##############ECHO OF PROBLEM################# ##############temp/cos_sqrt_linpostode.ode################# diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=2.0 x_end=3.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_display_interval=0.1 $glob_max_minutes=10 $glob_max_h=0.00001 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 1.0 estimated_steps 1000000.0 step_error 1.0e-16 est_needed_step_err 1.0e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.188174820698805e-174 estimated_step_error 6.188174820698805e-174 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.152813288011036e-166 estimated_step_error 4.152813288011036e-166 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.7869051015555175e-158 estimated_step_error 2.7869051015555175e-158 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8702593879514654e-150 estimated_step_error 1.8702593879514654e-150 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2551085319482906e-142 estimated_step_error 1.2551085319482906e-142 best_h 1.0e-05 START of Soultion TOP MAIN SOLVE Loop x[1] 2.0 y[1] (analytic) 0.37920523045202315 y[1] (numeric) 0.37920523045202315 absolute error 0.0 relative error 0.0% Correct digits 16 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0100000000000655 y[1] (analytic) 0.3704005770756198 y[1] (numeric) 0.370400586029134 absolute error 8.9535142078212e-09 relative error 2.4172516896466064e-06% Correct digits 8 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.020000000000131 y[1] (analytic) 0.36157809232760796 y[1] (numeric) 0.36157811015916075 absolute error 1.7831552789893124e-08 relative error 4.931591036145199e-06% Correct digits 8 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0300000000001965 y[1] (analytic) 0.35273792696314776 y[1] (numeric) 0.35273795359745974 absolute error 2.6634311978135372e-08 relative error 7.550736663743558e-06% Correct digits 8 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.040000000000262 y[1] (analytic) 0.34388023134695633 y[1] (numeric) 0.3438802667089421 absolute error 3.53619857840215e-08 relative error 1.0283227286869884e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0500000000003276 y[1] (analytic) 0.33500515545393805 y[1] (numeric) 0.3350051994687082 absolute error 4.401477016191535e-08 relative error 1.3138535167399003e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.060000000000393 y[1] (analytic) 0.32611284886982106 y[1] (numeric) 0.3261129014626796 absolute error 5.259285856817897e-08 relative error 1.6127196076586723e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0700000000004586 y[1] (analytic) 0.31720346079178485 y[1] (numeric) 0.31720352188823026 absolute error 6.109644540286396e-08 relative error 1.9260964319354703e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.080000000000524 y[1] (analytic) 0.3082771400290987 y[1] (numeric) 0.3082772095548231 absolute error 6.952572439988813e-08 relative error 2.255299383967475e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0900000000005896 y[1] (analytic) 0.2993340350037449 y[1] (numeric) 0.2993341128846344 absolute error 7.788088951521388e-08 relative error 2.60180535481839e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.100000000000655 y[1] (analytic) 0.2903742937510554 y[1] (numeric) 0.2903743799131896 absolute error 8.616213420520324e-08 relative error 2.967278304568931e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1100000000007206 y[1] (analytic) 0.2813980639203403 y[1] (numeric) 0.2813981582899898 absolute error 9.436964953923876e-08 relative error 3.353599816022666e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.120000000000786 y[1] (analytic) 0.2724054927755124 y[1] (numeric) 0.2724055952791429 absolute error 1.0250363047248356e-07 relative error 3.762906152445176e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1300000000008517 y[1] (analytic) 0.2633967271957206 y[1] (numeric) 0.2633968377599875 absolute error 1.10564266908586e-07 relative error 4.1976325251159894e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.140000000000917 y[1] (analytic) 0.25437191367597234 y[1] (numeric) 0.2543720322277234 absolute error 1.185517510826628e-07 relative error 4.660567645596207e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1500000000009827 y[1] (analytic) 0.2453311983277634 y[1] (numeric) 0.24533132479403955 absolute error 1.2646627614576467e-07 relative error 5.154920246906602e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.160000000001048 y[1] (analytic) 0.2362747268797023 y[1] (numeric) 0.23627486118773494 absolute error 1.343080326399182e-07 relative error 5.6844011381843743e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1700000000011137 y[1] (analytic) 0.22720264467813633 y[1] (numeric) 0.22720278675534675 absolute error 1.420772104132606e-07 relative error 6.253325555014222e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.180000000001179 y[1] (analytic) 0.21811509668777163 y[1] (numeric) 0.21811524646177433 absolute error 1.4977400270010932e-07 relative error 6.866741687051056e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1900000000012447 y[1] (analytic) 0.20901222749230475 y[1] (numeric) 0.20901238489090193 absolute error 1.5739859718366667e-07 relative error 7.530592782638118e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2000000000013102 y[1] (analytic) 0.19989418129503556 y[1] (numeric) 0.19989434624622146 absolute error 1.6495118590476032e-07 relative error 8.251925335500345e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2100000000013758 y[1] (analytic) 0.19076110191949802 y[1] (numeric) 0.19076127435145493 absolute error 1.7243195690741508e-07 relative error 9.03915710133516e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2200000000014413 y[1] (analytic) 0.18161313281007352 y[1] (numeric) 0.18161331265117509 absolute error 1.7984110156632482e-07 relative error 9.90242824313802e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2300000000015068 y[1] (analytic) 0.17245041703261943 y[1] (numeric) 0.17245060421142633 absolute error 1.8717880689855804e-07 relative error 0.00010854065192730308% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2400000000015723 y[1] (analytic) 0.16327309727508066 y[1] (numeric) 0.16327329172034422 absolute error 1.9444526355716363e-07 relative error 0.00011909204076012869% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.250000000001638 y[1] (analytic) 0.15408131584811535 y[1] (numeric) 0.15408151748877452 absolute error 2.0164065916983276e-07 relative error 0.0001308663922422617% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2600000000017033 y[1] (analytic) 0.14487521468570985 y[1] (numeric) 0.14487542345089047 absolute error 2.0876518061485605e-07 relative error 0.00014409999741346244% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.270000000001769 y[1] (analytic) 0.13565493534579343 y[1] (numeric) 0.13565515116481155 absolute error 2.1581901812894877e-07 relative error 0.00015909411447420752% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2800000000018343 y[1] (analytic) 0.12642061901086254 y[1] (numeric) 0.12642084181322047 absolute error 2.2280235792426772e-07 relative error 0.0001762389392391155% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2900000000019 y[1] (analytic) 0.11717240648858906 y[1] (numeric) 0.11717263620397701 absolute error 2.297153879476932e-07 relative error 0.0001960490484336551% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3000000000019654 y[1] (analytic) 0.10791043821244128 y[1] (numeric) 0.1079106747707354 absolute error 2.3655829411994844e-07 relative error 0.0002192172490804277% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.310000000002031 y[1] (analytic) 0.09863485424229435 y[1] (numeric) 0.09863509757355772 absolute error 2.4333126337483524e-07 relative error 0.0002466990651976809% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3200000000020964 y[1] (analytic) 0.08934579426504607 y[1] (numeric) 0.08934604429952832 absolute error 2.500344822436995e-07 relative error 0.0002798503100235107% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.330000000002162 y[1] (analytic) 0.08004339759522794 y[1] (numeric) 0.08004365426336578 absolute error 2.5666813784075426e-07 relative error 0.00032066122322630693% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3400000000022274 y[1] (analytic) 0.07072780317562188 y[1] (numeric) 0.07072806640803614 absolute error 2.632324142548548e-07 relative error 0.00037217671472310687% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.350000000002293 y[1] (analytic) 0.06139914957786696 y[1] (numeric) 0.06139941930536361 absolute error 2.6972749665038487e-07 relative error 0.0004393016817086595% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3600000000023584 y[1] (analytic) 0.05205757500307007 y[1] (numeric) 0.05205785115664255 absolute error 2.7615357248156336e-07 relative error 0.0005304772119432712% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.370000000002424 y[1] (analytic) 0.04270321728242099 y[1] (numeric) 0.04270349979324618 absolute error 2.825108251919284e-07 relative error 0.0006615680109616132% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3800000000024895 y[1] (analytic) 0.03333621387779806 y[1] (numeric) 0.03333650267723645 absolute error 2.8879943839155153e-07 relative error 0.0008663234506780392% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.390000000002555 y[1] (analytic) 0.023956701882375198 y[1] (numeric) 0.023956996901972647 absolute error 2.95019597449514e-07 relative error 0.0012314700032501475% Correct digits 5 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4000000000026205 y[1] (analytic) 0.014564818021233661 y[1] (numeric) 0.014565119192719148 absolute error 3.0117148548669537e-07 relative error 0.0020678012251689345% Correct digits 5 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.410000000002686 y[1] (analytic) 0.005160698651965223 y[1] (numeric) 0.005161005907252458 absolute error 3.0725528723466594e-07 relative error 0.00595375370576349% Correct digits 5 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4200000000027515 y[1] (analytic) -0.004255520234716648 y[1] (numeric) -0.004255206963532382 absolute error 3.132711842660646e-07 relative error 0.007361524960224367% Correct digits 5 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.430000000002817 y[1] (analytic) -0.013683703014377269 y[1] (numeric) -0.013683383795016204 absolute error 3.192193610643962e-07 relative error 0.002332843388438035% Correct digits 5 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4400000000028825 y[1] (analytic) -0.023123714428251452 y[1] (numeric) -0.023123389328250803 absolute error 3.2510000064905897e-07 relative error 0.0014059159987370683% Correct digits 5 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.450000000002948 y[1] (analytic) -0.032575419582638876 y[1] (numeric) -0.03257508866935484 absolute error 3.3091328403844766e-07 relative error 0.0010158373653452754% Correct digits 5 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4600000000030136 y[1] (analytic) -0.04203868394830368 y[1] (numeric) -0.0420383472889106 absolute error 3.366593930784201e-07 relative error 0.00080083237974914% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.470000000003079 y[1] (analytic) -0.05151337335987172 y[1] (numeric) -0.051513031021360706 absolute error 3.4233851101128643e-07 relative error 0.0006645624013393848% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4800000000031446 y[1] (analytic) -0.06099935401522438 y[1] (numeric) -0.060999006064406815 absolute error 3.479508175682766e-07 relative error 0.0005704172170109114% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.49000000000321 y[1] (analytic) -0.07049649247490497 y[1] (numeric) -0.07049613897840816 absolute error 3.5349649681049033e-07 relative error 0.0005014384182820535% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5000000000032756 y[1] (analytic) -0.08000465566150683 y[1] (numeric) -0.08000429668578096 absolute error 3.5897572586707227e-07 relative error 0.000448693545268002% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.510000000003341 y[1] (analytic) -0.08952371085908761 y[1] (numeric) -0.08952334647039872 absolute error 3.6438868888932774e-07 relative error 0.00040703036703079027% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5200000000034066 y[1] (analytic) -0.09905352571255754 y[1] (numeric) -0.0990531559769937 absolute error 3.697355638460076e-07 relative error 0.00037326845378420916% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.530000000003472 y[1] (analytic) -0.108593968227088 y[1] (numeric) -0.1085935932105575 absolute error 3.750165304960973e-07 relative error 0.00034533826935201% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5400000000035377 y[1] (analytic) -0.11814490676751555 y[1] (numeric) -0.1181445265357447 absolute error 3.8023177084678395e-07 relative error 0.00032183509323427753% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.550000000003603 y[1] (analytic) -0.1277062100577373 y[1] (numeric) -0.12770582467627517 absolute error 3.8538146213129565e-07 relative error 0.00030177190440234717% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5600000000036687 y[1] (analytic) -0.13727774718012054 y[1] (numeric) -0.1372773567143373 absolute error 3.9046578323431724e-07 relative error 0.00028443487109530697% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.570000000003734 y[1] (analytic) -0.1468593875749108 y[1] (numeric) -0.1468589920899956 absolute error 3.9548491520546847e-07 relative error 0.0002692949505892073% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5800000000037997 y[1] (analytic) -0.15645100103962517 y[1] (numeric) -0.1564506006005919 absolute error 4.004390332656982e-07 relative error 0.00025595172329020565% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.590000000003865 y[1] (analytic) -0.16605245772847366 y[1] (numeric) -0.16605205240015344 absolute error 4.053283202132274e-07 relative error 0.00024409654982404045% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6000000000039307 y[1] (analytic) -0.17566362815175118 y[1] (numeric) -0.17566321799880188 absolute error 4.101529492983591e-07 relative error 0.00023348769100000528% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6100000000039962 y[1] (analytic) -0.18528438317525742 y[1] (numeric) -0.18528396826215587 absolute error 4.1491310154295746e-07 relative error 0.00022393312076954595% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6200000000040617 y[1] (analytic) -0.19491459401969558 y[1] (numeric) -0.19491417441074357 absolute error 4.196089520014379e-07 relative error 0.000215278365435806% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6300000000041273 y[1] (analytic) -0.20455413226008712 y[1] (numeric) -0.20455370801940925 absolute error 4.242406778653951e-07 relative error 0.00020739775490136774% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6400000000041928 y[1] (analytic) -0.21420286982518189 y[1] (numeric) -0.21420244101672373 absolute error 4.2880845815829183e-07 relative error 0.00020018800798899506% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6500000000042583 y[1] (analytic) -0.22386067899686157 y[1] (numeric) -0.22386024568439525 absolute error 4.333124663247201e-07 relative error 0.0001935634557468643% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.660000000004324 y[1] (analytic) -0.23352743240955776 y[1] (numeric) -0.2335269946566785 absolute error 4.377528792509633e-07 relative error 0.0001874524439095606% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6700000000043893 y[1] (analytic) -0.24320300304966214 y[1] (numeric) -0.24320256091978928 absolute error 4.4212987285185967e-07 relative error 0.00018179457790723768% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.680000000004455 y[1] (analytic) -0.2528872642549389 y[1] (numeric) -0.2528868178113142 absolute error 4.4644362467982646e-07 relative error 0.0001765385955655564% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6900000000045203 y[1] (analytic) -0.262580089713935 y[1] (numeric) -0.2625796390196277 absolute error 4.5069430726352167e-07 relative error 0.00017164070122549112% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.700000000004586 y[1] (analytic) -0.27228135346539817 y[1] (numeric) -0.2722808985833003 absolute error 4.5488209787780676e-07 relative error 0.00016706325721111627% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7100000000046514 y[1] (analytic) -0.2819909298976889 y[1] (numeric) -0.2819904708905202 absolute error 4.5900716871827285e-07 relative error 0.0001627737349158033% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.720000000004717 y[1] (analytic) -0.2917086937481974 y[1] (numeric) -0.291708230678502 absolute error 4.6306969542220244e-07 relative error 0.00015874387885810617% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7300000000047824 y[1] (analytic) -0.30143452010275995 y[1] (numeric) -0.30143405303290755 absolute error 4.670698524056327e-07 relative error 0.0001549490258270377% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.740000000004848 y[1] (analytic) -0.31116828439507427 y[1] (numeric) -0.3111678133872611 absolute error 4.710078131409112e-07 relative error 0.00015136755150242014% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7500000000049134 y[1] (analytic) -0.3209098624061173 y[1] (numeric) -0.32090938752236514 absolute error 4.748837521550975e-07 relative error 0.00014798041686675352% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.760000000004979 y[1] (analytic) -0.330659130263563 y[1] (numeric) -0.3306586515657241 absolute error 4.78697838868225e-07 relative error 0.0001447707911427284% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7700000000050444 y[1] (analytic) -0.3404159644412059 y[1] (numeric) -0.3404154819909547 absolute error 4.824502511935336e-07 relative error 0.00014172374435654844% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.78000000000511 y[1] (analytic) -0.35018024175837303 y[1] (numeric) -0.35017975561721476 absolute error 4.861411582735009e-07 relative error 0.00013882598168086876% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7900000000051755 y[1] (analytic) -0.35995183937934994 y[1] (numeric) -0.3599513496086138 absolute error 4.897707361339876e-07 relative error 0.0001360656294960123% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.800000000005241 y[1] (analytic) -0.3697306348127989 y[1] (numeric) -0.3697301414736466 absolute error 4.93339152307648e-07 relative error 0.00013343204642954034% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8100000000053065 y[1] (analytic) -0.37951650591118347 y[1] (numeric) -0.3795160090646021 absolute error 4.968465813770528e-07 relative error 0.00013091567129186409% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.820000000005372 y[1] (analytic) -0.3893093308701896 y[1] (numeric) -0.3893088305769951 absolute error 5.002931944830813e-07 relative error 0.00012850788686847526% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8300000000054375 y[1] (analytic) -0.3991089882281471 y[1] (numeric) -0.3991084845489852 absolute error 5.036791619339454e-07 relative error 0.00012620090671724526% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.840000000005503 y[1] (analytic) -0.40891535686545477 y[1] (numeric) -0.40891484986080046 absolute error 5.070046543154128e-07 relative error 0.00012398767759711022% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8500000000055685 y[1] (analytic) -0.4187283160040074 y[1] (numeric) -0.41872780573416396 absolute error 5.102698434344966e-07 relative error 0.00012186179532926861% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.860000000005634 y[1] (analytic) -0.4285477452066172 y[1] (numeric) -0.4285472317317199 absolute error 5.134748973234515e-07 relative error 0.00011981743062861948% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8700000000056995 y[1] (analytic) -0.43837352437644306 y[1] (numeric) -0.43837300775645455 absolute error 5.166199885109357e-07 relative error 0.00011784926775534471% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.880000000005765 y[1] (analytic) -0.4482055337564145 y[1] (numeric) -0.4482050140511284 absolute error 5.197052860839158e-07 relative error 0.00011595244746941458% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8900000000058306 y[1] (analytic) -0.45804365392866175 y[1] (numeric) -0.4580431311977018 absolute error 5.227309599620256e-07 relative error 0.00011412251986869325% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.900000000005896 y[1] (analytic) -0.46788776581394 y[1] (numeric) -0.46788724011676125 absolute error 5.256971787326314e-07 relative error 0.00011235540168872035% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9100000000059616 y[1] (analytic) -0.4777377506710645 y[1] (numeric) -0.4777372220669538 absolute error 5.286041107055439e-07 relative error 0.00011064733945831764% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.920000000006027 y[1] (analytic) -0.4875934900963336 y[1] (numeric) -0.48759295864440927 absolute error 5.31451924357107e-07 relative error 0.00010899487691111468% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9300000000060926 y[1] (analytic) -0.49745486602296285 y[1] (numeric) -0.49745433178217274 absolute error 5.342407901065549e-07 relative error 0.00010739482646489863% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.940000000006158 y[1] (analytic) -0.5073217607205147 y[1] (numeric) -0.507321223749639 absolute error 5.369708757640979e-07 relative error 0.00010584424271520987% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9500000000062236 y[1] (analytic) -0.5171940567943303 y[1] (numeric) -0.5171935171519826 absolute error 5.396423476966561e-07 relative error 0.00010434040001183786% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.960000000006289 y[1] (analytic) -0.52707163718496 y[1] (numeric) -0.5270710949295893 absolute error 5.422553707168376e-07 relative error 0.00010288077226332506% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9700000000063547 y[1] (analytic) -0.5369543851676023 y[1] (numeric) -0.536953840357485 absolute error 5.448101173533004e-07 relative error 0.00010146301667379922% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.98000000000642 y[1] (analytic) -0.5468421843515292 y[1] (numeric) -0.5468416370447791 absolute error 5.473067501426954e-07 relative error 0.00010008495427098717% Correct digits 6 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9900000000064857 y[1] (analytic) -0.5567349186795278 y[1] (numeric) -0.5567343689340902 absolute error 5.497454376168776e-07 relative error 9.874455852720212e-05% Correct digits 7 h 1.0e-05 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations 100000 Total Elapsed Time 2 Minutes 7 Seconds Elapsed Time(since restart) 2 Minutes 7 Seconds Time to Timeout 7 Minutes 53.0 Seconds Percent Done 100.00100000065513%