##############ECHO OF PROBLEM################# ##############temp/expt_lin_lin_newpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln ( 2.0 * x + 1.0 ) + ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=1.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $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(expt(2.0*x+1.0,3.0*x+2.0)) 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 0.9 estimated_steps 900000.0000000001 step_error 1.111111111111111e-16 est_needed_step_err 1.111111111111111e-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 1.0595270250829718e-152 estimated_step_error 1.0595270250829718e-152 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 1.4732301750687347e-142 estimated_step_error 1.4732301750687347e-142 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 9.886657497008343e-135 estimated_step_error 9.886657497008343e-135 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 6.634792866711534e-127 estimated_step_error 6.634792866711534e-127 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 4.45249296148839e-119 estimated_step_error 4.45249296148839e-119 best_h 1.0e-05 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 1.5209567545525315 y[1] (numeric) 1.5209567545525315 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] 0.11000999999999612 y[1] (analytic) 1.589416016111751 y[1] (numeric) 1.5894160168779707 absolute error 7.66219754311237e-10 relative error 4.8207627615686777e-08% Correct digits 10 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] 0.12000999999999225 y[1] (analytic) 1.6614776780932727 y[1] (numeric) 1.6614776788595198 absolute error 7.662470657976428e-10 relative error 4.611840868527317e-08% Correct digits 10 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] 0.13000999999999532 y[1] (analytic) 1.737421092673896 y[1] (numeric) 1.7374210934401193 absolute error 7.662233070249158e-10 relative error 4.4101185962102944e-08% Correct digits 10 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] 0.14000000000000531 y[1] (analytic) 1.8173899685525425 y[1] (numeric) 1.8173899693186821 absolute error 7.661395962088591e-10 relative error 4.2156037474942695e-08% Correct digits 10 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] 0.15000000000001532 y[1] (analytic) 1.9017841044839194 y[1] (numeric) 1.9017841052499762 absolute error 7.66056773571222e-10 relative error 4.0280953645845314e-08% Correct digits 10 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] 0.16000000000002532 y[1] (analytic) 1.9907803683433645 y[1] (numeric) 1.9907803691093302 absolute error 7.659657352832028e-10 relative error 3.8475652435763374e-08% Correct digits 10 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] 0.17000000000003532 y[1] (analytic) 2.0846494905002113 y[1] (numeric) 2.084649491266079 absolute error 7.658678136124308e-10 relative error 3.6738445340691826e-08% Correct digits 10 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] 0.18000000000004532 y[1] (analytic) 2.1836791491489462 y[1] (numeric) 2.183679149914715 absolute error 7.657687817186343e-10 relative error 3.5067824960323515e-08% Correct digits 10 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] 0.19000000000005532 y[1] (analytic) 2.288175082965221 y[1] (numeric) 2.2881750837308896 absolute error 7.656684175572082e-10 relative error 3.346196815345908e-08% Correct digits 10 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] 0.20000000000006532 y[1] (analytic) 2.39846227969988 y[1] (numeric) 2.3984622804654383 absolute error 7.655582834331653e-10 relative error 3.19187126648896e-08% Correct digits 10 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] 0.21000000000007532 y[1] (analytic) 2.5148862460827304 y[1] (numeric) 2.5148862468481745 absolute error 7.654441525062339e-10 relative error 3.043653181922303e-08% Correct digits 10 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] 0.22000000000008532 y[1] (analytic) 2.637814364797841 y[1] (numeric) 2.6378143655631643 absolute error 7.653233602411547e-10 relative error 2.9013541303533244e-08% Correct digits 10 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] 0.23000000000009532 y[1] (analytic) 2.7676373447114426 y[1] (numeric) 2.7676373454766368 absolute error 7.651941302810883e-10 relative error 2.7647918963922942e-08% Correct digits 10 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] 0.24000000000010532 y[1] (analytic) 2.904770770984286 y[1] (numeric) 2.9047707717493374 absolute error 7.650515776447264e-10 relative error 2.633776080669827e-08% Correct digits 10 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] 0.2500000000001153 y[1] (analytic) 3.049656762184943 y[1] (numeric) 3.0496567629498412 absolute error 7.648983668673281e-10 relative error 2.5081457570959973e-08% Correct digits 10 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] 0.2600000000001253 y[1] (analytic) 3.2027657420416396 y[1] (numeric) 3.2027657428063847 absolute error 7.647451560899299e-10 relative error 2.3877648809944942e-08% Correct digits 10 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] 0.2700000000001353 y[1] (analytic) 3.3645983340305223 y[1] (numeric) 3.364598334795103 absolute error 7.645808430822854e-10 relative error 2.272428287647572e-08% Correct digits 10 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] 0.2800000000001453 y[1] (analytic) 3.5356873876009005 y[1] (numeric) 3.5356873883653117 absolute error 7.644112010041226e-10 relative error 2.1619875209691686e-08% Correct digits 10 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] 0.2900000000001553 y[1] (analytic) 3.716600145486073 y[1] (numeric) 3.716600146250305 absolute error 7.642317889633432e-10 relative error 2.0562658318020208e-08% Correct digits 10 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] 0.3000000000001653 y[1] (analytic) 3.907940562245493 y[1] (numeric) 3.9079405630095376 absolute error 7.640448274059963e-10 relative error 1.9551086185583594e-08% Correct digits 10 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] 0.3100000000001753 y[1] (analytic) 4.110351784933933 y[1] (numeric) 4.11035178569778 absolute error 7.638476517968229e-10 relative error 1.858351040892965e-08% Correct digits 10 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] 0.3200000000001853 y[1] (analytic) 4.324518807600128 y[1] (numeric) 4.324518808363763 absolute error 7.636344889760949e-10 relative error 1.7658253390736675e-08% Correct digits 10 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] 0.3300000000001953 y[1] (analytic) 4.551171312185456 y[1] (numeric) 4.551171312948847 absolute error 7.63391128089097e-10 relative error 1.67735089655968e-08% Correct digits 10 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] 0.3400000000002053 y[1] (analytic) 4.791086709327331 y[1] (numeric) 4.7910867100904895 absolute error 7.631584253431356e-10 relative error 1.592871245384501e-08% Correct digits 10 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] 0.3500000000002153 y[1] (analytic) 5.04509339357734 y[1] (numeric) 5.045093394340235 absolute error 7.628946363524847e-10 relative error 1.5121516626901064e-08% Correct digits 10 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] 0.3600000000002253 y[1] (analytic) 5.314074228626133 y[1] (numeric) 5.314074229388751 absolute error 7.626184128639579e-10 relative error 1.4350917583270576e-08% Correct digits 10 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] 0.3700000000002353 y[1] (analytic) 5.598970279291816 y[1] (numeric) 5.598970280054156 absolute error 7.623404130185918e-10 relative error 1.3615725302885804e-08% Correct digits 10 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] 0.3800000000002453 y[1] (analytic) 5.900784808282486 y[1] (numeric) 5.900784809044534 absolute error 7.620482023185104e-10 relative error 1.2914353379721303e-08% Correct digits 10 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] 0.3900000000002553 y[1] (analytic) 6.220587557093526 y[1] (numeric) 6.220587557855244 absolute error 7.61717799946382e-10 relative error 1.2245110175770646e-08% Correct digits 10 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] 0.4000000000002653 y[1] (analytic) 6.559519331853952 y[1] (numeric) 6.559519332615331 absolute error 7.613785157900566e-10 relative error 1.1607230305621556e-08% Correct digits 10 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] 0.4100000000002753 y[1] (analytic) 6.918796916501542 y[1] (numeric) 6.918796917262557 absolute error 7.610152508163992e-10 relative error 1.0999242498379374e-08% Correct digits 10 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] 0.4200000000002853 y[1] (analytic) 7.299718337352473 y[1] (numeric) 7.299718338113109 absolute error 7.606359986311872e-10 relative error 1.0420073261443967e-08% Correct digits 10 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] 0.4300000000002953 y[1] (analytic) 7.703668504947269 y[1] (numeric) 7.703668505707512 absolute error 7.602425355912601e-10 relative error 9.868578004142248e-09% Correct digits 11 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] 0.4400000000003053 y[1] (analytic) 8.13212526101118 y[1] (numeric) 8.132125261771 absolute error 7.598206508419025e-10 relative error 9.343444996903842e-09% Correct digits 11 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] 0.4500000000003153 y[1] (analytic) 8.58666586047486 y[1] (numeric) 8.586665861234213 absolute error 7.593534689931403e-10 relative error 8.843403031303545e-09% Correct digits 11 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] 0.4600000000003253 y[1] (analytic) 9.068973920772217 y[1] (numeric) 9.068973921531104 absolute error 7.58886287144378e-10 relative error 8.367939898979876e-09% Correct digits 11 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] 0.4700000000003353 y[1] (analytic) 9.5808468730796 y[1] (numeric) 9.580846873837988 absolute error 7.583871308725065e-10 relative error 7.91565861472469e-09% Correct digits 11 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] 0.4800000000003453 y[1] (analytic) 10.124203952797949 y[1] (numeric) 10.124203953555796 absolute error 7.578471183933289e-10 relative error 7.485498335737186e-09% Correct digits 11 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] 0.4900000000003553 y[1] (analytic) 10.701094769422355 y[1] (numeric) 10.70109477017963 absolute error 7.57275131491042e-10 relative error 7.07661363447508e-09% Correct digits 11 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] 0.5000000000003653 y[1] (analytic) 11.313708499007818 y[1] (numeric) 11.313708499764463 absolute error 7.566445248130549e-10 relative error 6.68785593052367e-09% Correct digits 11 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] 0.5100000000003198 y[1] (analytic) 11.964383745739962 y[1] (numeric) 11.964383746499593 absolute error 7.596305806600867e-10 relative error 6.349099099488185e-09% Correct digits 11 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] 0.5200000000002742 y[1] (analytic) 12.655619122703198 y[1] (numeric) 12.65561912346593 absolute error 7.627320997016795e-10 relative error 6.0268256519619606e-09% Correct digits 11 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] 0.5300000000002287 y[1] (analytic) 13.390084605726244 y[1] (numeric) 13.390084606492323 absolute error 7.660787559871096e-10 relative error 5.721239100009103e-09% Correct digits 11 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] 0.5400000000001832 y[1] (analytic) 14.170633718396827 y[1] (numeric) 14.170633719166457 absolute error 7.696296933090707e-10 relative error 5.431159315831513e-09% Correct digits 11 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] 0.5500000000001377 y[1] (analytic) 15.000316610753403 y[1] (numeric) 15.000316611526793 absolute error 7.73390240738081e-10 relative error 5.1558261122545525e-09% Correct digits 11 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] 0.5600000000000922 y[1] (analytic) 15.882394099000607 y[1] (numeric) 15.88239409977803 absolute error 7.77424347120359e-10 relative error 4.894881352738112e-09% Correct digits 11 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] 0.5700000000000467 y[1] (analytic) 16.820352738790113 y[1] (numeric) 16.82035273957185 absolute error 7.817355651695834e-10 relative error 4.647557499592685e-09% Correct digits 11 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] 0.5800000000000012 y[1] (analytic) 17.81792101021699 y[1] (numeric) 17.817921011003293 absolute error 7.863043549605209e-10 relative error 4.412997198212101e-09% Correct digits 11 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] 0.5900099999999556 y[1] (analytic) 18.88018109482638 y[1] (numeric) 18.88018109561755 absolute error 7.911715727004776e-10 relative error 4.190487203098266e-09% Correct digits 11 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] 0.6000099999999101 y[1] (analytic) 20.00928005473505 y[1] (numeric) 20.009280055531303 absolute error 7.962519532611623e-10 relative error 3.979413307640397e-09% Correct digits 11 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] 0.6100099999998646 y[1] (analytic) 21.210810693386605 y[1] (numeric) 21.210810694188293 absolute error 8.01687605189727e-10 relative error 3.779617935299796e-09% Correct digits 11 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] 0.6200099999998191 y[1] (analytic) 22.489656691641862 y[1] (numeric) 22.489656692449376 absolute error 8.075140556229599e-10 relative error 3.5906019673615886e-09% Correct digits 11 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] 0.6300099999997736 y[1] (analytic) 23.8510444662709 y[1] (numeric) 23.851044467084613 absolute error 8.137135409924667e-10 relative error 3.411647410842677e-09% Correct digits 11 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] 0.6400099999997281 y[1] (analytic) 25.300568042825667 y[1] (numeric) 25.300568043645963 absolute error 8.202967194392841e-10 relative error 3.24220672852399e-09% Correct digits 11 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] 0.6500099999996826 y[1] (analytic) 26.844215786551626 y[1] (numeric) 26.844215787378975 absolute error 8.273488560917031e-10 relative error 3.082037719672135e-09% Correct digits 11 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] 0.660009999999637 y[1] (analytic) 28.48839913371492 y[1] (numeric) 28.488399134549766 absolute error 8.348450819539721e-10 relative error 2.93047383264848e-09% Correct digits 11 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] 0.6700099999995915 y[1] (analytic) 30.239983476882387 y[1] (numeric) 30.2399834777252 absolute error 8.428138187355216e-10 relative error 2.7870842567749053e-09% Correct digits 11 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] 0.680009999999546 y[1] (analytic) 32.10632136974571 y[1] (numeric) 32.10632137059703 absolute error 8.513225679962488e-10 relative error 2.6515730599970368e-09% Correct digits 11 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] 0.6900099999995005 y[1] (analytic) 34.09528823010088 y[1] (numeric) 34.09528823096119 absolute error 8.603109336036141e-10 relative error 2.52325461453085e-09% Correct digits 11 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] 0.700009999999455 y[1] (analytic) 36.21532073365865 y[1] (numeric) 36.21532073452863 absolute error 8.699814202373091e-10 relative error 2.402246901623448e-09% Correct digits 11 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] 0.7100099999994095 y[1] (analytic) 38.47545810655649 y[1] (numeric) 38.47545810743684 absolute error 8.803553441794065e-10 relative error 2.288095808349551e-09% Correct digits 11 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] 0.720009999999364 y[1] (analytic) 40.88538654085972 y[1] (numeric) 40.88538654175098 absolute error 8.912621751733241e-10 relative error 2.1799039964624557e-09% Correct digits 11 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] 0.7300099999993185 y[1] (analytic) 43.4554869750801 y[1] (numeric) 43.45548697598307 absolute error 9.029719194586505e-10 relative error 2.0779238303702983e-09% Correct digits 11 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] 0.740009999999273 y[1] (analytic) 46.19688650091138 y[1] (numeric) 46.19688650182671 absolute error 9.153282576335187e-10 relative error 1.981363522443143e-09% Correct digits 11 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] 0.7500099999992275 y[1] (analytic) 49.12151367810231 y[1] (numeric) 49.12151367903087 absolute error 9.285585633733717e-10 relative error 1.890329702497157e-09% Correct digits 11 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] 0.760009999999182 y[1] (analytic) 52.242158061784636 y[1] (numeric) 52.2421580627273 absolute error 9.426628366782097e-10 relative error 1.8044102151434124e-09% Correct digits 11 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] 0.7700099999991364 y[1] (analytic) 55.57253427078553 y[1] (numeric) 55.57253427174334 absolute error 9.57811607804615e-10 relative error 1.7235341529280165e-09% Correct digits 11 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] 0.7800099999990909 y[1] (analytic) 59.12735095162966 y[1] (numeric) 59.127350952603614 absolute error 9.739551387610845e-10 relative error 1.6472159213725785e-09% Correct digits 11 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] 0.7900099999990454 y[1] (analytic) 62.922385021239116 y[1] (numeric) 62.92238502223034 absolute error 9.91221327240055e-10 relative error 1.5753079399413634e-09% Correct digits 11 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] 0.8000099999989999 y[1] (analytic) 66.9745616019439 y[1] (numeric) 66.97456160295363 absolute error 1.009723860079248e-09 relative error 1.507622948068601e-09% Correct digits 11 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] 0.8100099999989544 y[1] (analytic) 71.30204009551397 y[1] (numeric) 71.30204009654338 absolute error 1.0294058938598027e-09 relative error 1.4437257229678743e-09% Correct digits 11 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] 0.8200099999989089 y[1] (analytic) 75.92430687872115 y[1] (numeric) 75.9243068797716 absolute error 1.050452169693017e-09 relative error 1.3835518727500175e-09% Correct digits 11 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] 0.8300099999988634 y[1] (analytic) 80.86227514166106 y[1] (numeric) 80.86227514273413 absolute error 1.0730758503996185e-09 relative error 1.3270413780959263e-09% Correct digits 11 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] 0.8400099999988179 y[1] (analytic) 86.13839243195277 y[1] (numeric) 86.13839243304976 absolute error 1.0969927188853035e-09 relative error 1.2735235565858754e-09% Correct digits 11 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] 0.8500099999987724 y[1] (analytic) 91.77675651325319 y[1] (numeric) 91.77675651437583 absolute error 1.122643311646243e-09 relative error 1.2232327163186745e-09% Correct digits 11 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] 0.8600099999987268 y[1] (analytic) 97.80324019555707 y[1] (numeric) 97.80324019670728 absolute error 1.150212369793735e-09 relative error 1.17604730425484e-09% Correct digits 11 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] 0.8700099999986813 y[1] (analytic) 104.24562584781485 y[1] (numeric) 104.24562584899452 absolute error 1.1796714716183487e-09 relative error 1.1316268304058308e-09% Correct digits 11 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] 0.8800099999986358 y[1] (analytic) 111.13375036082354 y[1] (numeric) 111.1337503620349 absolute error 1.2113616776332492e-09 relative error 1.0900034181337894e-09% Correct digits 11 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] 0.8900099999985903 y[1] (analytic) 118.4996613904961 y[1] (numeric) 118.4996613917408 absolute error 1.244700342795113e-09 relative error 1.0503830375459118e-09% Correct digits 11 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] 0.9000099999985448 y[1] (analytic) 126.37778577888882 y[1] (numeric) 126.37778578016905 absolute error 1.2802274795831181e-09 relative error 1.0130162288355092e-09% Correct digits 11 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] 0.9100099999984993 y[1] (analytic) 134.80511112319144 y[1] (numeric) 134.80511112450932 absolute error 1.3178862445784034e-09 relative error 9.77623350923286e-10% Correct digits 12 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] 0.9200099999984538 y[1] (analytic) 143.8213815417301 y[1] (numeric) 143.82138154308868 absolute error 1.358586132482742e-09 relative error 9.446343220451857e-10% Correct digits 12 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] 0.9300099999984083 y[1] (analytic) 153.46930877140187 y[1] (numeric) 153.46930877280406 absolute error 1.4021850347489817e-09 relative error 9.136582721158843e-10% Correct digits 12 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] 0.9400099999983628 y[1] (analytic) 163.7947998234018 y[1] (numeric) 163.79479982485105 absolute error 1.4492513855657307e-09 relative error 8.847969454025807e-10% Correct digits 12 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] 0.9500099999983173 y[1] (analytic) 174.84720252421488 y[1] (numeric) 174.84720252571438 absolute error 1.499500967838685e-09 relative error 8.576064965243105e-10% Correct digits 12 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] 0.9600099999982717 y[1] (analytic) 186.67957037727336 y[1] (numeric) 186.6795703788268 absolute error 1.5534453723375918e-09 relative error 8.32145354308524e-10% Correct digits 12 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] 0.9700099999982262 y[1] (analytic) 199.34894829812453 y[1] (numeric) 199.3489482997355 absolute error 1.6109709122247295e-09 relative error 8.081160828676845e-10% Correct digits 12 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] 0.9800099999981807 y[1] (analytic) 212.91668090318103 y[1] (numeric) 212.9166809048536 absolute error 1.672560756560415e-09 relative error 7.855470738438637e-10% Correct digits 12 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] 0.9900099999981352 y[1] (analytic) 227.44874516996043 y[1] (numeric) 227.44874517169944 absolute error 1.7390107132086996e-09 relative error 7.645725686062717e-10% Correct digits 12 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 ) = expt ( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln ( 2.0 * x + 1.0 ) + ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0 ) ) ; Iterations 90001 Total Elapsed Time 1 Minutes 25 Seconds Elapsed Time(since restart) 1 Minutes 25 Seconds Time to Timeout 8 Minutes 35.0 Seconds Percent Done 100.00222222200998%