##############ECHO OF PROBLEM################# ##############temp/lin_arccospostode.ode################# diff ( y , x , 1 ) = arccos ( 0.1 * x + 0.2 ) ; ! #BEGIN FIRST INPUT BLOCK max_terms=30 # Digits:=32; ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-0.8) x_end=c(0.8) $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=0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(0.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(1.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(1.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb #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(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arccos(c(0.1) * c(x) + c(0.2) )-c(10.0) * sqrt(c(1.0) - expt((c(0.1) * c(x) + c(0.2)) , c(2) ))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -0.8 y[1] (closed_form) -8.187131183512555 y[1] (numeric) -8.187131183512555 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] -0.79 y[1] (closed_form) -8.172631155666924 y[1] (numeric) -8.17263115566487 absolute error 2.0534685063466895e-12 relative error 2.5126161541290273e-11% Desired digits 8 Estimated correct digits 13 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] -0.78 y[1] (closed_form) -8.158141201840962 y[1] (numeric) -8.158141201836838 absolute error 4.1247005810873816e-12 relative error 5.0559318342720074e-11% Desired digits 8 Estimated correct digits 13 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] -0.77 y[1] (closed_form) -8.143661323277081 y[1] (numeric) -8.143661323270871 absolute error 6.210143510543276e-12 relative error 7.625738920149811e-11% Desired digits 8 Estimated correct digits 13 Correct digits 13 h 0.001 TOP MAIN SOLVE Loop x[1] -0.76 y[1] (closed_form) -8.129191521228385 y[1] (numeric) -8.129191521220068 absolute error 8.316902722071973e-12 relative error 1.0230910048500398e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.75 y[1] (closed_form) -8.114731796958676 y[1] (numeric) -8.114731796948233 absolute error 1.0443201858834072e-11 relative error 1.2869435638954926e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.74 y[1] (closed_form) -8.100282151742475 y[1] (numeric) -8.10028215172989 absolute error 1.2583711850311374e-11 relative error 1.5534905592892782e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.73 y[1] (closed_form) -8.085842586865027 y[1] (numeric) -8.085842586850287 absolute error 1.4740209053343278e-11 relative error 1.8229651263911416e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.72 y[1] (closed_form) -8.07141310362232 y[1] (numeric) -8.071413103605398 absolute error 1.6921575252126786e-11 relative error 2.096482367447239e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.71 y[1] (closed_form) -8.05699370332108 y[1] (numeric) -8.056993703301968 absolute error 1.9111823235107295e-11 relative error 2.37207871060262e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.7 y[1] (closed_form) -8.042584387278817 y[1] (numeric) -8.042584387257492 absolute error 2.1325163857000007e-11 relative error 2.6515312529055487e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.69 y[1] (closed_form) -8.028185156823803 y[1] (numeric) -8.028185156800241 absolute error 2.3561597117804922e-11 relative error 2.934859704596875e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6799999999999999 y[1] (closed_form) -8.013796013295094 y[1] (numeric) -8.013796013269287 absolute error 2.580691216280684e-11 relative error 3.2203105893876645e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6699999999999999 y[1] (closed_form) -7.999416958042559 y[1] (numeric) -7.999416958014485 absolute error 2.807443166830126e-11 relative error 3.5095597361099444e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6599999999999999 y[1] (closed_form) -7.985047992426874 y[1] (numeric) -7.985047992396512 absolute error 3.036149109902908e-11 relative error 3.8022928763639647e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6499999999999999 y[1] (closed_form) -7.970689117819537 y[1] (numeric) -7.970689117786875 absolute error 3.2662761384472105e-11 relative error 4.0978591564247753e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6399999999999999 y[1] (closed_form) -7.956340335602894 y[1] (numeric) -7.956340335567911 absolute error 3.498268341672883e-11 relative error 4.3968309475386477e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6299999999999999 y[1] (closed_form) -7.942001647170137 y[1] (numeric) -7.942001647132815 absolute error 3.732214537421896e-11 relative error 4.699337400353907e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6199999999999999 y[1] (closed_form) -7.927673053925329 y[1] (numeric) -7.927673053885647 absolute error 3.9682035435362195e-11 relative error 5.005508572999732e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.6099999999999999 y[1] (closed_form) -7.913354557283403 y[1] (numeric) -7.913354557241345 absolute error 4.205880088647973e-11 relative error 5.314914248062987e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5999999999999999 y[1] (closed_form) -7.899046158670194 y[1] (numeric) -7.89904615862574 absolute error 4.445332990599127e-11 relative error 5.627683268719497e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5899999999999999 y[1] (closed_form) -7.884747859522434 y[1] (numeric) -7.884747859475569 absolute error 4.686473431547711e-11 relative error 5.94372009738757e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5799999999999998 y[1] (closed_form) -7.87045966128778 y[1] (numeric) -7.870459661238485 absolute error 4.929567865019635e-11 relative error 6.263379875087308e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5699999999999998 y[1] (closed_form) -7.856181565424819 y[1] (numeric) -7.856181565373075 absolute error 5.1744386553309596e-11 relative error 6.586455025560696e-10% Desired digits 8 Estimated correct digits 13 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5599999999999998 y[1] (closed_form) -7.841913573403087 y[1] (numeric) -7.841913573348876 absolute error 5.4210858024816844e-11 relative error 6.91296295443504e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5499999999999998 y[1] (closed_form) -7.827655686703078 y[1] (numeric) -7.827655686646382 absolute error 5.6696869421557494e-11 relative error 7.243148100889141e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5399999999999998 y[1] (closed_form) -7.8134079068162645 y[1] (numeric) -7.813407906757064 absolute error 5.920064438669215e-11 relative error 7.576801965637384e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5299999999999998 y[1] (closed_form) -7.7991702352451036 y[1] (numeric) -7.799170235183381 absolute error 6.17221829202208e-11 relative error 7.91394226033086e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5199999999999998 y[1] (closed_form) -7.7849426735030605 y[1] (numeric) -7.784942673438798 absolute error 6.426237320056316e-11 relative error 8.254700888073007e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.5099999999999998 y[1] (closed_form) -7.7707252231146136 y[1] (numeric) -7.770725223047792 absolute error 6.682121522771922e-11 relative error 8.599096391795508e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.4999999999999998 y[1] (closed_form) -7.7565178856152786 y[1] (numeric) -7.75651788554588 absolute error 6.939870900168899e-11 relative error 8.947147421704681e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.48999999999999977 y[1] (closed_form) -7.742320662551613 y[1] (numeric) -7.74232066247962 absolute error 7.199307816563305e-11 relative error 9.298643301336283e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.47999999999999976 y[1] (closed_form) -7.7281335554812385 y[1] (numeric) -7.728133555406633 absolute error 7.460521089797112e-11 relative error 9.653716562009568e-10% Desired digits 8 Estimated correct digits 12 Correct digits 12 h 0.001 TOP MAIN SOLVE Loop x[1] -0.46999999999999975 y[1] (closed_form) -7.713956565972856 y[1] (numeric) -7.713956565895617 absolute error 7.723865991238199e-11 relative error 1.0012846099379215e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.45999999999999974 y[1] (closed_form) -7.6997896956062535 y[1] (numeric) -7.699789695526364 absolute error 7.988987249518686e-11 relative error 1.0375591497099535e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.44999999999999973 y[1] (closed_form) -7.68563294597233 y[1] (numeric) -7.685632945889769 absolute error 8.256062500322514e-11 relative error 1.074220244234942e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.4399999999999997 y[1] (closed_form) -7.6714863186731 y[1] (numeric) -7.671486318587853 absolute error 8.524736472281802e-11 relative error 1.1112235775656424e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.4299999999999997 y[1] (closed_form) -7.657349815321725 y[1] (numeric) -7.65734981523377 absolute error 8.7954532546064e-11 relative error 1.1486288946872225e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.4199999999999997 y[1] (closed_form) -7.643223437542514 y[1] (numeric) -7.643223437451832 absolute error 9.068212847296309e-11 relative error 1.186438277174318e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.4099999999999997 y[1] (closed_form) -7.629107186970943 y[1] (numeric) -7.629107186877517 absolute error 9.342571161141677e-11 relative error 1.224595608919613e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3999999999999997 y[1] (closed_form) -7.615001065253674 y[1] (numeric) -7.615001065157487 absolute error 9.618705831826446e-11 relative error 1.2631259995110748e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3899999999999997 y[1] (closed_form) -7.600905074048573 y[1] (numeric) -7.600905073949604 absolute error 9.896883312876525e-11 relative error 1.3020664271504991e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.37999999999999967 y[1] (closed_form) -7.586819215024715 y[1] (numeric) -7.5868192149229445 absolute error 1.0177014786449945e-10 relative error 1.3414073141871738e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.36999999999999966 y[1] (closed_form) -7.572743489862411 y[1] (numeric) -7.572743489757824 absolute error 1.0458744981178825e-10 relative error 1.3811038225683846e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.35999999999999965 y[1] (closed_form) -7.5586779002532225 y[1] (numeric) -7.558677900145797 absolute error 1.0742517986273015e-10 relative error 1.4212165312551724e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.34999999999999964 y[1] (closed_form) -7.544622447899971 y[1] (numeric) -7.544622447789689 absolute error 1.1028156166048575e-10 relative error 1.461724061370127e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.33999999999999964 y[1] (closed_form) -7.530577134516765 y[1] (numeric) -7.530577134403607 absolute error 1.1315748338347476e-10 relative error 1.5026402540226558e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3299999999999996 y[1] (closed_form) -7.516541961829004 y[1] (numeric) -7.516541961712953 absolute error 1.1605116867485776e-10 relative error 1.543943601515117e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3199999999999996 y[1] (closed_form) -7.50251693157341 y[1] (numeric) -7.502516931454446 absolute error 1.1896439389147417e-10 relative error 1.5856597855957819e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3099999999999996 y[1] (closed_form) -7.488502045498028 y[1] (numeric) -7.488502045376132 absolute error 1.218962708549043e-10 relative error 1.6277790953958067e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.2999999999999996 y[1] (closed_form) -7.474497305362258 y[1] (numeric) -7.474497305237411 absolute error 1.248467995651481e-10 relative error 1.6703036266476692e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.2899999999999996 y[1] (closed_form) -7.460502712936863 y[1] (numeric) -7.460502712809046 absolute error 1.2781686820062532e-10 relative error 1.7132473925515079e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.2799999999999996 y[1] (closed_form) -7.446518270003987 y[1] (numeric) -7.446518269873183 absolute error 1.3080470040449654e-10 relative error 1.7565887259204496e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.2699999999999996 y[1] (closed_form) -7.432543978357177 y[1] (numeric) -7.432543978223366 absolute error 1.3381118435518147e-10 relative error 1.8003416427111122e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.25999999999999956 y[1] (closed_form) -7.418579839801397 y[1] (numeric) -7.418579839664558 absolute error 1.368389845879392e-10 relative error 1.844544205803176e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.24999999999999956 y[1] (closed_form) -7.404625856153042 y[1] (numeric) -7.404625856013158 absolute error 1.3988366021067122e-10 relative error 1.889138802258749e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.23999999999999955 y[1] (closed_form) -7.390682029239967 y[1] (numeric) -7.390682029097017 absolute error 1.4294965211547606e-10 relative error 1.9341875560323155e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.22999999999999954 y[1] (closed_form) -7.376748360901489 y[1] (numeric) -7.3767483607554585 absolute error 1.460307430534158e-10 relative error 1.9796085742522175e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.21999999999999953 y[1] (closed_form) -7.362824852988426 y[1] (numeric) -7.362824852839291 absolute error 1.4913581480868743e-10 relative error 2.025524411981036e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.20999999999999952 y[1] (closed_form) -7.348911507363089 y[1] (numeric) -7.34891150721083 absolute error 1.5225865013235307e-10 relative error 2.071853089805214e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.1999999999999995 y[1] (closed_form) -7.33500832589932 y[1] (numeric) -7.335008325743921 absolute error 1.553992490244127e-10 relative error 2.1185967639015563e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.1899999999999995 y[1] (closed_form) -7.32111531048251 y[1] (numeric) -7.321115310323946 absolute error 1.5856382873380426e-10 relative error 2.165842525479275e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.1799999999999995 y[1] (closed_form) -7.307232463009601 y[1] (numeric) -7.307232462847858 absolute error 1.617435074763307e-10 relative error 2.2134714927313814e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.16999999999999948 y[1] (closed_form) -7.293359785389122 y[1] (numeric) -7.29335978522418 absolute error 1.6494272614409056e-10 relative error 2.2615465436728124e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.15999999999999948 y[1] (closed_form) -7.279497279541203 y[1] (numeric) -7.279497279373042 absolute error 1.681605965586641e-10 relative error 2.310057825439047e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.14999999999999947 y[1] (closed_form) -7.265644947397586 y[1] (numeric) -7.265644947226188 absolute error 1.7139800689847107e-10 relative error 2.359019854938859e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.13999999999999946 y[1] (closed_form) -7.2518027909016585 y[1] (numeric) -7.251802790727002 absolute error 1.7465673352035083e-10 relative error 2.408459503883375e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.12999999999999945 y[1] (closed_form) -7.237970812008458 y[1] (numeric) -7.237970811830523 absolute error 1.77935000067464e-10 relative error 2.45835476114733e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.11999999999999944 y[1] (closed_form) -7.224149012684695 y[1] (numeric) -7.224149012503465 absolute error 1.8123014200455145e-10 relative error 2.508671148481768e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.10999999999999943 y[1] (closed_form) -7.210337394908786 y[1] (numeric) -7.210337394724237 absolute error 1.8454837658055112e-10 relative error 2.55949710079948e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.09999999999999942 y[1] (closed_form) -7.19653596067085 y[1] (numeric) -7.196535960482968 absolute error 1.878825983681054e-10 relative error 2.6107366015383774e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.08999999999999941 y[1] (closed_form) -7.182744711972754 y[1] (numeric) -7.182744711781514 absolute error 1.9123991279457186e-10 relative error 2.6624907394494807e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.0799999999999994 y[1] (closed_form) -7.168963650828103 y[1] (numeric) -7.168963650633491 absolute error 1.9461232625417324e-10 relative error 2.714650760318657e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.0699999999999994 y[1] (closed_form) -7.155192779262291 y[1] (numeric) -7.155192779064284 absolute error 1.9800694417426712e-10 relative error 2.7673180902706844e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.05999999999999939 y[1] (closed_form) -7.141432099312498 y[1] (numeric) -7.141432099111074 absolute error 2.014237665548535e-10 relative error 2.820495437802237e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.04999999999999938 y[1] (closed_form) -7.12768161302772 y[1] (numeric) -7.127681612822863 absolute error 2.0485746432541418e-10 relative error 2.874110762060178e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.03999999999999937 y[1] (closed_form) -7.113941322468791 y[1] (numeric) -7.11394132226048 absolute error 2.0831070202120827e-10 relative error 2.9282038265240714e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.02999999999999936 y[1] (closed_form) -7.100211229708398 y[1] (numeric) -7.1002112294966135 absolute error 2.1178436782065546e-10 relative error 2.9827896800382e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.01999999999999935 y[1] (closed_form) -7.086491336831104 y[1] (numeric) -7.086491336615826 absolute error 2.1527757354533605e-10 relative error 3.0378584169920488e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] -0.009999999999999343 y[1] (closed_form) -7.0727816459333726 y[1] (numeric) -7.072781645714581 absolute error 2.1879120737366975e-10 relative error 3.0934251660302257e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 6.591949208711867e-16 y[1] (closed_form) -7.059082159123578 y[1] (numeric) -7.059082158901257 absolute error 2.2232171659197775e-10 relative error 3.14944225864599e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.010000000000000661 y[1] (closed_form) -7.045392878522046 y[1] (numeric) -7.045392878296169 absolute error 2.2587709480603735e-10 relative error 3.206025536129093e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.02000000000000067 y[1] (closed_form) -7.031713806261049 y[1] (numeric) -7.031713806031599 absolute error 2.2945023658849095e-10 relative error 3.2630770095362544e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.03000000000000068 y[1] (closed_form) -7.018044944484847 y[1] (numeric) -7.0180449442518045 absolute error 2.3304291829617796e-10 relative error 3.320624477894167e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.04000000000000069 y[1] (closed_form) -7.004386295349711 y[1] (numeric) -7.004386295113053 absolute error 2.3665780446435747e-10 relative error 3.378708633209981e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.0500000000000007 y[1] (closed_form) -6.9907378610239235 y[1] (numeric) -6.990737860783633 absolute error 2.40290454200931e-10 relative error 3.437268840255669e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.060000000000000706 y[1] (closed_form) -6.977099643687822 y[1] (numeric) -6.977099643443879 absolute error 2.439435320411576e-10 relative error 3.4963458241828776e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.07000000000000071 y[1] (closed_form) -6.96347164553381 y[1] (numeric) -6.963471645286194 absolute error 2.476161498066176e-10 relative error 3.555929605392049e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.08000000000000072 y[1] (closed_form) -6.949853868766386 y[1] (numeric) -6.949853868515076 absolute error 2.5131008385415043e-10 relative error 3.6160484608686963e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.09000000000000073 y[1] (closed_form) -6.936246315602156 y[1] (numeric) -6.936246315347131 absolute error 2.5502444600533636e-10 relative error 3.6766924702730508e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.10000000000000074 y[1] (closed_form) -6.922648988269866 y[1] (numeric) -6.9226489880111055 absolute error 2.587601244385951e-10 relative error 3.737877290572627e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000075 y[1] (closed_form) -6.909061889010415 y[1] (numeric) -6.909061888747901 absolute error 2.625135664402478e-10 relative error 3.7995544208078825e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000076 y[1] (closed_form) -6.895485020076892 y[1] (numeric) -6.895485019810602 absolute error 2.6629010108081275e-10 relative error 3.861803778929003e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.13000000000000075 y[1] (closed_form) -6.88191838373458 y[1] (numeric) -6.8819183834644955 absolute error 2.700843992897717e-10 relative error 3.9245510369334865e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.14000000000000076 y[1] (closed_form) -6.868361982260994 y[1] (numeric) -6.8683619819870945 absolute error 2.738991256023837e-10 relative error 3.987837657796524e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.15000000000000077 y[1] (closed_form) -6.854815817945896 y[1] (numeric) -6.854815817668161 absolute error 2.7773516819706856e-10 relative error 4.051679513692525e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000078 y[1] (closed_form) -6.841279893091326 y[1] (numeric) -6.841279892809735 absolute error 2.815916388954065e-10 relative error 4.116066632206821e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1700000000000008 y[1] (closed_form) -6.8277542100116175 y[1] (numeric) -6.827754209726147 absolute error 2.8547031405423695e-10 relative error 4.181027981875042e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1800000000000008 y[1] (closed_form) -6.814238771033423 y[1] (numeric) -6.814238770744055 absolute error 2.893685291383008e-10 relative error 4.24652758527298e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1900000000000008 y[1] (closed_form) -6.800733578495738 y[1] (numeric) -6.800733578202452 absolute error 2.9328539596917835e-10 relative error 4.312555293984189e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.20000000000000082 y[1] (closed_form) -6.787238634749932 y[1] (numeric) -6.787238634452707 absolute error 2.972253554389681e-10 relative error 4.379179389939323e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.21000000000000082 y[1] (closed_form) -6.773753942159763 y[1] (numeric) -6.773753941858577 absolute error 3.0118574301241097e-10 relative error 4.446363797448185e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.22000000000000083 y[1] (closed_form) -6.760279503101406 y[1] (numeric) -6.760279502796237 absolute error 3.0516833504634633e-10 relative error 4.514137838625527e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000084 y[1] (closed_form) -6.74681531996347 y[1] (numeric) -6.746815319654301 absolute error 3.091686906486757e-10 relative error 4.582438913569516e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000085 y[1] (closed_form) -6.733361395147043 y[1] (numeric) -6.733361394833852 absolute error 3.1319036253307786e-10 relative error 4.651322632983944e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.25000000000000083 y[1] (closed_form) -6.71991773106569 y[1] (numeric) -6.719917730748455 absolute error 3.1723512705639223e-10 relative error 4.720818613445777e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.26000000000000084 y[1] (closed_form) -6.706484330145499 y[1] (numeric) -6.7064843298242 absolute error 3.2129943150494e-10 relative error 4.790877241906108e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.27000000000000085 y[1] (closed_form) -6.693061194825092 y[1] (numeric) -6.693061194499709 absolute error 3.253832758787212e-10 relative error 4.861501582120591e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.28000000000000086 y[1] (closed_form) -6.679648327555661 y[1] (numeric) -6.679648327226172 absolute error 3.2948932471299486e-10 relative error 4.932734607505417e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.29000000000000087 y[1] (closed_form) -6.666245730800988 y[1] (numeric) -6.666245730467371 absolute error 3.3361668982934134e-10 relative error 5.004566337659674e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3000000000000009 y[1] (closed_form) -6.652853407037465 y[1] (numeric) -6.6528534066997 absolute error 3.377653712277606e-10 relative error 5.0770000564038956e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3100000000000009 y[1] (closed_form) -6.6394713587541325 y[1] (numeric) -6.639471358412198 absolute error 3.41934480729833e-10 relative error 5.150025691111582e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000009 y[1] (closed_form) -6.6260995884526945 y[1] (numeric) -6.6260995881065705 absolute error 3.461240183355585e-10 relative error 5.223646486369582e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3300000000000009 y[1] (closed_form) -6.612738098647552 y[1] (numeric) -6.612738098297215 absolute error 3.503366485801962e-10 relative error 5.297906001325648e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3400000000000009 y[1] (closed_form) -6.599386891865819 y[1] (numeric) -6.5993868915112515 absolute error 3.545679305716476e-10 relative error 5.372740473947299e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3500000000000009 y[1] (closed_form) -6.586045970647364 y[1] (numeric) -6.5860459702885406 absolute error 3.588231933804309e-10 relative error 5.4482339628303715e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.36000000000000093 y[1] (closed_form) -6.572715337544821 y[1] (numeric) -6.572715337181723 absolute error 3.630979961144476e-10 relative error 5.5243225587505756e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.37000000000000094 y[1] (closed_form) -6.559394995123624 y[1] (numeric) -6.559394994756232 absolute error 3.67391450595278e-10 relative error 5.600995989239917e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.38000000000000095 y[1] (closed_form) -6.54608494596204 y[1] (numeric) -6.546084945590329 absolute error 3.717106622502797e-10 relative error 5.6783660053108516e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.39000000000000096 y[1] (closed_form) -6.532785192651178 y[1] (numeric) -6.53278519227513 absolute error 3.760485256520951e-10 relative error 5.7563277310130664e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.40000000000000097 y[1] (closed_form) -6.519495737795036 y[1] (numeric) -6.519495737414626 absolute error 3.8040948169282274e-10 relative error 5.83495253302338e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.410000000000001 y[1] (closed_form) -6.506216584010515 y[1] (numeric) -6.506216583625722 absolute error 3.8479264219404286e-10 relative error 5.9142304475337915e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.420000000000001 y[1] (closed_form) -6.492947733927451 y[1] (numeric) -6.492947733538254 absolute error 3.891971189773358e-10 relative error 5.994151422837935e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.430000000000001 y[1] (closed_form) -6.479689190188645 y[1] (numeric) -6.479689189795022 absolute error 3.936229120427015e-10 relative error 6.074719025701322e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.440000000000001 y[1] (closed_form) -6.466440955449886 y[1] (numeric) -6.466440955051816 absolute error 3.9807002139014003e-10 relative error 6.155936845826273e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.450000000000001 y[1] (closed_form) -6.453203032379985 y[1] (numeric) -6.453203031977444 absolute error 4.0254111155491046e-10 relative error 6.23784978614644e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.460000000000001 y[1] (closed_form) -6.439975423660794 y[1] (numeric) -6.439975423253761 absolute error 4.07032629823334e-10 relative error 6.320406570619441e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.47000000000000103 y[1] (closed_form) -6.4267581319872455 y[1] (numeric) -6.426758131575701 absolute error 4.1154457619541063e-10 relative error 6.403610774568782e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.48000000000000104 y[1] (closed_form) -6.413551160067376 y[1] (numeric) -6.413551159651296 absolute error 4.1608050338481917e-10 relative error 6.4875213902628025e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.49000000000000105 y[1] (closed_form) -6.40035451062235 y[1] (numeric) -6.400354510201712 absolute error 4.206377468563005e-10 relative error 6.572100750953545e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.500000000000001 y[1] (closed_form) -6.387168186386496 y[1] (numeric) -6.38716818596128 absolute error 4.2521630660985466e-10 relative error 6.657352588838252e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.510000000000001 y[1] (closed_form) -6.373992190107333 y[1] (numeric) -6.373992189677518 absolute error 4.298152944670619e-10 relative error 6.743266725901403e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.520000000000001 y[1] (closed_form) -6.360826524545601 y[1] (numeric) -6.360826524111164 absolute error 4.3443737496318136e-10 relative error 6.829888746167564e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.530000000000001 y[1] (closed_form) -6.347671192475289 y[1] (numeric) -6.347671192036203 absolute error 4.390861008118918e-10 relative error 6.917278597108134e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.540000000000001 y[1] (closed_form) -6.334526196683662 y[1] (numeric) -6.334526196239906 absolute error 4.4375525476425537e-10 relative error 7.005342483176977e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.550000000000001 y[1] (closed_form) -6.3213915399712945 y[1] (numeric) -6.321391539522851 absolute error 4.4844394864185233e-10 relative error 7.094070123741911e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.560000000000001 y[1] (closed_form) -6.308267225152101 y[1] (numeric) -6.308267224698948 absolute error 4.531530706231024e-10 relative error 7.183479305003225e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5700000000000011 y[1] (closed_form) -6.2951532550533695 y[1] (numeric) -6.2951532545954825 absolute error 4.5788706160010406e-10 relative error 7.2736443903496695e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5800000000000011 y[1] (closed_form) -6.282049632515781 y[1] (numeric) -6.282049632053135 absolute error 4.6264592157285733e-10 relative error 7.364569664941996e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.5900000000000011 y[1] (closed_form) -6.268956360393442 y[1] (numeric) -6.268956359926021 absolute error 4.674216569355849e-10 relative error 7.456131931124965e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6000000000000011 y[1] (closed_form) -6.255873441553934 y[1] (numeric) -6.255873441081713 absolute error 4.722213731156444e-10 relative error 7.548448310654227e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6100000000000011 y[1] (closed_form) -6.242800878878322 y[1] (numeric) -6.242800878401276 absolute error 4.770459582914555e-10 relative error 7.641537309086317e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6200000000000011 y[1] (closed_form) -6.2297386752611885 y[1] (numeric) -6.2297386747792975 absolute error 4.818909715709196e-10 relative error 7.735332037033092e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6300000000000011 y[1] (closed_form) -6.216686833610681 y[1] (numeric) -6.216686833123921 absolute error 4.867599656677157e-10 relative error 7.829893618511313e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6400000000000011 y[1] (closed_form) -6.203645356848524 y[1] (numeric) -6.203645356356873 absolute error 4.916511642250043e-10 relative error 7.925197782014493e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6500000000000011 y[1] (closed_form) -6.190614247910064 y[1] (numeric) -6.1906142474135 absolute error 4.965636790643657e-10 relative error 8.021234390949241e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6600000000000011 y[1] (closed_form) -6.177593509744298 y[1] (numeric) -6.177593509242795 absolute error 5.015028392563181e-10 relative error 8.118093857507244e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6700000000000012 y[1] (closed_form) -6.1645831453139 y[1] (numeric) -6.1645831448074375 absolute error 5.064624275519236e-10 relative error 8.215680048648847e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6800000000000012 y[1] (closed_form) -6.151583157595259 y[1] (numeric) -6.151583157083814 absolute error 5.114451084864413e-10 relative error 8.314040392268264e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.6900000000000012 y[1] (closed_form) -6.1385935495785136 y[1] (numeric) -6.138593549062063 absolute error 5.164508820598712e-10 relative error 8.413179303837956e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7000000000000012 y[1] (closed_form) -6.125614324267577 y[1] (numeric) -6.125614323746099 absolute error 5.214779719153739e-10 relative error 8.51307222933474e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7100000000000012 y[1] (closed_form) -6.112645484680179 y[1] (numeric) -6.112645484153649 absolute error 5.265299307666282e-10 relative error 8.6137815792891e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7200000000000012 y[1] (closed_form) -6.099687033847889 y[1] (numeric) -6.099687033316284 absolute error 5.316049822567948e-10 relative error 8.71528292036715e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7300000000000012 y[1] (closed_form) -6.086738974816161 y[1] (numeric) -6.0867389742794575 absolute error 5.367031263858735e-10 relative error 8.817580786796983e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7400000000000012 y[1] (closed_form) -6.073801310644354 y[1] (numeric) -6.073801310102528 absolute error 5.418261395107038e-10 relative error 8.920708989297228e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7500000000000012 y[1] (closed_form) -6.060874044405777 y[1] (numeric) -6.0608740438588065 absolute error 5.469704689176069e-10 relative error 9.024613692846232e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7600000000000012 y[1] (closed_form) -6.047957179187718 y[1] (numeric) -6.0479571786355795 absolute error 5.52138779141842e-10 relative error 9.129343392871012e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7700000000000012 y[1] (closed_form) -6.035050718091478 y[1] (numeric) -6.035050717534148 absolute error 5.573301820049892e-10 relative error 9.234888123379997e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7800000000000012 y[1] (closed_form) -6.0221546642324055 y[1] (numeric) -6.02215466366986 absolute error 5.625455656854683e-10 relative error 9.341267321256542e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 TOP MAIN SOLVE Loop x[1] 0.7900000000000013 y[1] (closed_form) -6.009269020739932 y[1] (numeric) -6.009269020172147 absolute error 5.677849301832794e-10 relative error 9.448485801245872e-09% Desired digits 8 Estimated correct digits 12 Correct digits 11 h 0.001 Finished! diff ( y , x , 1 ) = arccos ( 0.1 * x + 0.2 ) ; Iterations 1600 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.06250000000009%