##############ECHO OF PROBLEM################# ##############temp/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(1.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(1.570796327); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.0); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(neg(ln(cos(c(x))))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.005008355623235254 y[1] (numeric) = 0.005008355623235254 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) = 0.006062240346532338 y[1] (numeric) = 0.006062240346532249 absolute error = 8.933825901280557e-17 relative error = 1.473683884274036e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.007217346646627739 y[1] (numeric) = 0.007217346646627682 absolute error = 5.637851296924623e-17 relative error = 7.811529046562943e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.008473908649082243 y[1] (numeric) = 0.00847390864908224 absolute error = 3.469446951953614e-18 relative error = 4.094269947469128e-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) = 0.009832181658295606 y[1] (numeric) = 0.009832181658295499 absolute error = 1.07552855510562e-16 relative error = 1.093885968022342e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.01129244236664183 y[1] (numeric) = 0.01129244236664174 absolute error = 9.71445146547012e-17 relative error = 8.602613278919059e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.01285498908200967 y[1] (numeric) = 0.0128549890820096 absolute error = 6.938893903907228e-17 relative error = 5.397821701473156e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.01452014197414718 y[1] (numeric) = 0.01452014197414707 absolute error = 1.110223024625157e-16 relative error = 7.646089319249677e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.01628824334024881 y[1] (numeric) = 0.0162882433402488 absolute error = 1.734723475976807e-17 relative error = 1.065015692447476e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.01815965789025992 y[1] (numeric) = 0.01815965789025985 absolute error = 6.591949208711867e-17 relative error = 3.629996362567773e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 0.02013477305240835 y[1] (numeric) = 0.0201347730524083 absolute error = 5.551115123125783e-17 relative error = 2.756979236208379e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 0.02221399929951903 y[1] (numeric) = 0.02221399929951901 absolute error = 2.081668171172169e-17 relative error = 9.370974326163953e-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) = 0.02439777049670313 y[1] (numeric) = 0.0243977704967031 absolute error = 2.081668171172169e-17 relative error = 8.532206545075357e-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) = 0.02668654427106085 y[1] (numeric) = 0.02668654427106075 absolute error = 1.07552855510562e-16 relative error = 4.030227908796472e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 0.02908080240408099 y[1] (numeric) = 0.02908080240408089 absolute error = 9.367506770274758e-17 relative error = 3.221199552925744e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 0.03158105124746966 y[1] (numeric) = 0.03158105124746956 absolute error = 9.71445146547012e-17 relative error = 3.076038029686697e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 0.03418782216318843 y[1] (numeric) = 0.03418782216318839 absolute error = 4.85722573273506e-17 relative error = 1.420747337911759e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 0.03690167198853801 y[1] (numeric) = 0.03690167198853799 absolute error = 1.387778780781446e-17 relative error = 3.760747700571677e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 0.03972318352717689 y[1] (numeric) = 0.0397231835271768 absolute error = 9.020562075079397e-17 relative error = 2.270855775924384e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 0.04265296606702416 y[1] (numeric) = 0.04265296606702404 absolute error = 1.249000902703301e-16 relative error = 2.928286161249939e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 0.04569165592605806 y[1] (numeric) = 0.045691655926058 absolute error = 6.245004513516506e-17 relative error = 1.366771325517875e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 0.04883991702708585 y[1] (numeric) = 0.04883991702708582 absolute error = 3.469446951953614e-17 relative error = 7.103711806122671e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 0.05209844150263039 y[1] (numeric) = 0.05209844150263034 absolute error = 4.85722573273506e-17 relative error = 9.323168971359391e-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) = 0.05546795033115276 y[1] (numeric) = 0.05546795033115269 absolute error = 6.938893903907228e-17 relative error = 1.250973555446144e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 0.05894919400590685 y[1] (numeric) = 0.05894919400590681 absolute error = 4.163336342344337e-17 relative error = 7.062583997208105e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 0.06254295323780479 y[1] (numeric) = 0.06254295323780475 absolute error = 4.163336342344337e-17 relative error = 6.656763275175439e-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) = 0.0662500396937582 y[1] (numeric) = 0.06625003969375816 absolute error = 4.163336342344337e-17 relative error = 6.284277506231576e-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) = 0.07007129677205522 y[1] (numeric) = 0.07007129677205519 absolute error = 2.775557561562891e-17 relative error = 3.961047803342206e-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) = 0.07400760041643002 y[1] (numeric) = 0.07400760041642994 absolute error = 8.326672684688674e-17 relative error = 1.125110480252798e-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) = 0.07805985997058702 y[1] (numeric) = 0.07805985997058701 absolute error = 1.387778780781446e-17 relative error = 1.777839188161958e-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) = 0.08222901907505553 y[1] (numeric) = 0.08222901907505546 absolute error = 6.938893903907228e-17 relative error = 8.43849772496212e-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) = 0.08651605660836616 y[1] (numeric) = 0.08651605660836607 absolute error = 8.326672684688674e-17 relative error = 9.624424657241578e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 0.09092198767467256 y[1] (numeric) = 0.09092198767467245 absolute error = 1.110223024625157e-16 relative error = 1.221072100400663e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 0.09544786464007339 y[1] (numeric) = 0.09544786464007325 absolute error = 1.387778780781446e-16 relative error = 1.453965246906941e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 0.1000947782200377 y[1] (numeric) = 0.1000947782200375 absolute error = 1.52655665885959e-16 relative error = 1.52511118562426e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 0.1048638586204904 y[1] (numeric) = 0.1048638586204902 absolute error = 1.387778780781446e-16 relative error = 1.323409989903112e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 0.1097562767352823 y[1] (numeric) = 0.1097562767352821 absolute error = 1.52655665885959e-16 relative error = 1.390860463079888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 0.1147732454029447 y[1] (numeric) = 0.1147732454029447 absolute error = 5.551115123125783e-17 relative error = 4.836593322456801e-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) = 0.1199160207258237 y[1] (numeric) = 0.1199160207258236 absolute error = 1.249000902703301e-16 relative error = 1.041562999792179e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 0.1251859034548867 y[1] (numeric) = 0.1251859034548866 absolute error = 1.110223024625157e-16 relative error = 8.868594578024896e-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) = 0.1305842404437229 y[1] (numeric) = 0.1305842404437228 absolute error = 1.387778780781446e-16 relative error = 1.062745991450269e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 0.1361124261754862 y[1] (numeric) = 0.1361124261754861 absolute error = 1.665334536937735e-16 relative error = 1.223499267282667e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 0.1417719043667884 y[1] (numeric) = 0.1417719043667884 absolute error = 5.551115123125783e-17 relative error = 3.915525539365042e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 0.1475641696528218 y[1] (numeric) = 0.1475641696528217 absolute error = 1.387778780781446e-16 relative error = 9.404578252610443e-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) = 0.1534907693582817 y[1] (numeric) = 0.1534907693582815 absolute error = 1.665334536937735e-16 relative error = 1.084973737443763e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 0.159553305358981 y[1] (numeric) = 0.1595533053589809 absolute error = 1.387778780781446e-16 relative error = 8.697900539628839e-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) = 0.1657534360393848 y[1] (numeric) = 0.1657534360393846 absolute error = 1.942890293094024e-16 relative error = 1.172156873195903e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 0.1720928783516632 y[1] (numeric) = 0.1720928783516629 absolute error = 2.498001805406602e-16 relative error = 1.451542811842603e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 0.1785734099822599 y[1] (numeric) = 0.1785734099822597 absolute error = 1.942890293094024e-16 relative error = 1.088006491720709e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 0.1851968716324019 y[1] (numeric) = 0.1851968716324016 absolute error = 3.05311331771918e-16 relative error = 1.648577155114866e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 0.1919651694194379 y[1] (numeric) = 0.1919651694194377 absolute error = 2.220446049250313e-16 relative error = 1.156692152001131e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 0.1988802774064051 y[1] (numeric) = 0.1988802774064047 absolute error = 3.33066907387547e-16 relative error = 1.674710593383456e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 0.2059442402677548 y[1] (numeric) = 0.2059442402677545 absolute error = 3.33066907387547e-16 relative error = 1.617267406723858e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 0.2131591760997758 y[1] (numeric) = 0.2131591760997755 absolute error = 3.05311331771918e-16 relative error = 1.432316156209046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 0.220527279384879 y[1] (numeric) = 0.2205272793848786 absolute error = 3.885780586188048e-16 relative error = 1.762040776554597e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 0.2280508241196166 y[1] (numeric) = 