775736754 absolute error = 1.342259636771814e-13 relative error = 1.771146808475788e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = 0.7495607360538195 y[1] (numeric) = 0.7495607360539525 absolute error = 1.330047183500938e-13 relative error = 1.774435505391038e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = 0.7410178855338593 y[1] (numeric) = 0.7410178855339911 absolute error = 1.317834730230061e-13 relative error = 1.778411501202349e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 0.7322209971823318 y[1] (numeric) = 0.7322209971824629 absolute error = 1.31117339208231e-13 relative error = 1.790679859124296e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 0.7231719544550943 y[1] (numeric) = 0.7231719544552249 absolute error = 1.305622276959184e-13 relative error = 1.805410551274714e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 0.7138727325036056 y[1] (numeric) = 0.7138727325037348 absolute error = 1.292299600663682e-13 relative error = 1.810266090611824e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 0.7043253977548609 y[1] (numeric) = 0.704325397754989 absolute error = 1.281197370417431e-13 relative error = 1.819041844155319e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 0.6945321074567998 y[1] (numeric) = 0.6945321074569271 absolute error = 1.272315586220429e-13 relative error = 1.831903194338021e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 0.6844951091892795 y[1] (numeric) = 0.6844951091894058 absolute error = 1.263433802023428e-13 relative error = 1.845789378275978e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 0.6742167403407265 y[1] (numeric) = 0.6742167403408517 absolute error = 1.251221348752551e-13 relative error = 1.855814716377742e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 0.6636994275505919 y[1] (numeric) = 0.6636994275507156 absolute error = 1.23789867245705e-13 relative error = 1.865149525630242e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 0.6529456861177495 y[1] (numeric) = 0.6529456861178724 absolute error = 1.229016888260048e-13 relative error = 1.882265116976992e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 0.6419581193749891 y[1] (numeric) = 0.6419581193751112 absolute error = 1.220135104063047e-13 relative error = 1.90064595685926e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 0.6307394180297637 y[1] (numeric) = 0.6307394180298844 absolute error = 1.206812427767545e-13 relative error = 1.913329646555556e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 0.6192923594713737 y[1] (numeric) = 0.6192923594714927 absolute error = 1.190159082398168e-13 relative error = 1.921804886167309e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 0.6076198070447779 y[1] (numeric) = 0.607619807044896 absolute error = 1.181277298201167e-13 relative error = 1.944105976311785e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 0.5957247092912368 y[1] (numeric) = 0.5957247092913539 absolute error = 1.17128529097954e-13 relative error = 1.96615193681168e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 0.583610099156 y[1] (numeric) = 0.5836100991561155 absolute error = 1.154631945610163e-13 relative error = 1.978430372058259e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 0.5712790931632697 y[1] (numeric) = 0.5712790931633835 absolute error = 1.137978600240785e-13 relative error = 1.99198362737135e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 0.558734890558688 y[1] (numeric) = 0.5587348905588007 absolute error = 1.126876369994534e-13 relative error = 2.016835513650762e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 0.5459807724195975 y[1] (numeric) = 0.545980772419709 absolute error = 1.114663916723657e-13 relative error = 2.041580899971721e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 0.5330201007333448 y[1] (numeric) = 0.5330201007334546 absolute error = 1.09801057135428e-13 relative error = 2.059979670266852e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 0.5198563174439064 y[1] (numeric) = 0.5198563174440145 absolute error = 1.081357225984902e-13 relative error = 2.080107886928936e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 0.5064929434671352 y[1] (numeric) = 0.5064929434672422 absolute error = 1.069144772714026e-13 relative error = 2.110877923382953e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 0.4929335776749299 y[1] (numeric) = 0.4929335776750356 absolute error = 1.056932319443149e-13 relative error = 2.144167829727667e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 0.4791818958486431 y[1] (numeric) = 0.4791818958487469 absolute error = 1.038058528024521e-13 relative error = 2.166314163823101e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 0.4652416496020604 y[1] (numeric) = 0.4652416496021623 absolute error = 1.018629625093581e-13 relative error = 2.189463531403208e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 0.4511166652742962 y[1] (numeric) = 0.4511166652743968 absolute error = 1.005862060310392e-13 relative error = 2.22971603077175e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 0.4368108427929562 y[1] (numeric) = 0.4368108427930556 absolute error = 9.936496070395151e-14 relative error = 2.274782376477075e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 0.4223281545079333 y[1] (numeric) = 0.4223281545080307 absolute error = 9.742207041085749e-14 relative error = 2.306786070759757e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 0.4076726439962134 y[1] (numeric) = 0.407672643996309 absolute error = 9.559020242022598e-14 relative error = 2.344778435050301e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 0.3928484248380866 y[1] (numeric) = 0.3928484248381808 absolute error = 9.425793479067579e-14 relative error = 2.399346130241567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 0.3778596793651599 y[1] (numeric) = 0.3778596793652527 absolute error = 9.281464485866309e-14 relative error = 2.456325718970611e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 0.3627106573805827 y[1] (numeric) = 0.3627106573806736 absolute error = 9.087175456556906e-14 relative error = 2.505351103323653e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 0.3474056748519098 y[1] (numeric) = 0.3474056748519986 absolute error = 8.881784197001252e-14 relative error = 2.556603083926977e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 0.3319491125770394 y[1] (numeric) = 0.3319491125771268 absolute error = 8.743006318923108e-14 relative error = 2.63383934093031e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 0.3163454148236698 y[1] (numeric) = 0.3163454148237558 absolute error = 8.604228440844963e-14 relative error = 2.719884037402894e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 0.3005990879427266 y[1] (numeric) = 0.3005990879428105 absolute error = 8.398837181289309e-14 relative error = 2.794032822511274e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 0.2847146989562308 y[1] (numeric) = 0.2847146989563127 absolute error = 8.187894806610529e-14 relative error = 2.875824408303294e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 0.2686968741200877 y[1] (numeric) = 0.2686968741201681 absolute error = 8.038014698286133e-14 relative error = 2.99148053903066e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 0.252550297462279 y[1] (numeric) = 0.2525502974623579 absolute error = 7.888134589961737e-14 relative error = 3.123391526054295e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 0.2362797092969561 y[1] (numeric) = 0.2362797092970329 absolute error = 7.682743330406083e-14 relative error = 3.251545955116451e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 0.2198899047149418 y[1] (numeric) = 0.2198899047150165 absolute error = 7.471800955727304e-14 relative error = 3.397973620213946e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 0.2033857320511606 y[1] (numeric) = 0.2033857320512338 absolute error = 7.316369732279782e-14 relative error = 3.597287606408588e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 0.1867720913295211 y[1] (numeric) = 0.1867720913295928 absolute error = 7.166489623955385e-14 relative error = 3.837023814929384e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 0.1700539326857843 y[1] (numeric) = 0.1700539326858537 absolute error = 6.947220576591917e-14 relative error = 4.085304271926828e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 0.1532362547689639 y[1] (numeric) = 0.1532362547690312 absolute error = 6.730727086790012e-14 relative error = 4.392385533657169e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 0.1363241031218158 y[1] (numeric) = 0.1363241031218815 absolute error = 6.572520305780927e-14 relative error = 4.82124595377524e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 0.1193225685409756 y[1] (numeric) = 0.1193225685410398 absolute error = 6.421252418675749e-14 relative error = 5.381423227132994e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 0.1022367854173137 y[1] (numeric) = 0.1022367854173757 absolute error = 6.201983371312281e-14 relative error = 6.066293405056515e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 0.08507193005708752 y[1] (numeric) = 0.08507193005714737 absolute error = 5.985489881510375e-14 relative error = 7.035798855737506e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 0.0678332189844833 y[1] (numeric) = 0.06783321898454157 absolute error = 5.82728310050129e-14 relative error = 8.590603818807815e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 0.05052590722613742 y[1] (numeric) = 0.05052590722619407 absolute error = 5.664219093759471e-14 relative error = 1.121052427303933e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 0.03315528657823896 y[1] (numeric) = 0.03315528657829336 absolute error = 5.439398931272876e-14 relative error = 1.640582692125772e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 0.01572668385682574 y[1] (numeric) = 0.01572668385687792 absolute error = 5.218395160433431e-14 relative error = 3.318178967633109e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = -0.001754540868106447 y[1] (numeric) = -0.001754540868055869 absolute error = 5.057781450601428e-14 relative error = 2.882680901049594e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = -0.01928299605405981 y[1] (numeric) = -0.01928299605401092 absolute error = 4.889144644693033e-14 relative error = 2.535469400598503e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = -0.03685326048242721 y[1] (numeric) = -0.0368532604823805 absolute error = 4.671263376110346e-14 relative error = 1.267530556309326e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = -0.05445988506918048 y[1] (numeric) = -0.05445988506913596 absolute error = 4.451994328746878e-14 relative error = 8.174814036224098e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = -0.07209739468920998 y[1] (numeric) = -0.07209739468916718 absolute error = 4.279909759929978e-14 relative error = 5.936289068945379e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = -0.08976029001366703 y[1] (numeric) = -0.0897602900136259 absolute error = 4.113376306236205e-14 relative error = 4.582623680928277e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = -0.1074430493596554 y[1] (numeric) = -0.1074430493596166 absolute error = 3.884392807407266e-14 relative error = 3.615303949913623e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = -0.1251401305516102 y[1] (numeric) = -0.1251401305515736 absolute error = 3.666511538824579e-14 relative error = 2.929924655394569e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = -0.142845972793693 y[1] (numeric) = -0.142845972793658 absolute error = 3.499978085130806e-14 relative error = 2.450176239960011e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = -0.1605549985525365 y[1] (numeric) = -0.1605549985525032 absolute error = 3.325117958752344e-14 relative error = 2.071014909986938e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = -0.1782616154496638 y[1] (numeric) = -0.1782616154496327 absolute error = 3.116951141635127e-14 relative error = 1.748526251023046e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = -0.1959602181628977 y[1] (numeric) = -0.1959602181628687 absolute error = 2.894906536710096e-14 relative error = 1.477292974997415e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = -0.2136451903360754 y[1] (numeric) = -0.2136451903360481 absolute error = 2.731148640577885e-14 relative error = 1.278357184770526e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = -0.2313109064963806 y[1] (numeric) = -0.2313109064963549 absolute error = 2.564615186884112e-14 relative error = 1.108730766624807e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = -0.248951733978601 y[1] (numeric) = -0.2489517339785776 absolute error = 2.34257058195908e-14 relative error = 9.409737962140239e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = -0.2665620348556152 y[1] (numeric) = -0.2665620348555941 absolute error = 2.114974861910923e-14 relative error = 7.934268895630657e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = -0.2841361678744052 y[1] (numeric) = -0.2841361678743857 absolute error = 1.953992523340276e-14 relative error = 6.876958107649237e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = -0.3016684903968945 y[1] (numeric) = -0.3016684903968768 absolute error = 1.770805724277125e-14 relative error = 5.870038736718372e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = -0.31915336034491 y[1] (numeric) = -0.3191533603448946 absolute error = 1.548761119352093e-14 relative error = 4.852717570256326e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = -0.3365851381485559 y[1] (numeric) = -0.3365851381485424 absolute error = 1.348920974919565e-14 relative error = 4.007666477312503e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = -0.3539581886972877 y[1] (numeric) = -0.3539581886972759 absolute error = 1.182387521225792e-14 relative error = 3.340472290180561e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = -0.3712668832929791 y[1] (numeric) = -0.371266883292969 absolute error = 1.010302952408892e-14 relative error = 2.721231000858292e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = -0.3885056016042673 y[1] (numeric) = -0.3885056016042593 absolute error = 7.993605777301127e-15 relative error = 2.057526518097269e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = -0.4056687336214601 y[1] (numeric) = -0.4056687336214543 absolute error = 5.828670879282072e-15 relative error = 1.436805549998575e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = -0.4227506816112901 y[1] (numeric) = -0.4227506816112859 absolute error = 4.218847493575595e-15 relative error = 9.979516715373936e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = -0.4397458620707961 y[1] (numeric) = -0.4397458620707935 absolute error = 2.664535259100376e-15 relative error = 6.05926169845665e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = -0.456648707679621 y[1] (numeric) = -0.4566487076796204 absolute error = 5.551115123125783e-16 relative error = 1.215620460492002e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = -0.473453669250003 y[1] (numeric) = -0.4734536692500046 absolute error = 1.609823385706477e-15 relative error = 3.400170893715102e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = -0.4901552176737433 y[1] (numeric) = -0.4901552176737466 absolute error = 3.33066907387547e-15 relative error = 6.795131325302808e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = -0.5067478458654329 y[1] (numeric) = -0.506747845865438 absolute error = 5.10702591327572e-15 relative error = 1.007804168275023e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = -0.5232260707012307 y[1] (numeric) = -0.5232260707012307 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = -0.5395844349524423 y[1] (numeric) = -0.5395844349524364 absolute error = 5.995204332975845e-15 relative error = 1.111078071313204e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = -0.5558175092132447 y[1] (numeric) = -0.5558175092132337 absolute error = 1.099120794378905e-14 relative error = 1.977485012904149e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = -0.5719198938217938 y[1] (numeric) = -0.5719198938217768 absolute error = 1.69864122767649e-14 relative error = 2.970068441448155e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = -0.58788622077401 y[1] (numeric) = -0.5878862207739882 absolute error = 2.176037128265307e-14 relative error = 3.701459655578149e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = -0.6037111556293546 y[1] (numeric) = -0.6037111556293275 absolute error = 2.708944180085382e-14 relative error = 4.487152763081496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = -0.619389399407861 y[1] (numeric) = -0.619389399407829 absolute error = 3.197442310920451e-14 relative error = 5.162249005193211e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = -0.6349156904777388 y[1] (numeric) = -0.6349156904777012 absolute error = 3.752553823233029e-14 relative error = 5.910318298181355e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = -0.6502848064328286 y[1] (numeric) = -0.6502848064327863 absolute error = 4.229949723821846e-14 relative error = 6.504764807631686e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = -0.6654915659592253 y[1] (numeric) = -0.6654915659591777 absolute error = 4.762856775641922e-14 relative error = 7.156900281338415e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = -0.6805308306903556 y[1] (numeric) = -0.6805308306903031 absolute error = 5.25135490647699e-14 relative error = 7.716556942982028e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = -0.6953975070498336 y[1] (numeric) = -0.6953975070497759 absolute error = 5.773159728050814e-14 relative error = 8.301956319261148e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = -0.7100865480813898 y[1] (numeric) = -0.7100865480813273 absolute error = 6.250555628639631e-14 relative error = 8.802526460370568e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = -0.724592955265203 y[1] (numeric) = -0.7245929552651353 absolute error = 6.761258219967203e-14 relative error = 9.331112275984749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = -0.7389117803199379 y[1] (numeric) = -0.7389117803198657 absolute error = 7.216449660063518e-14 relative error = 9.766321030825766e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = -0.7530381269898301 y[1] (numeric) = -0.7530381269897529 absolute error = 7.716050021144838e-14 relative error = 1.024655956264621e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = -0.7669671528161288 y[1] (numeric) = -0.7669671528160474 absolute error = 8.137934770502397e-14 relative error = 1.061053884853054e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = -0.780694070892248 y[1] (numeric) = -0.7806940708921616 absolute error = 8.637535131583718e-14 relative error = 1.106391793357923e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = -0.7942141516019462 y[1] (numeric) = -0.7942141516018556 absolute error = 9.059419880941277e-14 relative error = 1.140677216927984e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = -0.8075227243399019 y[1] (numeric) = -0.8075227243398064 absolute error = 9.547918011776346e-14 relative error = 1.182371433519863e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = -0.8206151792140098 y[1] (numeric) = -0.8206151792139101 absolute error = 9.969802761133906e-14 relative error = 1.21491815087835e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = -0.8334869687287787 y[1] (numeric) = -0.8334869687286746 absolute error = 1.041389197098397e-13 relative error = 1.249436687278635e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = -0.8461336094491722 y[1] (numeric) = -0.8461336094490639 absolute error = 1.082467449009528e-13 relative error = 1.279310308586143e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = -0.85855068364428 y[1] (numeric) = -0.8585506836441674 absolute error = 1.125766146969909e-13 relative error = 1.311240173022031e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = -0.8707338409101809 y[1] (numeric) = -0.8707338409100644 absolute error = 1.164623952831789e-13 relative error = 1.337520029788212e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = -0.8826787997713927 y[1] (numeric) = -0.8826787997712719 absolute error = 1.20792265079217e-13 relative error = 1.36847361815534e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = -0.8943813492602894 y[1] (numeric) = -0.894381349260165 absolute error = 1.2445600106048e-13 relative error = 1.39153171254536e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = -0.9058373504738958 y[1] (numeric) = -0.9058373504737673 absolute error = 1.284528039491306e-13 relative error = 1.418055944391447e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = -0.9170427381074497 y[1] (numeric) = -0.9170427381073178 absolute error = 1.318944953254686e-13 relative error = 1.438258980139424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = -0.9279935219641647 y[1] (numeric) = -0.9279935219640287 absolute error = 1.360023205165817e-13 relative error = 1.465552477443194e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = -0.9386857884405957 y[1] (numeric) = -0.9386857884404564 absolute error = 1.393329895904571e-13 relative error = 1.484341100145193e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = -0.9491157019870581 y[1] (numeric) = -0.949115701986915 absolute error = 1.431077478741827e-13 relative error = 1.507800867424002e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = -0.9592795065425206 y[1] (numeric) = -0.9592795065423744 absolute error = 1.462163723431331e-13 relative error = 1.524231168766785e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = -0.9691735269434383 y[1] (numeric) = -0.9691735269432885 absolute error = 1.497690860219336e-13 relative error = 1.545327868109157e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = -0.978794170305967 y[1] (numeric) = -0.9787941703058142 absolute error = 1.528777104908841e-13 relative error = 1.561898457600081e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = -0.9881379273810396 y[1] (numeric) = -0.9881379273808836 absolute error = 1.559863349598345e-13 relative error = 1.57858868319386e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = -0.9972013738817709 y[1] (numeric) = -0.9972013738816118 absolute error = 1.590949594287849e-13 relative error = 1.595414563153694e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = -1.005981171782684 y[1] (numeric) = -1.005981171782522 absolute error = 1.620925615952729e-13 relative error = 1.611288224291824e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = -1.014474070590247 y[1] (numeric) = -1.014474070590082 absolute error = 1.647570968543732e-13 relative error = 1.624064149402196e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = -1.022676908584238 y[1] (numeric) = -1.02267690858407 absolute error = 1.671995875085486e-13 relative error = 1.63492092277721e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = -1.030586614029439 y[1] (numeric) = -1.03058661402927 absolute error = 1.694200335577989e-13 relative error = 1.643918436854055e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = -1.038200206357205 y[1] (numeric) = -1.038200206357033 absolute error = 1.720845688168993e-13 relative error = 1.657527784748789e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = -1.045514797316424 y[1] (numeric) = -1.04551479731625 absolute error = 1.740829702612245e-13 relative error = 1.665045494411482e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = -1.052527592093442 y[1] (numeric) = -1.052527592093265 absolute error = 1.767475055203249e-13 relative error = 1.679267193069781e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = -1.059235890400488 y[1] (numeric) = -1.05923589040031 absolute error = 1.787459069646502e-13 relative error = 1.687498588223515e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = -1.065637087532195 y[1] (numeric) = -1.065637087532014 absolute error = 1.809663530139005e-13 relative error = 1.698198712593449e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = -1.07172867538977 y[1] (numeric) = -1.071728675389587 absolute error = 1.827427098533008e-13 relative error = 1.705121025961541e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = -1.077508243472443 y[1] (numeric) = -1.077508243472258 absolute error = 1.849631559025511e-13 relative error = 1.716582281602576e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = -1.082973479835769 y[1] (numeric) = -1.082973479835582 absolute error = 1.865174681370263e-13 relative error = 1.722271797138665e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = -1.088122172016417 y[1] (numeric) = -1.088122172016229 absolute error = 1.880717803715015e-13 relative error = 1.728406838939626e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = -1.09295220792308 y[1] (numeric) = -1.09295220792289 absolute error = 1.896260926059767e-13 relative error = 1.734989793984864e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = -1.097461576693133 y[1] (numeric) = -1.097461576692943 absolute error = 1.909583602355269e-13 relative error = 1.740000418155156e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = -1.101648369514709 y[1] (numeric) = -1.101648369514517 absolute error = 1.922906278650771e-13 relative error = 1.745480982736658e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = -1.105510780413846 y[1] (numeric) = -1.105510780413653 absolute error = 1.931788062847772e-13 relative error = 1.747416757098118e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = -1.109047107006404 y[1] (numeric) = -1.10904710700621 absolute error = 1.942890293094024e-13 relative error = 1.75185551706489e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = -1.112255751214421 y[1] (numeric) = -1.112255751214225 absolute error = 1.953992523340276e-13 relative error = 1.756783474670103e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = -1.115135219946634 y[1] (numeric) = -1.115135219946437 absolute error = 1.967315199635777e-13 relative error = 1.764194300786164e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = -1.117684125742869 y[1] (numeric) = -1.117684125742672 absolute error = 1.971756091734278e-13 relative error = 1.764144310829995e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = -1.119901187382044 y[1] (numeric) = -1.119901187381846 absolute error = 1.978417429882029e-13 relative error = 1.766599993082345e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = -1.121785230453518 y[1] (numeric) = -1.12178523045332 absolute error = 1.98507876802978e-13 relative error = 1.769571139055956e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = -1.123335187891552 y[1] (numeric) = -1.123335187891353 absolute error = 1.98729921407903e-13 relative error = 1.769106171960213e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = -1.124550100472651 y[1] (numeric) = -1.124550100472452 absolute error = 1.989519660128281e-13 relative error = 1.769169429883186e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = -1.125429117275575 y[1] (numeric) = -1.125429117275375 absolute error = 1.996180998276031e-13 relative error = 1.773706551247192e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = -1.12597149610381 y[1] (numeric) = -1.125971496103611 absolute error = 1.991740106177531e-13 relative error = 1.768908105639915e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = -1.126176603870324 y[1] (numeric) = -1.126176603870124 absolute error = 1.996180998276031e-13 relative error = 1.77252927419711e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = -1.126043916944421 y[1] (numeric) = -1.126043916944222 absolute error = 1.991740106177531e-13 relative error = 1.768794339373745e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = -1.125573021460544 y[1] (numeric) = -1.125573021460345 absolute error = 1.991740106177531e-13 relative error = 1.769534333359419e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = -1.124763613588874 y[1] (numeric) = -1.124763613588675 absolute error = 1.98729921407903e-13 relative error = 1.76685944501529e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = -1.123615499767597 y[1] (numeric) = -1.123615499767398 absolute error = 1.98507876802978e-13 relative error = 1.766688665687118e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = -1.122128596896719 y[1] (numeric) = -1.122128596896521 absolute error = 1.978417429882029e-13 relative error = 1.763093316892024e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = -1.120302932493328 y[1] (numeric) = -1.120302932493131 absolute error = 1.969535645685028e-13 relative error = 1.758038463133951e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = -1.118138644808209 y[1] (numeric) = -1.118138644808013 absolute error = 1.962874307537277e-13 relative error = 1.755483827208174e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = -1.115635982903745 y[1] (numeric) = -1.115635982903549 absolute error = 1.958433415438776e-13 relative error = 1.755441241991337e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = -1.112795306693027 y[1] (numeric) = -1.112795306692832 absolute error = 1.942890293094024e-13 relative error = 1.745954787379406e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = -1.109617086940146 y[1] (numeric) = -1.109617086939952 absolute error = 1.936228954946273e-13 relative error = 1.744952360354843e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = -1.106101905221622 y[1] (numeric) = -1.106101905221429 absolute error = 1.927347170749272e-13 relative error = 1.742467996529761e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = -1.102250453848952 y[1] (numeric) = -1.102250453848761 absolute error = 1.91402449445377e-13 relative error = 1.736469681432365e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = -1.098063535752278 y[1] (numeric) = -1.098063535752088 absolute error = 1.898481372109018e-13 relative error = 1.72893581317986e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = -1.093542064325183 y[1] (numeric) = -1.093542064324994 absolute error = 1.887379141862766e-13 relative error = 1.725931908277762e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = -1.088687063230636 y[1] (numeric) = -1.088687063230449 absolute error = 1.867395127419513e-13 relative error = 1.71527263479929e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = -1.083499666168137 y[1] (numeric) = -1.083499666167951 absolute error = 1.851852005074761e-13 relative error = 1.70913943298566e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = -1.077981116602097 y[1] (numeric) = -1.077981116601914 absolute error = 1.827427098533008e-13 relative error = 1.69523108558083e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = -1.07213276745154 y[1] (numeric) = -1.072132767451359 absolute error = 1.809663530139005e-13 relative error = 1.687909916642672e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = -1.065956080741192 y[1] (numeric) = -1.065956080741014 absolute error = 1.783018177548001e-13 relative error = 1.672693847112551e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = -1.05945262721407 y[1] (numeric) = -1.059452627213894 absolute error = 1.765254609153999e-13 relative error = 1.666194942378784e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = -1.052624085905664 y[1] (numeric) = -1.052624085905489 absolute error = 1.743050148661496e-13 relative error = 1.655909428636909e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = -1.04547224367985 y[1] (numeric) = -1.045472243679678 absolute error = 1.723066134218243e-13 relative error = 1.648122314709571e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = -1.037998994726671 y[1] (numeric) = -1.037998994726501 absolute error = 1.696420781627239e-13 relative error = 1.63431832809621e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = -1.030206340022131 y[1] (numeric) = -1.030206340021964 absolute error = 1.669775429036235e-13 relative error = 1.620816494878458e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = -1.022096386750178 y[1] (numeric) = -1.022096386750015 absolute error = 1.638689184346731e-13 relative error = 1.603262867954214e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = -1.013671347687056 y[1] (numeric) = -1.013671347686895 absolute error = 1.616484723854228e-13 relative error = 1.594683254629462e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = -1.004933540548211 y[1] (numeric) = -1.004933540548053 absolute error = 1.583178033115473e-13 relative error = 1.57540570518904e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = -0.9958853872979797 y[1] (numeric) = -0.9958853872978237 absolute error = 1.559863349598345e-13 relative error = 1.566308100805195e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = -0.9865294134222606 y[1] (numeric) = -0.9865294134221081 absolute error = 1.525446435834965e-13 relative error = 1.546275676204328e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = -0.9768682471644263 y[1] (numeric) = -0.9768682471642767 absolute error = 1.496580637194711e-13 relative error = 1.53201892019611e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = -0.9669046187247059 y[1] (numeric) = -0.9669046187245599 absolute error = 1.459943277382081e-13 relative error = 1.509914472544009e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = -0.956641359423323 y[1] (numeric) = -0.95664135942318 absolute error = 1.429967255717202e-13 relative error = 1.494778833918707e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = -0.9460814008276436 y[1] (numeric) = -0.9460814008275046 absolute error = 1.389999226830696e-13 relative error = 1.469217369260941e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = -0.9352277738436507 y[1] (numeric) = -0.9352277738435151 absolute error = 1.356692536091941e-13 relative error = 1.45065466834473e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; Iterations = 4900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %