##############ECHO OF PROBLEM################# ##############temp/lin_tanhpostode.ode################# diff ( y , x , 1 ) = tanh ( 3.0 * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(1.1) x_end=c(2.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # 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(ln(cosh(c(3.0)*c(x) + c(1.0)))/c(3.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 1.1 y[1] (closed_form) 1.2023456360961104 y[1] (numeric) 1.2023456360961104 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] 1.109999999999999 y[1] (closed_form) 1.2123420629058776 y[1] (numeric) 1.2123420629058794 absolute error 1.7763568394002505e-15 relative error 1.4652274252882712e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1199999999999979 y[1] (closed_form) 1.2223386977670228 y[1] (numeric) 1.2223386977670252 absolute error 2.4424906541753444e-15 relative error 1.9982110184659164e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1299999999999968 y[1] (closed_form) 1.2323355285675353 y[1] (numeric) 1.232335528567539 absolute error 3.774758283725532e-15 relative error 3.0630929614707327e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1399999999999957 y[1] (closed_form) 1.2423325439003077 y[1] (numeric) 1.2423325439003126 absolute error 4.884981308350689e-15 relative error 3.9321044372018717e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1499999999999946 y[1] (closed_form) 1.252329733022132 y[1] (numeric) 1.2523297330221383 absolute error 6.439293542825908e-15 relative error 5.141851521233593e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1599999999999935 y[1] (closed_form) 1.2623270858150855 y[1] (numeric) 1.2623270858150926 absolute error 7.105427357601002e-15 relative error 5.628832207947929e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1699999999999924 y[1] (closed_form) 1.2723245927501527 y[1] (numeric) 1.2723245927501614 absolute error 8.659739592076221e-15 relative error 6.806234542207532e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1799999999999913 y[1] (closed_form) 1.2823222448529707 y[1] (numeric) 1.28232224485298 absolute error 9.325873406851315e-15 relative error 7.272644176831391e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.1899999999999902 y[1] (closed_form) 1.2923200336715541 y[1] (numeric) 1.2923200336715652 absolute error 1.1102230246251565e-14 relative error 8.590929457859988e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.199999999999989 y[1] (closed_form) 1.3023179512459075 y[1] (numeric) 1.3023179512459195 absolute error 1.199040866595169e-14 relative error 9.20697488234778e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.209999999999988 y[1] (closed_form) 1.3123159900793941 y[1] (numeric) 1.3123159900794068 absolute error 1.2656542480726785e-14 relative error 9.644432115744527e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2199999999999869 y[1] (closed_form) 1.3223141431117773 y[1] (numeric) 1.3223141431117909 absolute error 1.354472090042691e-14 relative error 1.0243194456464308e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2299999999999858 y[1] (closed_form) 1.3323124036938234 y[1] (numeric) 1.3323124036938385 absolute error 1.509903313490213e-14 relative error 1.1332952461479908e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2399999999999847 y[1] (closed_form) 1.3423107655633864 y[1] (numeric) 1.3423107655634023 absolute error 1.5987211554602254e-14 relative error 1.191021629621826e-12% Desired digits 8 Estimated correct digits 13 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2499999999999836 y[1] (closed_form) 1.3523092228228781 y[1] (numeric) 1.3523092228228952 absolute error 1.709743457922741e-14 relative error 1.2643139816452164e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2599999999999825 y[1] (closed_form) 1.3623077699180548 y[1] (numeric) 1.3623077699180726 absolute error 1.7763568394002505e-14 relative error 1.3039321059639125e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2699999999999814 y[1] (closed_form) 1.3723064016180304 y[1] (numeric) 1.3723064016180495 absolute error 1.9095836023552692e-14 relative error 1.391514023474464e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2799999999999803 y[1] (closed_form) 1.382305112996461 y[1] (numeric) 1.382305112996481 absolute error 1.9984014443252818e-14 relative error 1.4457021286662913e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.2899999999999792 y[1] (closed_form) 1.3923038994138144 y[1] (numeric) 1.3923038994138355 absolute error 2.1094237467877974e-14 relative error 1.5150598570297071e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.299999999999978 y[1] (closed_form) 1.4023027565006796 y[1] (numeric) 1.4023027565007022 absolute error 2.2648549702353193e-14 relative error 1.61509699651954e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.309999999999977 y[1] (closed_form) 1.4123016801420405 y[1] (numeric) 1.4123016801420643 absolute error 2.375877272697835e-14 relative error 1.6822732041633514e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3199999999999759 y[1] (closed_form) 1.4223006664624716 y[1] (numeric) 1.4223006664624962 absolute error 2.4646951146678475e-14 relative error 1.7328931728605643e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3299999999999748 y[1] (closed_form) 1.4322997118121856 y[1] (numeric) 1.432299711812212 absolute error 2.6423307986078726e-14 relative error 1.844816958920366e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3399999999999737 y[1] (closed_form) 1.4422988127539051 y[1] (numeric) 1.4422988127539322 absolute error 2.708944180085382e-14 relative error 1.878212861392406e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3499999999999726 y[1] (closed_form) 1.4522979660504853 y[1] (numeric) 1.452297966050514 absolute error 2.864375403532904e-14 relative error 1.9723055946449846e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3599999999999715 y[1] (closed_form) 1.4622971686532678 y[1] (numeric) 1.4622971686532975 absolute error 2.9753977059954195e-14 relative error 2.0347421644368445e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3699999999999704 y[1] (closed_form) 1.4722964176911042 y[1] (numeric) 1.4722964176911357 absolute error 3.1530333899354446e-14 relative error 2.1415751285193767e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3799999999999693 y[1] (closed_form) 1.4822957104600265 y[1] (numeric) 1.4822957104600585 absolute error 3.197442310920451e-14 relative error 2.157088014461118e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.3899999999999681 y[1] (closed_form) 1.4922950444135077 y[1] (numeric) 1.492295044413541 absolute error 3.3306690738754696e-14 relative error 2.231910563761517e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.399999999999967 y[1] (closed_form) 1.5022944171533021 y[1] (numeric) 1.5022944171533363 absolute error 3.419486915845482e-14 relative error 2.2761762786318996e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.409999999999966 y[1] (closed_form) 1.5122938264208072 y[1] (numeric) 1.5122938264208428 absolute error 3.552713678800501e-14 relative error 2.3492218355534908e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4199999999999648 y[1] (closed_form) 1.5222932700889382 y[1] (numeric) 1.5222932700889744 absolute error 3.6193270602780103e-14 relative error 2.3775491433832296e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4299999999999637 y[1] (closed_form) 1.5322927461544653 y[1] (numeric) 1.5322927461545028 absolute error 3.752553823233029e-14 relative error 2.4489796957211116e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4399999999999626 y[1] (closed_form) 1.5422922527308083 y[1] (numeric) 1.5422922527308467 absolute error 3.8413716652030416e-14 relative error 2.4906898536262795e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4499999999999615 y[1] (closed_form) 1.5522917880412397 y[1] (numeric) 1.5522917880412794 absolute error 3.9745984281580604e-14 relative error 2.5604712070102553e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4599999999999604 y[1] (closed_form) 1.562291350412493 y[1] (numeric) 1.5622913504125335 absolute error 4.063416270128073e-14 relative error 2.6009337304819655e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4699999999999593 y[1] (closed_form) 1.5722909382687345 y[1] (numeric) 1.5722909382687762 absolute error 4.1744385725905886e-14 relative error 2.655003899715345e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4799999999999582 y[1] (closed_form) 1.5822905501258946 y[1] (numeric) 1.582290550125937 absolute error 4.241051954068098e-14 relative error 2.680324390315457e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.4899999999999571 y[1] (closed_form) 1.59229018458632 y[1] (numeric) 1.592290184586364 absolute error 4.39648317751562e-14 relative error 2.761106750562451e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.499999999999956 y[1] (closed_form) 1.6022898403337473 y[1] (numeric) 1.6022898403337917 absolute error 4.440892098500626e-14 relative error 2.771590998527217e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.509999999999955 y[1] (closed_form) 1.612289516128558 y[1] (numeric) 1.6122895161286037 absolute error 4.574118861455645e-14 relative error 2.8370331852303144e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5199999999999538 y[1] (closed_form) 1.622289210803321 y[1] (numeric) 1.622289210803368 absolute error 4.707345624410664e-14 relative error 2.9016685761472164e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5299999999999527 y[1] (closed_form) 1.6322889232585853 y[1] (numeric) 1.6322889232586337 absolute error 4.8405723873656825e-14 relative error 2.9655119987595755e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5399999999999516 y[1] (closed_form) 1.642288652458925 y[1] (numeric) 1.6422886524589746 absolute error 4.951594689828198e-14 relative error 3.015057482382526e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5499999999999505 y[1] (closed_form) 1.652288397429208 y[1] (numeric) 1.6522883974292586 absolute error 5.062616992290714e-14 relative error 3.0640032334352944e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5599999999999494 y[1] (closed_form) 1.6622881572510873 y[1] (numeric) 1.6622881572511385 absolute error 5.129230373768223e-14 relative error 3.0856445384598005e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5699999999999483 y[1] (closed_form) 1.6722879310596923 y[1] (numeric) 1.6722879310597454 absolute error 5.306866057708248e-14 relative error 3.1734164668314045e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5799999999999472 y[1] (closed_form) 1.6822877180405191 y[1] (numeric) 1.682287718040573 absolute error 5.395683899678261e-14 relative error 3.2073490413179736e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.5899999999999461 y[1] (closed_form) 1.692287517426492 y[1] (numeric) 1.6922875174265473 absolute error 5.5289106626332796e-14 relative error 3.2671225224430217e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.599999999999945 y[1] (closed_form) 1.702287328495206 y[1] (numeric) 1.7022873284952627 absolute error 5.6621374255882984e-14 relative error 3.326193722298065e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.609999999999944 y[1] (closed_form) 1.712287150566323 y[1] (numeric) 1.7122871505663813 absolute error 5.81756864903582e-14 relative error 3.3975426651491913e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6199999999999428 y[1] (closed_form) 1.7222869829991254 y[1] (numeric) 1.7222869829991845 absolute error 5.906386491005833e-14 relative error 3.429385781410642e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6299999999999417 y[1] (closed_form) 1.7322868251902042 y[1] (numeric) 1.7322868251902643 absolute error 6.017408793468348e-14 relative error 3.473679246395954e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6399999999999406 y[1] (closed_form) 1.7422866765712912 y[1] (numeric) 1.7422866765713523 absolute error 6.106226635438361e-14 relative error 3.5047198130763558e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6499999999999395 y[1] (closed_form) 1.7522865366072085 y[1] (numeric) 1.7522865366072709 absolute error 6.23945339839338e-14 relative error 3.5607494939008438e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6599999999999384 y[1] (closed_form) 1.7622864047939464 y[1] (numeric) 1.762286404794009 absolute error 6.261657858885883e-14 relative error 3.5531442799832648e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6699999999999373 y[1] (closed_form) 1.7722862806568427 y[1] (numeric) 1.7722862806569069 absolute error 6.417089082333405e-14 relative error 3.6207971321400236e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.6799999999999362 y[1] (closed_form) 1.7822861637488794 y[1] (numeric) 1.7822861637489444 absolute error 6.505906924303417e-14 relative error 3.650315564712024e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.689999999999935 y[1] (closed_form) 1.792286053649068 y[1] (numeric) 1.792286053649134 absolute error 6.616929226765933e-14 relative error 3.691893497298583e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.699999999999934 y[1] (closed_form) 1.8022859499609372 y[1] (numeric) 1.8022859499610047 absolute error 6.750155989720952e-14 relative error 3.745330195725742e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.709999999999933 y[1] (closed_form) 1.8122858523111034 y[1] (numeric) 1.812285852311172 absolute error 6.861178292183467e-14 relative error 3.785924987183343e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7199999999999318 y[1] (closed_form) 1.822285760347927 y[1] (numeric) 1.8222857603479967 absolute error 6.972200594645983e-14 relative error 3.826074233996532e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7299999999999307 y[1] (closed_form) 1.8322856737402458 y[1] (numeric) 1.8322856737403168 absolute error 7.105427357601002e-14 relative error 3.877903680323325e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7399999999999296 y[1] (closed_form) 1.8422855921761832 y[1] (numeric) 1.8422855921762549 absolute error 7.172040739078511e-14 relative error 3.8930124458101e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7499999999999285 y[1] (closed_form) 1.8522855153620226 y[1] (numeric) 1.8522855153620956 absolute error 7.30526750203353e-14 relative error 3.943920870431113e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7599999999999274 y[1] (closed_form) 1.862285443021155 y[1] (numeric) 1.862285443021229 absolute error 7.394085344003543e-14 relative error 3.970436095987648e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7699999999999263 y[1] (closed_form) 1.8722853748930766 y[1] (numeric) 1.872285374893152 absolute error 7.549516567451064e-14 relative error 4.0322467230094166e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.7799999999999252 y[1] (closed_form) 1.8822853107324562 y[1] (numeric) 1.8822853107325328 absolute error 7.66053886991358e-14 relative error 4.0698074974258945e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.789999999999924 y[1] (closed_form) 1.892285250308248 y[1] (numeric) 1.8922852503083258 absolute error 7.793765632868599e-14 relative error 4.118705481427294e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.799999999999923 y[1] (closed_form) 1.9022851934028617 y[1] (numeric) 1.9022851934029406 absolute error 7.882583474838611e-14 relative error 4.143744325075686e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.809999999999922 y[1] (closed_form) 1.912285139811378 y[1] (numeric) 1.9122851398114584 absolute error 8.038014698286133e-14 relative error 4.203355729197884e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8199999999999208 y[1] (closed_form) 1.9222850893408117 y[1] (numeric) 1.9222850893408934 absolute error 8.171241461241152e-14 relative error 4.250795840092183e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8299999999999197 y[1] (closed_form) 1.9322850418094148 y[1] (numeric) 1.9322850418094977 absolute error 8.282263763703668e-14 relative error 4.2862536243348736e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8399999999999186 y[1] (closed_form) 1.9422849970460252 y[1] (numeric) 1.942284997046109 absolute error 8.37108160567368e-14 relative error 4.309914156987804e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8499999999999175 y[1] (closed_form) 1.9522849548894465 y[1] (numeric) 1.9522849548895318 absolute error 8.526512829121202e-14 relative error 4.367453023579767e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8599999999999164 y[1] (closed_form) 1.9622849151878714 y[1] (numeric) 1.9622849151879573 absolute error 8.593126210598712e-14 relative error 4.379142979742061e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8699999999999153 y[1] (closed_form) 1.9722848777983313 y[1] (numeric) 1.9722848777984185 absolute error 8.72635297355373e-14 relative error 4.424489115028347e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.8799999999999142 y[1] (closed_form) 1.9822848425861848 y[1] (numeric) 1.9822848425862731 absolute error 8.837375276016246e-14 relative error 4.4581762853448336e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.889999999999913 y[1] (closed_form) 1.9922848094246302 y[1] (numeric) 1.99228480942472 absolute error 8.992806499463768e-14 relative error 4.5138157239982574e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.899999999999912 y[1] (closed_form) 2.002284778194252 y[1] (numeric) 2.0022847781943423 absolute error 9.015010959956271e-14 relative error 4.502362030682969e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9099999999999109 y[1] (closed_form) 2.012284748782586 y[1] (numeric) 2.0122847487826774 absolute error 9.14823772291129e-14 relative error 4.546194433191372e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9199999999999098 y[1] (closed_form) 2.02228472108372 y[1] (numeric) 2.0222847210838117 absolute error 9.192646643896296e-14 relative error 4.545673785721953e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9299999999999087 y[1] (closed_form) 2.0322846949979074 y[1] (numeric) 2.0322846949980007 absolute error 9.325873406851315e-14 relative error 4.588861703188154e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9399999999999076 y[1] (closed_form) 2.042284670431213 y[1] (numeric) 2.042284670431308 absolute error 9.459100169806334e-14 relative error 4.6316266810195054e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9499999999999065 y[1] (closed_form) 2.0522846472951697 y[1] (numeric) 2.052284647295266 absolute error 9.636735853746359e-14 relative error 4.6956136744711304e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9599999999999054 y[1] (closed_form) 2.0622846255064635 y[1] (numeric) 2.0622846255065603 absolute error 9.681144774731365e-14 relative error 4.694378581401601e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9699999999999043 y[1] (closed_form) 2.072284604986631 y[1] (numeric) 2.0722846049867285 absolute error 9.769962616701378e-14 relative error 4.714585338901558e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.9799999999999032 y[1] (closed_form) 2.0822845856617795 y[1] (numeric) 2.082284585661878 absolute error 9.85878045867139e-14 relative error 4.734598011509618e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.989999999999902 y[1] (closed_form) 2.092284567462318 y[1] (numeric) 2.0922845674624178 absolute error 9.992007221626409e-14 relative error 4.775644468737575e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 TOP MAIN SOLVE Loop x[1] 1.999999999999901 y[1] (closed_form) 2.1022845503227106 y[1] (numeric) 2.102284550322811 absolute error 1.0036416142611415e-13 relative error 4.774052181028861e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Finished! diff ( y , x , 1 ) = tanh ( 3.0 * x + 1.0 ) ; Iterations 901 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.2222222222112%