0.2280508241196162 absolute error = 4.163336342344337e-16 relative error = 1.825617757978632e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 0.2357321671170591 y[1] (numeric) = 0.2357321671170586 absolute error = 4.996003610813204e-16 relative error = 2.119355907983617e-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) = 0.2435737514949815 y[1] (numeric) = 0.2435737514949811 absolute error = 4.440892098500626e-16 relative error = 1.823222769795096e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 0.2515781103622067 y[1] (numeric) = 0.2515781103622062 absolute error = 4.996003610813204e-16 relative error = 1.985865782845839e-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) = 0.259747870716431 y[1] (numeric) = 0.2597478707164306 absolute error = 3.885780586188048e-16 relative error = 1.495981690040565e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 0.2680857575679316 y[1] (numeric) = 0.2680857575679311 absolute error = 4.440892098500626e-16 relative error = 1.656519219367827e-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) = 0.2765945983047113 y[1] (numeric) = 0.2765945983047109 absolute error = 3.33066907387547e-16 relative error = 1.204169963654253e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 0.285277327315926 y[1] (numeric) = 0.2852773273159257 absolute error = 3.33066907387547e-16 relative error = 1.167519727281717e-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) = 0.2941369908918218 y[1] (numeric) = 0.2941369908918214 absolute error = 3.885780586188048e-16 relative error = 1.321078513248667e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 0.3031767524199507 y[1] (numeric) = 0.3031767524199502 absolute error = 4.440892098500626e-16 relative error = 1.464786486118581e-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) = 0.3123998978991059 y[1] (numeric) = 0.3123998978991054 absolute error = 4.996003610813204e-16 relative error = 1.599233432664801e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 0.32180984179426 y[1] (numeric) = 0.3218098417942596 absolute error = 4.440892098500626e-16 relative error = 1.379973985177179e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 0.3314101332578185 y[1] (numeric) = 0.3314101332578181 absolute error = 3.885780586188048e-16 relative error = 1.172499026505363e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 0.3412044627447259 y[1] (numeric) = 0.3412044627447255 absolute error = 3.885780586188048e-16 relative error = 1.138842251631163e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 0.351196669051421 y[1] (numeric) = 0.3511966690514206 absolute error = 3.885780586188048e-16 relative error = 1.106440045881843e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 0.3613907468113444 y[1] (numeric) = 0.3613907468113441 absolute error = 2.775557561562891e-16 relative error = 7.680212031028582e-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) = 0.3717908544826952 y[1] (numeric) = 0.371790854482695 absolute error = 1.665334536937735e-16 relative error = 4.479224049916072e-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) = 0.3824013228674413 y[1] (numeric) = 0.3824013228674412 absolute error = 1.110223024625157e-16 relative error = 2.903292845066891e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 0.3932266642042512 y[1] (numeric) = 0.393226664204251 absolute error = 2.220446049250313e-16 relative error = 5.646733172949231e-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) = 0.4042715818820776 y[1] (numeric) = 0.4042715818820775 absolute error = 1.665334536937735e-16 relative error = 4.119346032646682e-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) = 0.4155409808256353 y[1] (numeric) = 0.4155409808256351 absolute error = 2.775557561562891e-16 relative error = 6.679383477528874e-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) = 0.4270399786090209 y[1] (numeric) = 0.4270399786090207 absolute error = 2.220446049250313e-16 relative error = 5.199621020221286e-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) = 0.4387739173593156 y[1] (numeric) = 0.4387739173593153 absolute error = 3.33066907387547e-16 relative error = 7.590854747977093e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 0.4507483765182265 y[1] (numeric) = 0.4507483765182262 absolute error = 3.33066907387547e-16 relative error = 7.389198158855244e-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) = 0.4629691865367751 y[1] (numeric) = 0.4629691865367748 absolute error = 3.33066907387547e-16 relative error = 7.194148489212476e-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) = 0.4754424435858151 y[1] (numeric) = 0.4754424435858149 absolute error = 2.220446049250313e-16 relative error = 4.670273088165157e-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) = 0.488174525373867 y[1] (numeric) = 0.4881745253738667 absolute error = 2.775557561562891e-16 relative error = 5.685584595872223e-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) = 0.5011721081735231 y[1] (numeric) = 0.5011721081735228 absolute error = 3.33066907387547e-16 relative error = 6.645759050745651e-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) = 0.5144421851686615 y[1] (numeric) = 0.5144421851686614 absolute error = 1.110223024625157e-16 relative error = 2.158110389530296e-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) = 0.5279920862470625 y[1] (numeric) = 0.5279920862470624 absolute error = 1.110223024625157e-16 relative error = 2.102726638417174e-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) = 0.5418294993769632 y[1] (numeric) = 0.5418294993769632 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] = 0.9600000000000007 y[1] (closed_form) = 0.5559624937218419 y[1] (numeric) = 0.5559624937218417 absolute error = 2.220446049250313e-16 relative error = 3.993877418575006e-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) = 0.5703995446655491 y[1] (numeric) = 0.570399544665549 absolute error = 1.110223024625157e-16 relative error = 1.946395355690773e-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) = 0.5851495609401413 y[1] (numeric) = 0.5851495609401413 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] = 0.9900000000000008 y[1] (closed_form) = 0.6002219140717494 y[1] (numeric) = 0.6002219140717494 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] = 1.000000000000001 y[1] (closed_form) = 0.6156264703860153 y[1] (numeric) = 0.6156264703860154 absolute error = 1.110223024625157e-16 relative error = 1.803403651452829e-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) = 0.6313736258445025 y[1] (numeric) = 0.6313736258445044 absolute error = 1.887379141862766e-15 relative error = 2.989322113888232e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 0.6474743440177003 y[1] (numeric) = 0.6474743440177039 absolute error = 3.552713678800501e-15 relative error = 5.487033905861417e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 0.6639401975394141 y[1] (numeric) = 0.6639401975394195 absolute error = 5.329070518200751e-15 relative error = 8.026431503846996e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 0.680783413432427 y[1] (numeric) = 0.6807834134324343 absolute error = 7.327471962526033e-15 relative error = 1.076329390221453e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 0.6980169227472175 y[1] (numeric) = 0.6980169227472266 absolute error = 9.103828801926284e-15 relative error = 1.304241846472135e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 0.7156544150154879 y[1] (numeric) = 0.7156544150154989 absolute error = 1.099120794378905e-14 relative error = 1.535826191130419e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 0.7337103980897286 y[1] (numeric) = 0.7337103980897416 absolute error = 1.298960938811433e-14 relative error = 1.77040006819227e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 0.7522002640207033 y[1] (numeric) = 0.7522002640207183 absolute error = 1.498801083243961e-14 relative error = 1.992555912214767e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 0.7711403617187078 y[1] (numeric) = 0.7711403617187248 absolute error = 1.69864122767649e-14 relative error = 2.202765296697192e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 0.7905480772542113 y[1] (numeric) = 0.7905480772542303 absolute error = 1.898481372109018e-14 relative error = 2.401474909284405e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 0.8104419227821106 y[1] (numeric) = 0.8104419227821319 absolute error = 2.131628207280301e-14 relative error = 2.630204765275197e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 0.8308416352250318 y[1] (numeric) = 0.8308416352250554 absolute error = 2.353672812205332e-14 relative error = 2.832877786111242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 0.8517682860294555 y[1] (numeric) = 0.8517682860294814 absolute error = 2.586819647376615e-14 relative error = 3.036999251797875e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 0.8732444035195404 y[1] (numeric) = 0.8732444035195686 absolute error = 2.819966482547898e-14 relative error = 3.229298087891835e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 0.8952941096242921 y[1] (numeric) = 0.8952941096243227 absolute error = 3.05311331771918e-14 relative error = 3.410179163359415e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 0.9179432730527655 y[1] (numeric) = 0.9179432730527985 absolute error = 3.308464613382966e-14 relative error = 3.604214672634557e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 0.9412196813500059 y[1] (numeric) = 0.9412196813500414 absolute error = 3.552713678800501e-14 relative error = 3.77458498711458e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 0.9651532346968531 y[1] (numeric) = 0.9651532346968912 absolute error = 3.808064974464287e-14 relative error = 3.945554796446773e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 0.9897761648364393 y[1] (numeric) = 0.9897761648364799 absolute error = 4.063416270128073e-14 relative error = 4.105389091481662e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 1.015123283140605 y[1] (numeric) = 1.015123283140648 absolute error = 4.352074256530614e-14 relative error = 4.287237155142473e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 1.041232262597803 y[1] (numeric) = 1.04123226259785 absolute error = 4.662936703425657e-14 relative error = 4.478286805858234e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 1.068143959445243 y[1] (numeric) = 1.068143959445293 absolute error = 4.973799150320701e-14 relative error = 4.656487645077279e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 1.095902781327071 y[1] (numeric) = 1.095902781327124 absolute error = 5.262457136723242e-14 relative error = 4.801937933172072e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 1.124557110295759 y[1] (numeric) = 1.124557110295815 absolute error = 5.595524044110789e-14 relative error = 4.975758005424167e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 1.154159790761873 y[1] (numeric) = 1.154159790761932 absolute error = 5.906386491005833e-14 relative error = 5.117477266390443e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 1.184768694738706 y[1] (numeric) = 1.184768694738769 absolute error = 6.261657858885883e-14 relative error = 5.285131086508709e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 1.216447379556299 y[1] (numeric) = 1.216447379556365 absolute error = 6.59472476627343e-14 relative error = 5.421298838819371e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 1.249265856812876 y[1] (numeric) = 1.249265856812946 absolute error = 6.994405055138486e-14 relative error = 5.598812308040337e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 1.283301495931948 y[1] (numeric) = 1.283301495932021 absolute error = 7.327471962526033e-14 relative error = 5.70986006464891e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 1.318640091629052 y[1] (numeric) = 1.318640091629129 absolute error = 7.72715225139109e-14 relative error = 5.859940328255106e-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) = 1.355377132316079 y[1] (numeric) = 1.35537713231616 absolute error = 8.149037000748649e-14 relative error = 6.012376043871651e-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) = 1.393619316613149 y[1] (numeric) = 1.393619316613235 absolute error = 8.548717289613705e-14 relative error = 6.134183982458905e-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) = 1.433486378584554 y[1] (numeric) = 1.433486378584644 absolute error = 8.992806499463768e-14 relative error = 6.273381201112913e-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) = 1.475113300329181 y[1] (numeric) = 1.475113300329276 absolute error = 9.50350909079134e-14 relative error = 6.442562133139582e-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) = 1.518653014960218 y[1] (numeric) = 1.518653014960318 absolute error = 1.001421168211891e-13 relative error = 6.594140717773664e-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) = 1.564279736472824 y[1] (numeric) = 1.564279736472929 absolute error = 1.048050535246148e-13 relative error = 6.69989203855135e-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) = 1.6121930994905 y[1] (numeric) = 1.61219309949061 absolute error = 1.101341240428155e-13 relative error = 6.831323374205056e-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) = 1.662623357400167 y[1] (numeric) = 1.662623357400282 absolute error = 1.156852391659413e-13 relative error = 6.957994343760308e-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) = 1.715837981167588 y[1] (numeric) = 1.715837981167709 absolute error = 1.216804434989172e-13 relative error = 7.091604500800038e-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) = 1.772150137669448 y[1] (numeric) = 1.772150137669575 absolute error = 1.27897692436818e-13 relative error = 7.217091245159179e-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) = 1.831929728955606 y[1] (numeric) = 1.831929728955741 absolute error = 1.34559030584569e-13 relative error = 7.345206994445243e-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) = 1.895617980714245 y[1] (numeric) = 1.895617980714386 absolute error = 1.4166445794217e-13 relative error = 7.473259875325334e-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) = 1.963747043924039 y[1] (numeric) = 1.963747043924189 absolute error = 1.49213974509621e-13 relative error = 7.598431527690836e-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) = 2.036966830539076 y[1] (numeric) = 2.036966830539233 absolute error = 1.576516694967722e-13 relative error = 7.739530518278017e-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) = 2.116082544013316 y[1] (numeric) = 2.116082544013482 absolute error = 1.660893644839234e-13 relative error = 7.848907640857995e-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) = 2.202108465746448 y[1] (numeric) = 2.202108465746623 absolute error = 1.749711486809247e-13 relative error = 7.945619001179161e-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) = 2.29634725495213 y[1] (numeric) = 2.296347254952316 absolute error = 1.856292897173262e-13 relative error = 8.08367677480015e-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) = 2.400510821257009 y[1] (numeric) = 2.400510821257207 absolute error = 1.976196983832779e-13 relative error = 8.232401896851097e-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) = 2.51691201953459 y[1] (numeric) = 2.5169120195348 absolute error = 2.104982854689297e-13 relative error = 8.363354929976997e-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) = 2.648783653977668 y[1] (numeric) = 2.648783653977893 absolute error = 2.247091401841317e-13 relative error = 8.483484102096707e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = tan ( x ) ; Iterations = 1401 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %