##############ECHO OF PROBLEM################# ##############temp/lin_coshpostode.ode################# diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=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=c(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(sinh(c(2.0)*c(x)+c(3.0))/c(2)) 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) 6.122941998282746 y[1] (numeric) 6.122941998282746 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) 6.247041280769291 y[1] (numeric) 6.247041280769288 absolute error 2.6645352591003757e-15 relative error 4.265275575019495e-14% 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) 6.373639463063135 y[1] (numeric) 6.373639463063134 absolute error 8.881784197001252e-16 relative error 1.3935184518160237e-14% 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) 6.5027871861251985 y[1] (numeric) 6.5027871861251985 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] 0.14000000000000004 y[1] (closed_form) 6.634536110766698 y[1] (numeric) 6.634536110766697 absolute error 8.881784197001252e-16 relative error 1.3387197007772197e-14% 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) 6.768938938314164 y[1] (numeric) 6.768938938314164 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] 0.16000000000000006 y[1] (closed_form) 6.906049431690679 y[1] (numeric) 6.906049431690678 absolute error 8.881784197001252e-16 relative error 1.2860875504661557e-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) 7.045922436921756 y[1] (numeric) 7.045922436921756 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) 7.1886139050744875 y[1] (numeric) 7.1886139050744875 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) 7.334180914638712 y[1] (numeric) 7.334180914638713 absolute error 8.881784197001252e-16 relative error 1.2110124225697229e-14% 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) 7.482681694359175 y[1] (numeric) 7.482681694359177 absolute error 1.7763568394002505e-15 relative error 2.3739575087623444e-14% 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) 7.634175646527801 y[1] (numeric) 7.634175646527801 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] 0.2200000000000001 y[1] (closed_form) 7.788723370745403 y[1] (numeric) 7.788723370745403 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] 0.23000000000000012 y[1] (closed_form) 7.946386688162335 y[1] (numeric) 7.946386688162333 absolute error 1.7763568394002505e-15 relative error 2.2354271307315995e-14% 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) 8.107228666207765 y[1] (numeric) 8.107228666207762 absolute error 3.552713678800501e-15 relative error 4.3821555121650676e-14% 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) 8.271313643817498 y[1] (numeric) 8.2713136438175 absolute error 1.7763568394002505e-15 relative error 2.1476115111751465e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (closed_form) 8.438707257170421 y[1] (numeric) 8.438707257170417 absolute error 3.552713678800501e-15 relative error 4.21002123966528e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (closed_form) 8.609476465943798 y[1] (numeric) 8.609476465943798 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] 0.28000000000000014 y[1] (closed_form) 8.78368958009811 y[1] (numeric) 8.783689580098109 absolute error 1.7763568394002505e-15 relative error 2.0223356292384018e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (closed_form) 8.96141628720188 y[1] (numeric) 8.96141628720188 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] 0.30000000000000016 y[1] (closed_form) 9.14272768030768 y[1] (numeric) 9.142727680307676 absolute error 3.552713678800501e-15 relative error 3.8858356094895105e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (closed_form) 9.327696286390255 y[1] (numeric) 9.327696286390259 absolute error 3.552713678800501e-15 relative error 3.808779327414586e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (closed_form) 9.516396095358337 y[1] (numeric) 9.516396095358337 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] 0.3300000000000002 y[1] (closed_form) 9.708902589651528 y[1] (numeric) 9.708902589651531 absolute error 3.552713678800501e-15 relative error 3.659233003931101e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (closed_form) 9.905292774434347 y[1] (numeric) 9.905292774434347 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] 0.3500000000000002 y[1] (closed_form) 10.105645208399265 y[1] (numeric) 10.105645208399265 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] 0.3600000000000002 y[1] (closed_form) 10.310040035191284 y[1] (numeric) 10.31004003519128 absolute error 3.552713678800501e-15 relative error 3.445877675231149e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (closed_form) 10.518559015466401 y[1] (numeric) 10.518559015466403 absolute error 1.7763568394002505e-15 relative error 1.6887834510300415e-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) 10.731285559597039 y[1] (numeric) 10.731285559597035 absolute error 3.552713678800501e-15 relative error 3.3106133082287544e-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) 10.948304761037223 y[1] (numeric) 10.948304761037221 absolute error 1.7763568394002505e-15 relative error 1.6224948776745246e-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) 11.169703430361173 y[1] (numeric) 11.169703430361164 absolute error 8.881784197001252e-15 relative error 7.951674144596388e-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) 11.395570129988622 y[1] (numeric) 11.39557012998862 absolute error 1.7763568394002505e-15 relative error 1.55881348553644e-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) 11.625995209611037 y[1] (numeric) 11.625995209611032 absolute error 5.329070518200751e-15 relative error 4.5837542697379474e-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) 11.861070842332627 y[1] (numeric) 11.861070842332623 absolute error 3.552713678800501e-15 relative error 2.995272286985022e-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) 12.100891061540876 y[1] (numeric) 12.100891061540871 absolute error 5.329070518200751e-15 relative error 4.403866203818358e-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) 12.345551798521099 y[1] (numeric) 12.345551798521095 absolute error 3.552713678800501e-15 relative error 2.8777277328552365e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (closed_form) 12.595150920830289 y[1] (numeric) 12.59515092083028 absolute error 8.881784197001252e-15 relative error 7.051748925304464e-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) 12.849788271445387 y[1] (numeric) 12.849788271445382 absolute error 5.329070518200751e-15 relative error 4.1472049232460385e-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) 13.10956570870187 y[1] (numeric) 13.109565708701858 absolute error 1.2434497875801753e-14 relative error 9.485057058410393e-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) 13.374587147038362 y[1] (numeric) 13.374587147038357 absolute error 5.329070518200751e-15 relative error 3.984474780128678e-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) 13.644958598563887 y[1] (numeric) 13.644958598563875 absolute error 1.2434497875801753e-14 relative error 9.112887947575354e-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) 13.920788215464034 y[1] (numeric) 13.920788215464025 absolute error 8.881784197001252e-15 relative error 6.38023081705592e-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) 14.202186333263363 y[1] (numeric) 14.202186333263345 absolute error 1.7763568394002505e-14 relative error 1.2507629443220248e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (closed_form) 14.489265514960993 y[1] (numeric) 14.48926551496098 absolute error 1.2434497875801753e-14 relative error 8.58186901396929e-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) 14.782140596057403 y[1] (numeric) 14.782140596057387 absolute error 1.5987211554602254e-14 relative error 1.0815220874618294e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (closed_form) 15.08092873049006 y[1] (numeric) 15.080928730490049 absolute error 1.0658141036401503e-14 relative error 7.067297529795543e-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) 15.385749437496656 y[1] (numeric) 15.385749437496635 absolute error 2.1316282072803006e-14 relative error 1.3854562079928996e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (closed_form) 15.696724649424299 y[1] (numeric) 15.696724649424285 absolute error 1.4210854715202004e-14 relative error 9.053388546076846e-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) 16.013978760504177 y[1] (numeric) 16.01397876050416 absolute error 1.7763568394002505e-14 relative error 1.109253899962288e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (closed_form) 16.33763867661081 y[1] (numeric) 16.337638676610798 absolute error 1.0658141036401503e-14 relative error 6.523672880377656e-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) 16.667833866026182 y[1] (numeric) 16.667833866026168 absolute error 1.4210854715202004e-14 relative error 8.525915742517566e-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) 17.004696411228704 y[1] (numeric) 17.004696411228693 absolute error 1.0658141036401503e-14 relative error 6.267763198267755e-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) 17.34836106172804 y[1] (numeric) 17.348361061728024 absolute error 1.4210854715202004e-14 relative error 8.191468153468606e-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) 17.698965287966615 y[1] (numeric) 17.698965287966608 absolute error 7.105427357601002e-15 relative error 4.014600425501668e-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) 18.056649336309743 y[1] (numeric) 18.056649336309725 absolute error 1.7763568394002505e-14 relative error 9.837688079970691e-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) 18.42155628514591 y[1] (numeric) 18.421556285145904 absolute error 7.105427357601002e-15 relative error 3.8571265356827706e-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) 18.79383210212018 y[1] (numeric) 18.79383210212016 absolute error 2.1316282072803006e-14 relative error 1.1342169046193757e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (closed_form) 19.173625702523054 y[1] (numeric) 19.173625702523037 absolute error 1.7763568394002505e-14 relative error 9.264584940585858e-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) 19.561089008858705 y[1] (numeric) 19.56108900885868 absolute error 2.4868995751603507e-14 relative error 1.27135026788851e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (closed_form) 19.956377011615874 y[1] (numeric) 19.956377011615864 absolute error 1.0658141036401503e-14 relative error 5.34071942527333e-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) 20.35964783126629 y[1] (numeric) 20.359647831266265 absolute error 2.4868995751603507e-14 relative error 1.221484573687577e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (closed_form) 20.77106278151478 y[1] (numeric) 20.771062781514765 absolute error 1.4210854715202004e-14 relative error 6.841659892265582e-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) 21.19078643382709 y[1] (numeric) 21.190786433827064 absolute error 2.4868995751603507e-14 relative error 1.1735758759714953e-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) 21.6189866832605 y[1] (numeric) 21.618986683260484 absolute error 1.4210854715202004e-14 relative error 6.573321369500365e-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) 22.05583481562423 y[1] (numeric) 22.055834815624205 absolute error 2.4868995751603507e-14 relative error 1.1275472435977099e-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) 22.501505575995914 y[1] (numeric) 22.501505575995893 absolute error 2.1316282072803006e-14 relative error 9.473269244500121e-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) 22.956177238622086 y[1] (numeric) 22.956177238622054 absolute error 3.197442310920451e-14 relative error 1.3928461510311868e-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) 23.420031678230135 y[1] (numeric) 23.42003167823011 absolute error 2.4868995751603507e-14 relative error 1.0618685787141886e-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) 23.893254442780744 y[1] (numeric) 23.893254442780716 absolute error 2.842170943040401e-14 relative error 1.1895285968040875e-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) 24.376034827689423 y[1] (numeric) 24.37603482768941 absolute error 1.4210854715202004e-14 relative error 5.829846739084691e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (closed_form) 24.86856595154733 y[1] (numeric) 24.868565951547303 absolute error 2.4868995751603507e-14 relative error 1.0000172828645213e-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) 25.371044833371133 y[1] (numeric) 25.371044833371116 absolute error 1.7763568394002505e-14 relative error 7.001512358149974e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (closed_form) 25.883672471413416 y[1] (numeric) 25.883672471413384 absolute error 3.197442310920451e-14 relative error 1.235312459795567e-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) 26.406653923564473 y[1] (numeric) 26.40665392356445 absolute error 2.4868995751603507e-14 relative error 9.41770048700157e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (closed_form) 26.940198389378395 y[1] (numeric) 26.940198389378356 absolute error 3.907985046680551e-14 relative error 1.450614798820983e-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) 27.484519293755483 y[1] (numeric) 27.484519293755454 absolute error 2.842170943040401e-14 relative error 1.034098836753585e-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) 28.039834372315237 y[1] (numeric) 28.039834372315195 absolute error 4.263256414560601e-14 relative error 1.5204285296242231e-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) 28.606365758493332 y[1] (numeric) 28.606365758493304 absolute error 2.842170943040401e-14 relative error 9.935449217964886e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (closed_form) 29.18434007239815 y[1] (numeric) 29.18434007239811 absolute error 3.907985046680551e-14 relative error 1.3390691847017743e-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) 29.773988511461624 y[1] (numeric) 29.773988511461592 absolute error 3.197442310920451e-14 relative error 1.073904596184546e-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) 30.375546942921513 y[1] (numeric) 30.375546942921467 absolute error 4.618527782440651e-14 relative error 1.5204755954252596e-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) 30.989255998171238 y[1] (numeric) 30.98925599817121 absolute error 2.842170943040401e-14 relative error 9.171472019877228e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (closed_form) 31.61536116901585 y[1] (numeric) 31.615361169015806 absolute error 4.263256414560601e-14 relative error 1.348476264993215e-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) 32.25411290587181 y[1] (numeric) 32.25411290587177 absolute error 3.552713678800501e-14 relative error 1.1014761711687738e-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) 32.90576671795072 y[1] (numeric) 32.90576671795066 absolute error 5.684341886080802e-14 relative error 1.7274607015857453e-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) 33.57058327546618 y[1] (numeric) 33.570583275466134 absolute error 4.263256414560601e-14 relative error 1.269938141848207e-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) 34.248828513905615 y[1] (numeric) 34.24882851390555 absolute error 6.394884621840902e-14 relative error 1.8671834627115693e-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) 34.9407737404077 y[1] (numeric) 34.940773740407664 absolute error 3.552713678800501e-14 relative error 1.0167816274463093e-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) 35.64669574228918 y[1] (numeric) 35.64669574228914 absolute error 4.263256414560601e-14 relative error 1.1959752021287403e-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) 36.36687689776317 y[1] (numeric) 36.36687689776315 absolute error 2.1316282072803006e-14 relative error 5.861455228264079e-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) 37.10160528889444 y[1] (numeric) 37.101605288894405 absolute error 3.552713678800501e-14 relative error 9.575633321353696e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 1.0099999999999996 y[1] (closed_form) 37.851174816835844 y[1] (numeric) 37.85117481683589 absolute error 4.973799150320701e-14 relative error 1.3140408915678893e-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) 38.61588531939304 y[1] (numeric) 38.61588531939317 absolute error 1.3500311979441904e-13 relative error 3.496051396408617e-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) 39.39604269096332 y[1] (numeric) 39.39604269096355 absolute error 2.2737367544323206e-13 relative error 5.77148515212131e-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) 40.191959004897555 y[1] (numeric) 40.191959004897875 absolute error 3.197442310920451e-13 relative error 7.955427876831854e-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) 41.00395263833368 y[1] (numeric) 41.00395263833409 absolute error 4.121147867408581e-13 relative error 1.0050611227064515e-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) 41.83234839955179 y[1] (numeric) 41.832348399552295 absolute error 5.044853423896711e-13 relative error 1.2059694511319293e-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) 42.6774776579018 y[1] (numeric) 42.6774776579024 absolute error 6.039613253960852e-13 relative error 1.415175775469619e-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) 43.53967847635559 y[1] (numeric) 43.539678476356286 absolute error 6.963318810448982e-13 relative error 1.5993041414466215e-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) 44.4192957467367 y[1] (numeric) 44.41929574673751 absolute error 8.100187187665142e-13 relative error 1.823573978716272e-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) 45.31668132768169 y[1] (numeric) 45.316681327682595 absolute error 9.023892744153272e-13 relative error 1.9912960260488068e-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) 46.23219418538822 y[1] (numeric) 46.23219418538922 absolute error 1.0018652574217413e-12 relative error 2.1670294371154527e-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) 47.16620053720636 y[1] (numeric) 47.166200537207466 absolute error 1.1084466677857563e-12 relative error 2.35008683158902e-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) 48.119073998130446 y[1] (numeric) 48.119073998131654 absolute error 1.2079226507921703e-12 relative error 2.5102782543967936e-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) 49.091195730249986 y[1] (numeric) 49.0911957302513 absolute error 1.3145040611561853e-12 relative error 2.6776778230850635e-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) 50.082954595219626 y[1] (numeric) 50.08295459522103 absolute error 1.4068746168049984e-12 relative error 2.8090886972935965e-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) 51.09474730980898 y[1] (numeric) 51.094747309810494 absolute error 1.5134560271690134e-12 relative error 2.9620579547879783e-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) 52.12697860459464 y[1] (numeric) 52.12697860459626 absolute error 1.6200374375330284e-12 relative error 3.107867520620566e-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) 53.180061385857776 y[1] (numeric) 53.18006138585952 absolute error 1.7408297026122455e-12 relative error 3.273463131193726e-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) 54.2544169007522 y[1] (numeric) 54.25441690075405 absolute error 1.8545165403338615e-12 relative error 3.4181853686241534e-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) 55.35047490580878 y[1] (numeric) 55.350474905810756 absolute error 1.9753088054130785e-12 relative error 3.5687296428341554e-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) 56.468673838843856 y[1] (numeric) 56.46867383884595 absolute error 2.0961010704922955e-12 relative error 3.711971484356735e-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) 57.60946099434015 y[1] (numeric) 57.60946099434237 absolute error 2.2239987629291136e-12 relative error 3.860474867396539e-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) 58.77329270237057 y[1] (numeric) 58.77329270237291 absolute error 2.3447910280083306e-12 relative error 3.9895519209420704e-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) 59.96063451113628 y[1] (numeric) 59.96063451113876 absolute error 2.4797941478027496e-12 relative error 4.13570364626843e-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) 61.17196137319222 y[1] (numeric) 61.17196137319484 absolute error 2.6219026949547697e-12 relative error 4.286118404736623e-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) 62.40775783543447 y[1] (numeric) 62.407757835437216 absolute error 2.7498003873915877e-12 relative error 4.406183594422103e-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) 63.66851823292541 y[1] (numeric) 63.6685182329283 absolute error 2.8919089345436078e-12 relative error 4.5421332470214325e-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) 64.95474688663441 y[1] (numeric) 64.95474688663745 absolute error 3.0411229090532288e-12 relative error 4.68191018334796e-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) 66.2669583051729 y[1] (numeric) 66.26695830517609 absolute error 3.183231456205249e-12 relative error 4.8036480587290824e-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) 67.6056773906047 y[1] (numeric) 67.60567739060801 absolute error 3.311129148642067e-12 relative error 4.897708707970466e-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) 68.97143964841376 y[1] (numeric) 68.97143964841723 absolute error 3.467448550509289e-12 relative error 5.027368673446321e-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) 70.36479140171363 y[1] (numeric) 70.36479140171726 absolute error 3.623767952376511e-12 relative error 5.149973275254049e-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) 71.78629000978394 y[1] (numeric) 71.78629000978769 absolute error 3.751665644813329e-12 relative error 5.226158984260093e-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) 73.23650409102142 y[1] (numeric) 73.23650409102534 absolute error 3.922195901395753e-12 relative error 5.355520378909788e-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) 74.71601375039506 y[1] (numeric) 74.71601375039913 absolute error 4.064304448547773e-12 relative error 5.4396698171364676e-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) 76.22541081149565 y[1] (numeric) 76.2254108114999 absolute error 4.249045559845399e-12 relative error 5.574316379026448e-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) 77.7652990532732 y[1] (numeric) 77.76529905327762 absolute error 4.419575816427823e-12 relative error 5.68322358459676e-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) 79.33629445155651 y[1] (numeric) 79.3362944515611 absolute error 4.590106073010247e-12 relative error 5.785632042359892e-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) 80.93902542545182 y[1] (numeric) 80.93902542545658 absolute error 4.760636329592671e-12 relative error 5.881756426604634e-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) 82.5741330887187 y[1] (numeric) 82.57413308872364 absolute error 4.945377440890297e-12 relative error 5.989015271376717e-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) 84.24227150622417 y[1] (numeric) 84.2422715062293 absolute error 5.130118552187923e-12 relative error 6.08972011374229e-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) 85.94410795557738 y[1] (numeric) 85.9441079555827 absolute error 5.314859663485549e-12 relative error 6.1840884615763116e-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) 87.68032319404954 y[1] (numeric) 87.68032319405505 absolute error 5.5138116294983774e-12 relative error 6.2885393536877095e-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) 89.45161173088587 y[1] (numeric) 89.45161173089159 absolute error 5.7127635955112055e-12 relative error 6.3864289138780284e-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) 91.25868210511862 y[1] (numeric) 91.2586821051245 absolute error 5.8832938520936295e-12 relative error 6.446831924788053e-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) 93.10225716899205 y[1] (numeric) 93.10225716899814 absolute error 6.0822458181064576e-12 relative error 6.532866122747629e-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) 94.98307437711306 y[1] (numeric) 94.98307437711935 absolute error 6.295408638834488e-12 relative error 6.627926796557153e-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) 96.90188608144277 y[1] (numeric) 96.90188608144929 absolute error 6.52278231427772e-12 relative error 6.731326476757678e-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) 98.85945983224742 y[1] (numeric) 98.85945983225416 absolute error 6.73594513500575e-12 relative error 6.813657637251747e-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) 100.85657868512868 y[1] (numeric) 100.85657868513566 absolute error 6.977529665164184e-12 relative error 6.918269245428034e-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) 102.8940415142563 y[1] (numeric) 102.89404151426349 absolute error 7.190692485892214e-12 relative error 6.988444014900436e-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) 104.97266333192844 y[1] (numeric) 104.97266333193585 absolute error 7.403855306620244e-12 relative error 7.053127044332398e-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) 107.09327561458753 y[1] (numeric) 107.09327561459516 absolute error 7.631228982063476e-12 relative error 7.125777914877786e-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) 109.25672663542183 y[1] (numeric) 109.25672663542967 absolute error 7.844391802791506e-12 relative error 7.179779263355943e-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) 111.46388180368606 y[1] (numeric) 111.46388180369415 absolute error 8.08597633294994e-12 relative error 7.254346611749296e-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) 113.71562401087667 y[1] (numeric) 113.715624010885 absolute error 8.327560863108374e-12 relative error 7.32314572913205e-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) 116.01285398390013 y[1] (numeric) 116.01285398390873 absolute error 8.597567102697212e-12 relative error 7.410874577648398e-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) 118.35649064537584 y[1] (numeric) 118.35649064538468 absolute error 8.839151632855646e-12 relative error 7.468244102758879e-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) 120.74747148121727 y[1] (numeric) 120.74747148122637 absolute error 9.094947017729282e-12 relative error 7.532204944882872e-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) 123.18675291563893 y[1] (numeric) 123.18675291564828 absolute error 9.350742402602918e-12 relative error 7.590704504571621e-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) 125.67531069373877 y[1] (numeric) 125.6753106937484 absolute error 9.634959496906959e-12 relative error 7.666549176382486e-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) 128.21414027180924 y[1] (numeric) 128.21414027181913 absolute error 9.890754881780595e-12 relative error 7.714246541615893e-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) 130.8042572155331 y[1] (numeric) 130.8042572155433 absolute error 1.0174971976084635e-11 relative error 7.778777382848323e-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) 133.44669760622315 y[1] (numeric) 133.44669760623364 absolute error 1.0487610779819079e-11 relative error 7.859026089027773e-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) 136.14251845526874 y[1] (numeric) 136.14251845527951 absolute error 1.0771827874123119e-11 relative error 7.912170272993982e-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) 138.8927981269542 y[1] (numeric) 138.89279812696526 absolute error 1.1056044968427159e-11 relative error 7.960128327403586e-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) 141.6986367698191 y[1] (numeric) 141.69863676983044 absolute error 1.1340262062731199e-11 relative error 8.003084801128166e-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) 144.56115675673226 y[1] (numeric) 144.5611567567439 absolute error 1.1652900866465643e-11 relative error 8.060879649763153e-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) 147.48150313385585 y[1] (numeric) 147.48150313386785 absolute error 1.1993961379630491e-11 relative error 8.132519078507518e-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) 150.4608440786793 y[1] (numeric) 150.46084407869154 absolute error 1.2249756764504127e-11 relative error 8.141491455476921e-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) 153.50037136730552 y[1] (numeric) 153.50037136731805 absolute error 1.2533973858808167e-11 relative error 8.165435527720042e-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) 156.6013008511775 y[1] (numeric) 156.60130085119044 absolute error 1.2931877790833823e-11 relative error 8.257835484472342e-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) 159.7648729434352 y[1] (numeric) 159.76487294344844 absolute error 1.3244516594568267e-11 relative error 8.290005400159203e-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) 162.99235311509693 y[1] (numeric) 162.99235311511055 absolute error 1.361399881716352e-11 relative error 8.352538359606358e-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) 166.28503240126503 y[1] (numeric) 166.285032401279 absolute error 1.3983481039758772e-11 relative error 8.409344387662633e-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) 169.64422791755698 y[1] (numeric) 169.6442279175713 absolute error 1.432454155292362e-11 relative error 8.443872054335384e-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) 173.0712833869691 y[1] (numeric) 173.0712833869838 absolute error 1.4694023775518872e-11 relative error 8.49015705434193e-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) 176.5675696773839 y[1] (numeric) 176.56756967739895 absolute error 1.5063505998114124e-11 relative error 8.53129825915227e-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) 180.1344853499353 y[1] (numeric) 180.13448534995075 absolute error 1.546140993013978e-11 relative error 8.583259279922957e-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) 183.77345721845177 y[1] (numeric) 183.77345721846766 absolute error 1.588773557159584e-11 relative error 8.645283063217375e-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) 187.48594092020107 y[1] (numeric) 187.48594092021736 absolute error 1.6285639503621496e-11 relative error 8.686325717912412e-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) 191.2734214981643 y[1] (numeric) 191.27342149818108 absolute error 1.6768808563938364e-11 relative error 8.76693083262449e-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) 195.1374139950731 y[1] (numeric) 195.1374139950903 absolute error 1.7195134205394424e-11 relative error 8.811807973343633e-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) 199.07946405944676 y[1] (numeric) 199.07946405946439 absolute error 1.7621459846850485e-11 relative error 8.85147040660536e-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) 203.10114856387244 y[1] (numeric) 203.1011485638905 absolute error 1.8047785488306545e-11 relative error 8.886107053516131e-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) 207.20407623577506 y[1] (numeric) 207.20407623579354 absolute error 1.8474111129762605e-11 relative error 8.915901397973046e-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) 211.38988830092984 y[1] (numeric) 211.3898883009488 absolute error 1.8957280190079473e-11 relative error 8.967921948609159e-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) 215.6602591399744 y[1] (numeric) 215.66025913999383 absolute error 1.944044925039634e-11 relative error 9.014386483593395e-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) 220.0168969581834 y[1] (numeric) 220.01689695820335 absolute error 1.9952040020143613e-11 relative error 9.068412606480726e-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) 224.46154446877338 y[1] (numeric) 224.4615444687938 absolute error 2.0406787371030077e-11 relative error 9.091440326371375e-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) 228.99597959001133 y[1] (numeric) 228.99597959003222 absolute error 2.0889956431346945e-11 relative error 9.122411873233671e-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) 233.62201615640572 y[1] (numeric) 233.62201615642715 absolute error 2.142996891052462e-11 relative error 9.17292353824121e-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) 238.34150464426438 y[1] (numeric) 238.34150464428637 absolute error 2.1998403099132702e-11 relative error 9.22978275729455e-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) 243.15633291190986 y[1] (numeric) 243.15633291193234 absolute error 2.248157215944957e-11 relative error 9.245727590238887e-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) 248.06842695484775 y[1] (numeric) 248.06842695487074 absolute error 2.2993162929196842e-11 relative error 9.268879240880561e-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) 253.07975167619065 y[1] (numeric) 253.07975167621422 absolute error 2.3561597117804922e-11 relative error 9.3099495166059e-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) 258.1923116726457 y[1] (numeric) 258.19231167266986 absolute error 2.4158453015843406e-11 relative error 9.356767000278918e-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) 263.4081520363799 y[1] (numeric) 263.40815203640454 absolute error 2.467004378559068e-11 relative error 9.365710056757638e-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) 268.72935917308405 y[1] (numeric) 268.7293591731094 absolute error 2.5352164811920375e-11 relative error 9.434088217949968e-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) 274.1580616365634 y[1] (numeric) 274.15806163658925 absolute error 2.5863755581667647e-11 relative error 9.43388475512124e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 0.001 Finished! diff ( y , x , 1 ) = cosh ( 2.0 * x + 3.0 ) ; Iterations 1901 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.10526315788897%