##############ECHO OF PROBLEM################# ##############temp/lin_sinhpostode.ode################# diff ( y , x , 1 ) = sinh ( 2.0 * x + 3.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(2.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=0.000000001 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=false $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(cosh(c(2.0)*c(x)+c(3.0))/c(2.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 6.14332310027193 y[1] (numeric) 6.14332310027193 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y[1] (closed_form) 6.267018809899617 y[1] (numeric) 6.267018809899617 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y[1] (closed_form) 6.393221410612629 y[1] (numeric) 6.393221410612629 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y[1] (closed_form) 6.521981385133975 y[1] (numeric) 6.521981385133976 absolute error 8.881784197001252e-16 relative error 1.3618229909772738e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (closed_form) 6.653350239170286 y[1] (numeric) 6.653350239170286 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y[1] (closed_form) 6.787380522014783 y[1] (numeric) 6.787380522014784 absolute error 8.881784197001252e-16 relative error 1.3085731922931531e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y[1] (closed_form) 6.9241258475677006 y[1] (numeric) 6.924125847567701 absolute error 8.881784197001252e-16 relative error 1.2827300358963343e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (closed_form) 7.063640915782555 y[1] (numeric) 7.063640915782555 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y[1] (closed_form) 7.205981534546856 y[1] (numeric) 7.205981534546856 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y[1] (closed_form) 7.351204642006011 y[1] (numeric) 7.351204642006011 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y[1] (closed_form) 7.499368329339338 y[1] (numeric) 7.499368329339338 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y[1] (closed_form) 7.65053186399731 y[1] (numeric) 7.650531863997311 absolute error 8.881784197001252e-16 relative error 1.1609368283005397e-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) 7.8047557134093335 y[1] (numeric) 7.804755713409334 absolute error 8.881784197001252e-16 relative error 1.1379964374466555e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y[1] (closed_form) 7.9621015691715185 y[1] (numeric) 7.9621015691715185 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y[1] (closed_form) 8.12263237172414 y[1] (numeric) 8.12263237172414 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (closed_form) 8.286412335528658 y[1] (numeric) 8.286412335528661 absolute error 3.552713678800501e-15 relative error 4.2873966862208344e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (closed_form) 8.453506974754365 y[1] (numeric) 8.453506974754365 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (closed_form) 8.623983129484897 y[1] (numeric) 8.623983129484902 absolute error 5.329070518200751e-15 relative error 6.17936101936583e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (closed_form) 8.797908992455204 y[1] (numeric) 8.797908992455204 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (closed_form) 8.975354136329502 y[1] (numeric) 8.975354136329507 absolute error 5.329070518200751e-15 relative error 5.937448748267543e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (closed_form) 9.156389541531325 y[1] (numeric) 9.156389541531325 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (closed_form) 9.341087624636573 y[1] (numeric) 9.34108762463658 absolute error 7.105427357601002e-15 relative error 7.606638159416096e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (closed_form) 9.52952226734118 y[1] (numeric) 9.529522267341184 absolute error 3.552713678800501e-15 relative error 3.7281130985716656e-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) 9.721768846014706 y[1] (numeric) 9.721768846014715 absolute error 8.881784197001252e-15 relative error 9.135975497547658e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (closed_form) 9.917904261851962 y[1] (numeric) 9.917904261851966 absolute error 3.552713678800501e-15 relative error 3.582121368589522e-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) 10.118006971634435 y[1] (numeric) 10.11800697163444 absolute error 5.329070518200751e-15 relative error 5.26691722306642e-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) 10.322157019114128 y[1] (numeric) 10.322157019114128 absolute error 0.0 relative error 0.0% 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) 10.530436067032053 y[1] (numeric) 10.53043606703206 absolute error 7.105427357601002e-15 relative error 6.747514834495956e-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) 10.742927429784489 y[1] (numeric) 10.74292742978449 absolute error 1.7763568394002505e-15 relative error 1.6535128353146526e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (closed_form) 10.959716106749768 y[1] (numeric) 10.959716106749775 absolute error 7.105427357601002e-15 relative error 6.483222091149767e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (closed_form) 11.180888816289256 y[1] (numeric) 11.180888816289258 absolute error 1.7763568394002505e-15 relative error 1.5887438544351722e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (closed_form) 11.406534030435752 y[1] (numeric) 11.406534030435761 absolute error 8.881784197001252e-15 relative error 7.786575811111616e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (closed_form) 11.636742010283584 y[1] (numeric) 11.636742010283587 absolute error 3.552713678800501e-15 relative error 3.053014044361307e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (closed_form) 11.871604842094145 y[1] (numeric) 11.871604842094154 absolute error 8.881784197001252e-15 relative error 7.48153624984919e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (closed_form) 12.111216474131732 y[1] (numeric) 12.111216474131734 absolute error 1.7763568394002505e-15 relative error 1.466703896503179e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (closed_form) 12.355672754243997 y[1] (numeric) 12.35567275424401 absolute error 1.2434497875801753e-14 relative error 1.00637967054693e-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) 12.605071468202475 y[1] (numeric) 12.60507146820248 absolute error 5.329070518200751e-15 relative error 4.2277193998017805e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (closed_form) 12.859512378818081 y[1] (numeric) 12.85951237881809 absolute error 8.881784197001252e-15 relative error 6.906781482345428e-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) 13.119097265847676 y[1] (numeric) 13.119097265847682 absolute error 5.329070518200751e-15 relative error 4.0620710481914546e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (closed_form) 13.38392996670723 y[1] (numeric) 13.383929966707239 absolute error 8.881784197001252e-15 relative error 6.63615561280943e-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) 13.654116418008256 y[1] (numeric) 13.654116418008257 absolute error 1.7763568394002505e-15 relative error 1.300967990178723e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (closed_form) 13.929764697933786 y[1] (numeric) 13.929764697933795 absolute error 8.881784197001252e-15 relative error 6.376119331232275e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (closed_form) 14.210985069471175 y[1] (numeric) 14.210985069471175 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (closed_form) 14.497890024518666 y[1] (numeric) 14.497890024518673 absolute error 7.105427357601002e-15 relative error 4.901007902242591e-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) 14.790594328883756 y[1] (numeric) 14.790594328883758 absolute error 1.7763568394002505e-15 relative error 1.2010043679795197e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (closed_form) 15.08921506819094 y[1] (numeric) 15.089215068190951 absolute error 1.0658141036401503e-14 relative error 7.063416478746841e-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) 15.393871694717632 y[1] (numeric) 15.393871694717634 absolute error 1.7763568394002505e-15 relative error 1.1539376672924998e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (closed_form) 15.704686075176555 y[1] (numeric) 15.704686075176562 absolute error 7.105427357601002e-15 relative error 4.524399484069993e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (closed_form) 16.02178253946417 y[1] (numeric) 16.02178253946417 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (closed_form) 16.34528793039417 y[1] (numeric) 16.345287930394175 absolute error 3.552713678800501e-15 relative error 2.1735399791851978e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (closed_form) 16.675331654436423 y[1] (numeric) 16.675331654436416 absolute error 7.105427357601002e-15 relative error 4.261041102418268e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (closed_form) 17.012045733481155 y[1] (numeric) 17.012045733481152 absolute error 3.552713678800501e-15 relative error 2.0883518269695557e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (closed_form) 17.355564857649593 y[1] (numeric) 17.355564857649586 absolute error 7.105427357601002e-15 relative error 4.0940340552898985e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (closed_form) 17.706026439171694 y[1] (numeric) 17.706026439171698 absolute error 3.552713678800501e-15 relative error 2.0064997028021496e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (closed_form) 18.06357066735298 y[1] (numeric) 18.06357066735297 absolute error 1.0658141036401503e-14 relative error 5.900351172353974e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (closed_form) 18.42834056465201 y[1] (numeric) 18.428340564652007 absolute error 3.552713678800501e-15 relative error 1.9278532792122773e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (closed_form) 18.800482043891407 y[1] (numeric) 18.80048204389139 absolute error 1.7763568394002505e-14 relative error 9.448464327952797e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (closed_form) 19.180143966624776 y[1] (numeric) 19.18014396662477 absolute error 7.105427357601002e-15 relative error 3.704574569390669e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (closed_form) 19.56747820268347 y[1] (numeric) 19.567478202683457 absolute error 1.4210854715202004e-14 relative error 7.262486544256447e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (closed_form) 19.962639690926412 y[1] (numeric) 19.9626396909264 absolute error 1.0658141036401503e-14 relative error 5.339043934778791e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (closed_form) 20.36578650121782 y[1] (numeric) 20.365786501217805 absolute error 1.4210854715202004e-14 relative error 6.977807959615128e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (closed_form) 20.77707989765714 y[1] (numeric) 20.77707989765713 absolute error 7.105427357601002e-15 relative error 3.419839261628976e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (closed_form) 21.196684403086966 y[1] (numeric) 21.196684403086945 absolute error 2.1316282072803006e-14 relative error 1.0056422819456906e-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) 21.624767864904232 y[1] (numeric) 21.62476786490422 absolute error 1.0658141036401503e-14 relative error 4.928673039630201e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (closed_form) 22.061501522201567 y[1] (numeric) 22.06150152220154 absolute error 2.842170943040401e-14 relative error 1.2882944255540291e-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) 22.507060074265034 y[1] (numeric) 22.507060074265013 absolute error 2.1316282072803006e-14 relative error 9.470931344416864e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (closed_form) 22.961621750456363 y[1] (numeric) 22.961621750456327 absolute error 3.552713678800501e-14 relative error 1.5472398759159468e-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) 23.425368381506896 y[1] (numeric) 23.42536838150687 absolute error 2.4868995751603507e-14 relative error 1.0616266667224016e-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) 23.89848547225246 y[1] (numeric) 23.89848547225242 absolute error 3.907985046680551e-14 relative error 1.6352438112523701e-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) 24.381162275837625 y[1] (numeric) 24.381162275837596 absolute error 2.842170943040401e-14 relative error 1.165724140172377e-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) 24.873591869419645 y[1] (numeric) 24.873591869419602 absolute error 4.263256414560601e-14 relative error 1.7139689502592423e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (closed_form) 25.375971231401724 y[1] (numeric) 25.37597123140169 absolute error 3.552713678800501e-14 relative error 1.4000306220414387e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (closed_form) 25.88850132022718 y[1] (numeric) 25.888501320227135 absolute error 4.618527782440651e-14 relative error 1.7840073959136858e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (closed_form) 26.41138715476533 y[1] (numeric) 26.41138715476529 absolute error 3.907985046680551e-14 relative error 1.4796591423920892e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (closed_form) 26.94483789632193 y[1] (numeric) 26.944837896321875 absolute error 5.3290705182007514e-14 relative error 1.977770487507067e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (closed_form) 27.489066932306326 y[1] (numeric) 27.489066932306287 absolute error 3.907985046680551e-14 relative error 1.421650671630371e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (closed_form) 28.04429196158945 y[1] (numeric) 28.0442919615894 absolute error 4.973799150320701e-14 relative error 1.7735513369825878e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (closed_form) 28.61073508158607 y[1] (numeric) 28.610735081586025 absolute error 4.618527782440651e-14 relative error 1.6142639359913353e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (closed_form) 29.188622877096897 y[1] (numeric) 29.188622877096837 absolute error 6.039613253960852e-14 relative error 2.0691669077337272e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (closed_form) 29.778186510945368 y[1] (numeric) 29.778186510945325 absolute error 4.263256414560601e-14 relative error 1.431670935701066e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (closed_form) 30.379661816446024 y[1] (numeric) 30.37966181644596 absolute error 6.394884621840902e-14 relative error 2.1049887455886794e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (closed_form) 30.993289391740788 y[1] (numeric) 30.993289391740742 absolute error 4.618527782440651e-14 relative error 1.4901702507483488e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (closed_form) 31.61931469604165 y[1] (numeric) 31.619314696041585 absolute error 6.394884621840902e-14 relative error 2.0224614870104896e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (closed_form) 32.25798814781737 y[1] (numeric) 32.257988147817336 absolute error 3.552713678800501e-14 relative error 1.1013438477690319e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (closed_form) 32.9095652249645 y[1] (numeric) 32.90956522496444 absolute error 6.394884621840902e-14 relative error 1.9431689778113133e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (closed_form) 33.57430656700164 y[1] (numeric) 33.57430656700159 absolute error 4.973799150320701e-14 relative error 1.4814301943645137e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (closed_form) 34.252478079329 y[1] (numeric) 34.252478079328945 absolute error 5.684341886080802e-14 relative error 1.659541792251008e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (closed_form) 34.94435103959386 y[1] (numeric) 34.944351039593826 absolute error 3.552713678800501e-14 relative error 1.0166775381735039e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (closed_form) 35.650202206205485 y[1] (numeric) 35.65020220620543 absolute error 5.684341886080802e-14 relative error 1.594476758701624e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (closed_form) 36.37031392904192 y[1] (numeric) 36.370313929041885 absolute error 3.552713678800501e-14 relative error 9.768168858074214e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y[1] (closed_form) 37.10497426239399 y[1] (numeric) 37.104974262393945 absolute error 4.263256414560601e-14 relative error 1.1489716673598197e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0099999999999996 y[1] (closed_form) 37.8544770801905 y[1] (numeric) 37.85447708019054 absolute error 4.263256414560601e-14 relative error 1.1262225087746864e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0199999999999985 y[1] (closed_form) 38.61912219355218 y[1] (numeric) 38.619122193552315 absolute error 1.3500311979441904e-13 relative error 3.495758373735358e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0299999999999974 y[1] (closed_form) 39.399215470719774 y[1] (numeric) 39.39921547072 absolute error 2.2737367544323206e-13 relative error 5.771020380144596e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0399999999999963 y[1] (closed_form) 40.19506895940553 y[1] (numeric) 40.19506895940585 absolute error 3.197442310920451e-13 relative error 7.954812353101482e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0499999999999952 y[1] (closed_form) 41.00700101161643 y[1] (numeric) 41.00700101161686 absolute error 4.263256414560601e-13 relative error 1.0396411123439408e-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) 41.83533641099929 y[1] (numeric) 41.83533641099981 absolute error 5.186961971048731e-13 relative error 1.2398518611374145e-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) 42.68040650275847 y[1] (numeric) 42.68040650275907 absolute error 5.968558980384842e-13 relative error 1.3984306780206248e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y[1] (closed_form) 43.54254932619842 y[1] (numeric) 43.54254932619912 absolute error 7.034373084024992e-13 relative error 1.615517050076026e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y[1] (closed_form) 44.422109749943914 y[1] (numeric) 44.42210974994471 absolute error 7.958078640513122e-13 relative error 1.7914679616321396e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0999999999999897 y[1] (closed_form) 45.319439609892065 y[1] (numeric) 45.31943960989295 absolute error 8.881784197001252e-13 relative error 1.959817745641892e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y[1] (closed_form) 46.23489784995142 y[1] (numeric) 46.234897849952425 absolute error 1.0018652574217413e-12 relative error 2.1669027163705388e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y[1] (closed_form) 47.1688506656243 y[1] (numeric) 47.16885066562539 absolute error 1.0942358130705543e-12 relative error 2.319827169051654e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1299999999999863 y[1] (closed_form) 48.1216716504898 y[1] (numeric) 48.121671650491 absolute error 1.2008172234345693e-12 relative error 2.4953772016819512e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y[1] (closed_form) 49.093741945646336 y[1] (numeric) 49.09374194564766 absolute error 1.3216094885137863e-12 relative error 2.692012130542002e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y[1] (closed_form) 50.08545039217308 y[1] (numeric) 50.085450392174515 absolute error 1.4352963262354024e-12 relative error 2.865695156970572e-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) 51.0971936866716 y[1] (numeric) 51.097193686673144 absolute error 1.5418777365994174e-12 relative error 3.0175389788609995e-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) 52.12937653994979 y[1] (numeric) 52.12937653995144 absolute error 1.6484591469634324e-12 relative error 3.162246043169386e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1799999999999808 y[1] (closed_form) 53.18241183891157 y[1] (numeric) 53.182411838913325 absolute error 1.7550405573274475e-12 relative error 3.300039424017529e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1899999999999797 y[1] (closed_form) 54.256720811717194 y[1] (numeric) 54.25672081171907 absolute error 1.8758328224066645e-12 relative error 3.45732804036613e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1999999999999786 y[1] (closed_form) 55.352733196280084 y[1] (numeric) 55.35273319628208 absolute error 1.9966250874858815e-12 relative error 3.6070939449473514e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2099999999999775 y[1] (closed_form) 56.47088741216777 y[1] (numeric) 56.470887412169894 absolute error 2.1245227799226996e-12 relative error 3.762155824498216e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2199999999999764 y[1] (closed_form) 57.61163073597552 y[1] (numeric) 57.611630735977776 absolute error 2.2595258997171186e-12 relative error 3.921996081090203e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2299999999999753 y[1] (closed_form) 58.775419480242974 y[1] (numeric) 58.77541948024537 absolute error 2.3945290195115376e-12 relative error 4.074031356452411e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2399999999999742 y[1] (closed_form) 59.96271917598523 y[1] (numeric) 59.96271917598775 absolute error 2.5224267119483557e-12 relative error 4.2066583147192816e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2499999999999731 y[1] (closed_form) 61.17400475891145 y[1] (numeric) 61.174004758914116 absolute error 2.6645352591003757e-12 relative error 4.355665890440535e-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) 62.409760759405515 y[1] (numeric) 62.409760759408314 absolute error 2.7995383788947947e-12 relative error 4.485738039739061e-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) 63.670481496344564 y[1] (numeric) 63.6704814963475 absolute error 2.9345414986892138e-12 relative error 4.608951322062314e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2799999999999698 y[1] (closed_form) 64.95667127483321 y[1] (numeric) 64.9566712748363 absolute error 3.083755473198835e-12 relative error 4.747403788829315e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2899999999999687 y[1] (closed_form) 66.26884458793229 y[1] (numeric) 66.26884458793552 absolute error 3.225864020350855e-12 relative error 4.867844068218887e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2999999999999676 y[1] (closed_form) 67.60752632246293 y[1] (numeric) 67.6075263224663 absolute error 3.367972567502875e-12 relative error 4.981653302087832e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3099999999999665 y[1] (closed_form) 68.97325196896824 y[1] (numeric) 68.97325196897175 absolute error 3.510081114654895e-12 relative error 5.089046861577754e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3199999999999654 y[1] (closed_form) 70.36656783591675 y[1] (numeric) 70.36656783592042 absolute error 3.666400516522117e-12 relative error 5.21042965328586e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3299999999999643 y[1] (closed_form) 71.78803126823304 y[1] (numeric) 71.78803126823686 absolute error 3.822719918389339e-12 relative error 5.325010103851299e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3399999999999632 y[1] (closed_form) 73.23821087024312 y[1] (numeric) 73.2382108702471 absolute error 3.979039320256561e-12 relative error 5.433009999802242e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3499999999999621 y[1] (closed_form) 74.7176867331238 y[1] (numeric) 74.71768673312795 absolute error 4.149569576838985e-12 relative error 5.553664411025456e-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) 76.22705066694682 y[1] (numeric) 76.22705066695113 absolute error 4.305888978706207e-12 relative error 5.648767650108368e-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) 77.76690643741085 y[1] (numeric) 77.76690643741532 absolute error 4.462208380573429e-12 relative error 5.737927075914674e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3799999999999588 y[1] (closed_form) 79.33787000735575 y[1] (numeric) 79.33787000736037 absolute error 4.618527782440651e-12 relative error 5.8213407821667614e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3899999999999577 y[1] (closed_form) 80.94056978315594 y[1] (numeric) 80.94056978316075 absolute error 4.817479748453479e-12 relative error 5.9518727893314346e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3999999999999566 y[1] (closed_form) 82.57564686609138 y[1] (numeric) 82.57564686609638 absolute error 5.002220859751105e-12 relative error 6.0577434747352885e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4099999999999555 y[1] (closed_form) 84.24375530879655 y[1] (numeric) 84.24375530880174 absolute error 5.186961971048731e-12 relative error 6.157087788923768e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4199999999999544 y[1] (closed_form) 85.94556237689028 y[1] (numeric) 85.94556237689568 absolute error 5.4001247917767614e-12 relative error 6.283192107227155e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4299999999999533 y[1] (closed_form) 87.68174881589088 y[1] (numeric) 87.68174881589647 absolute error 5.5848659030743875e-12 relative error 6.369473668689215e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4399999999999522 y[1] (closed_form) 89.4530091235234 y[1] (numeric) 89.45300912352917 absolute error 5.7696070143720135e-12 relative error 6.449874711766162e-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) 91.260051827528 y[1] (numeric) 91.26005182753399 absolute error 5.9827698351000436e-12 relative error 6.555737932745048e-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) 93.10359976908052 y[1] (numeric) 93.10359976908671 absolute error 6.195932655828074e-12 relative error 6.654879801850291e-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) 94.98439039193856 y[1] (numeric) 94.98439039194496 absolute error 6.394884621840902e-12 relative error 6.732563735423671e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4799999999999478 y[1] (closed_form) 96.90317603742878 y[1] (numeric) 96.90317603743539 absolute error 6.608047442568932e-12 relative error 6.819226895119081e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4899999999999467 y[1] (closed_form) 98.86072424539354 y[1] (numeric) 98.86072424540038 absolute error 6.835421118012164e-12 relative error 6.914192840672684e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4999999999999456 y[1] (closed_form) 100.85781806121702 y[1] (numeric) 100.85781806122407 absolute error 7.048583938740194e-12 relative error 6.988634172575457e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5099999999999445 y[1] (closed_form) 102.89525634905381 y[1] (numeric) 102.89525634906109 absolute error 7.275957614183426e-12 relative error 7.071227452411448e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5199999999999434 y[1] (closed_form) 104.97385411138525 y[1] (numeric) 104.97385411139275 absolute error 7.503331289626658e-12 relative error 7.147809664742854e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5299999999999423 y[1] (closed_form) 107.0944428150313 y[1] (numeric) 107.09444281503902 absolute error 7.716494110354688e-12 relative error 7.205317015078242e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5399999999999412 y[1] (closed_form) 109.2578707237483 y[1] (numeric) 109.25787072375624 absolute error 7.94386778579792e-12 relative error 7.270751052693946e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.54999999999994 y[1] (closed_form) 111.4650032375458 y[1] (numeric) 111.465003237554 absolute error 8.199663170671556e-12 relative error 7.356266929088992e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.559999999999939 y[1] (closed_form) 113.71672323885818 y[1] (numeric) 113.71672323886665 absolute error 8.469669410260394e-12 relative error 7.448042090054016e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.569999999999938 y[1] (closed_form) 116.01393144570929 y[1] (numeric) 116.01393144571804 absolute error 8.753886504564434e-12 relative error 7.545547673005949e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5799999999999368 y[1] (closed_form) 118.3575467720117 y[1] (numeric) 118.35754677202073 absolute error 9.023892744153272e-12 relative error 7.624264772516538e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5899999999999357 y[1] (closed_form) 120.74850669514458 y[1] (numeric) 120.74850669515386 absolute error 9.279688129026908e-12 relative error 7.6851369702281e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5999999999999346 y[1] (closed_form) 123.18776763095708 y[1] (numeric) 123.1877676309666 absolute error 9.521272659185342e-12 relative error 7.72907313955793e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6099999999999335 y[1] (closed_form) 125.6763053163474 y[1] (numeric) 125.6763053163572 absolute error 9.805489753489383e-12 relative error 7.802178564055806e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6199999999999324 y[1] (closed_form) 128.21511519957068 y[1] (numeric) 128.21511519958074 absolute error 1.0061285138363019e-11 relative error 7.847191123060902e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6299999999999313 y[1] (closed_form) 130.8052128384314 y[1] (numeric) 130.80521283844175 absolute error 1.0345502232667059e-11 relative error 7.909090171693437e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6399999999999302 y[1] (closed_form) 133.44763430652029 y[1] (numeric) 133.4476343065309 absolute error 1.0601297617540695e-11 relative error 7.944163021421738e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.649999999999929 y[1] (closed_form) 136.14343660765726 y[1] (numeric) 136.14343660766815 absolute error 1.0885514711844735e-11 relative error 7.995622104953159e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.659999999999928 y[1] (closed_form) 138.89369809870735 y[1] (numeric) 138.89369809871852 absolute error 1.1169731806148775e-11 relative error 8.041928438114449e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6699999999999269 y[1] (closed_form) 141.6995189209375 y[1] (numeric) 141.69951892094898 absolute error 1.1482370609883219e-11 relative error 8.103323636751307e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6799999999999258 y[1] (closed_form) 144.5620214400882 y[1] (numeric) 144.56202144009993 absolute error 1.1738165994756855e-11 relative error 8.119813127835641e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6899999999999247 y[1] (closed_form) 147.4823506953342 y[1] (numeric) 147.48235069534624 absolute error 1.2050804798491299e-11 relative error 8.171014864948543e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6999999999999236 y[1] (closed_form) 150.4616748573159 y[1] (numeric) 150.4616748573283 absolute error 1.2391865311656147e-11 relative error 8.235894837278304e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7099999999999225 y[1] (closed_form) 153.5011856954229 y[1] (numeric) 153.50118569543562 absolute error 1.2732925824820995e-11 relative error 8.2950016100108e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7199999999999214 y[1] (closed_form) 156.60209905451782 y[1] (numeric) 156.6020990545309 absolute error 1.3073986337985843e-11 relative error 8.348538376509502e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7299999999999203 y[1] (closed_form) 159.76565534129037 y[1] (numeric) 159.7656553413038 absolute error 1.3443468560581096e-11 relative error 8.414492170963305e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7399999999999192 y[1] (closed_form) 162.9931200204366 y[1] (numeric) 162.99312002045042 absolute error 1.3812950783176348e-11 relative error 8.474560632647829e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.749999999999918 y[1] (closed_form) 166.28578412086154 y[1] (numeric) 166.28578412087572 absolute error 1.41824330057716e-11 relative error 8.528950974824991e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.759999999999917 y[1] (closed_form) 169.64496475210814 y[1] (numeric) 169.64496475212266 absolute error 1.4523493518936448e-11 relative error 8.561110870669662e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7699999999999159 y[1] (closed_form) 173.07200563121862 y[1] (numeric) 173.0720056312335 absolute error 1.48929757415317e-11 relative error 8.605074915041785e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7799999999999148 y[1] (closed_form) 176.56827762023906 y[1] (numeric) 176.5682776202543 absolute error 1.5234036254696548e-11 relative error 8.62784440105472e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7899999999999137 y[1] (closed_form) 180.1351792745827 y[1] (numeric) 180.13517927459833 absolute error 1.5631940186722204e-11 relative error 8.677894151310783e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7999999999999126 y[1] (closed_form) 183.77413740247056 y[1] (numeric) 183.77413740248656 absolute error 1.6001422409317456e-11 relative error 8.707113326982396e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8099999999999115 y[1] (closed_form) 187.48660763567386 y[1] (numeric) 187.4866076356903 absolute error 1.6427748050773516e-11 relative error 8.76209146772558e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8199999999999104 y[1] (closed_form) 191.27407501178624 y[1] (numeric) 191.27407501180306 absolute error 1.6825651982799172e-11 relative error 8.79661918729048e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8299999999999093 y[1] (closed_form) 195.1380545682583 y[1] (numeric) 195.13805456827558 absolute error 1.7280399333685637e-11 relative error 8.85547381924987e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8399999999999082 y[1] (closed_form) 199.08009194843305 y[1] (numeric) 199.0800919484508 absolute error 1.77351466845721e-11 relative error 8.908548570072977e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.849999999999907 y[1] (closed_form) 203.10176401982378 y[1] (numeric) 203.10176401984197 absolute error 1.8189894035458565e-11 relative error 8.95604926094248e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.859999999999906 y[1] (closed_form) 207.20467950488205 y[1] (numeric) 207.20467950490067 absolute error 1.8616219676914625e-11 relative error 8.984459096868997e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8699999999999048 y[1] (closed_form) 211.39047962450815 y[1] (numeric) 211.39047962452725 absolute error 1.9099388737231493e-11 relative error 9.03512247626177e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8799999999999037 y[1] (closed_form) 215.66083875456135 y[1] (numeric) 215.66083875458088 absolute error 1.9525714378687553e-11 relative error 9.053898932902381e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8899999999999026 y[1] (closed_form) 220.01746509563253 y[1] (numeric) 220.01746509565257 absolute error 2.0037305148434825e-11 relative error 9.107142989637406e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8999999999999015 y[1] (closed_form) 224.4621013563473 y[1] (numeric) 224.4621013563678 absolute error 2.0520474208751693e-11 relative error 9.142066337592637e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9099999999999004 y[1] (closed_form) 228.9965254504725 y[1] (numeric) 228.9965254504935 absolute error 2.100364326906856e-11 relative error 9.172035788643981e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9199999999998993 y[1] (closed_form) 233.62255120810556 y[1] (numeric) 233.62255120812705 absolute error 2.148681232938543e-11 relative error 9.197233836491014e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9299999999998982 y[1] (closed_form) 238.34202910123074 y[1] (numeric) 238.34202910125276 absolute error 2.2026824808563106e-11 relative error 9.241687205410036e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9399999999998971 y[1] (closed_form) 243.15684698393247 y[1] (numeric) 243.156846983955 absolute error 2.2538415578310378e-11 relative error 9.26908530764083e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.949999999999896 y[1] (closed_form) 248.06893084756226 y[1] (numeric) 248.0689308475854 absolute error 2.3135271476348862e-11 relative error 9.326146324452629e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.959999999999895 y[1] (closed_form) 253.08024559116092 y[1] (numeric) 253.0802455911846 absolute error 2.3675283955526538e-11 relative error 9.354852608201128e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9699999999998938 y[1] (closed_form) 258.1927958074443 y[1] (numeric) 258.1927958074685 absolute error 2.4158453015843406e-11 relative error 9.356749455496179e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9799999999998927 y[1] (closed_form) 263.4086265846671 y[1] (numeric) 263.40862658469194 absolute error 2.4840574042173102e-11 relative error 9.430432998438124e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9899999999998916 y[1] (closed_form) 268.72982432468564 y[1] (numeric) 268.72982432471093 absolute error 2.5295321393059567e-11 relative error 9.412919260683611e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9999999999998905 y[1] (closed_form) 274.15851757754615 y[1] (numeric) 274.158517577572 absolute error 2.5863755581667647e-11 relative error 9.433869066042073e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Finished! diff ( y , x , 1 ) = sinh ( 2.0 * x + 3.0 ) ; Iterations 1901 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.10526315788897%