##############ECHO OF PROBLEM################# ##############temp/ln_sqrtpostode.ode################# diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(10.0); x_end=c(11.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.001; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); array_given_ord_poles[1][2]=c(0.0); // 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 double exact_soln_y (double x) { return(c(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 10 y[1] (closed_form) = -4.906070659236272 y[1] (numeric) = -4.906070659236272 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.00999999999999 y[1] (closed_form) = -4.905156968697433 y[1] (numeric) = -4.90515696869454 absolute error = 2.892797112963308e-12 relative error = 5.897460838509091e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.01999999999999 y[1] (closed_form) = -4.904239114960776 y[1] (numeric) = -4.904239114954997 absolute error = 5.778488798569015e-12 relative error = 1.17826408197375e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.02999999999998 y[1] (closed_form) = -4.903317101489863 y[1] (numeric) = -4.903317101481201 absolute error = 8.662404127335321e-12 relative error = 1.766641632192882e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.03999999999998 y[1] (closed_form) = -4.902390931742493 y[1] (numeric) = -4.902390931730955 absolute error = 1.153832585032433e-11 relative error = 2.353611943840467e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.04999999999997 y[1] (closed_form) = -4.901460609170727 y[1] (numeric) = -4.901460609156316 absolute error = 1.441158303805423e-11 relative error = 2.94026295163729e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.05999999999997 y[1] (closed_form) = -4.900526137220892 y[1] (numeric) = -4.900526137203611 absolute error = 1.728039933368564e-11 relative error = 3.5262334797964e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.06999999999996 y[1] (closed_form) = -4.899587519333599 y[1] (numeric) = -4.899587519313456 absolute error = 2.014299838037914e-11 relative error = 4.1111620725001e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.07999999999996 y[1] (closed_form) = -4.89864475894376 y[1] (numeric) = -4.898644758920759 absolute error = 2.300115653497414e-11 relative error = 4.695412234777691e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.08999999999995 y[1] (closed_form) = -4.897697859480601 y[1] (numeric) = -4.897697859454746 absolute error = 2.585487379747065e-11 relative error = 5.278985053645703e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.09999999999994 y[1] (closed_form) = -4.896746824367675 y[1] (numeric) = -4.89674682433897 absolute error = 2.870503834628835e-11 relative error = 5.862062993218988e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.10999999999994 y[1] (closed_form) = -4.895791657022873 y[1] (numeric) = -4.895791656991324 absolute error = 3.154898564616815e-11 relative error = 6.444102988106537e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.11999999999993 y[1] (closed_form) = -4.894832360858443 y[1] (numeric) = -4.894832360824056 absolute error = 3.438671569711005e-11 relative error = 7.025105899863626e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.12999999999993 y[1] (closed_form) = -4.893868939281004 y[1] (numeric) = -4.893868939243782 absolute error = 3.722266939121255e-11 relative error = 7.605980023788953e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.13999999999992 y[1] (closed_form) = -4.892901395691557 y[1] (numeric) = -4.892901395651504 absolute error = 4.005329401479685e-11 relative error = 8.186000651896595e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.14999999999992 y[1] (closed_form) = -4.891929733485499 y[1] (numeric) = -4.891929733442621 absolute error = 4.287858956786295e-11 relative error = 8.765168737882087e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.15999999999991 y[1] (closed_form) = -4.890953956052639 y[1] (numeric) = -4.89095395600694 absolute error = 4.569944422883054e-11 relative error = 9.343666826443275e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.16999999999991 y[1] (closed_form) = -4.889974066777211 y[1] (numeric) = -4.889974066728695 absolute error = 4.851585799769964e-11 relative error = 9.921495970156449e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.1799999999999 y[1] (closed_form) = -4.888990069037884 y[1] (numeric) = -4.888990068986558 absolute error = 5.132694269605054e-11 relative error = 1.049847554837666e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.18999999999989 y[1] (closed_form) = -4.888001966207786 y[1] (numeric) = -4.88800196615365 absolute error = 5.413536285914233e-11 relative error = 1.107515161274407e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.19999999999989 y[1] (closed_form) = -4.887009761654504 y[1] (numeric) = -4.887009761597565 absolute error = 5.693934213013563e-11 relative error = 1.165116193892331e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.20999999999988 y[1] (closed_form) = -4.886013458740107 y[1] (numeric) = -4.886013458680369 absolute error = 5.973710415219102e-11 relative error = 1.222614400403119e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.21999999999988 y[1] (closed_form) = -4.885013060821157 y[1] (numeric) = -4.885013060758626 absolute error = 6.253042528214792e-11 relative error = 1.280046225129984e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.22999999999987 y[1] (closed_form) = -4.884008571248722 y[1] (numeric) = -4.884008571183404 absolute error = 6.531752916316691e-11 relative error = 1.337375399946663e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.23999999999987 y[1] (closed_form) = -4.882999993368392 y[1] (numeric) = -4.88299999330029 absolute error = 6.81019685089268e-11 relative error = 1.394674761446164e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.24999999999986 y[1] (closed_form) = -4.881987330520286 y[1] (numeric) = -4.881987330449405 absolute error = 7.088107878416849e-11 relative error = 1.451889855203998e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.25999999999986 y[1] (closed_form) = -4.880970586039075 y[1] (numeric) = -4.880970585965419 absolute error = 7.365574816731169e-11 relative error = 1.509038968150873e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.26999999999985 y[1] (closed_form) = -4.879949763253984 y[1] (numeric) = -4.879949763177559 absolute error = 7.642508847993668e-11 relative error = 1.566104000812006e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.27999999999984 y[1] (closed_form) = -4.878924865488819 y[1] (numeric) = -4.878924865409626 absolute error = 7.919265243572227e-11 relative error = 1.623157859959952e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.28999999999984 y[1] (closed_form) = -4.877895896061965 y[1] (numeric) = -4.877895895980012 absolute error = 8.195222278573056e-11 relative error = 1.680073222798634e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.29999999999983 y[1] (closed_form) = -4.876862858286412 y[1] (numeric) = -4.876862858201702 absolute error = 8.471001677889944e-11 relative error = 1.736977627635486e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.30999999999983 y[1] (closed_form) = -4.87582575546976 y[1] (numeric) = -4.875825755382298 absolute error = 8.746248170155013e-11 relative error = 1.793798344894373e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.31999999999982 y[1] (closed_form) = -4.874784590914238 y[1] (numeric) = -4.874784590824029 absolute error = 9.020961755368262e-11 relative error = 1.850535462055449e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.32999999999982 y[1] (closed_form) = -4.873739367916712 y[1] (numeric) = -4.873739367823759 absolute error = 9.295231251371661e-11 relative error = 1.907207289860665e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.33999999999981 y[1] (closed_form) = -4.8726900897687 y[1] (numeric) = -4.87269008967301 absolute error = 9.569056658165209e-11 relative error = 1.963813926573655e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.34999999999981 y[1] (closed_form) = -4.871636759756388 y[1] (numeric) = -4.871636759657964 absolute error = 9.842437975748908e-11 relative error = 2.0203554700661e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.3599999999998 y[1] (closed_form) = -4.870579381160637 y[1] (numeric) = -4.870579381059483 absolute error = 1.011546402196473e-10 relative error = 2.076850253399269e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.36999999999979 y[1] (closed_form) = -4.869517957257003 y[1] (numeric) = -4.869517957153121 absolute error = 1.038813479681266e-10 relative error = 2.133298385588929e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.37999999999979 y[1] (closed_form) = -4.86845249131574 y[1] (numeric) = -4.868452491209139 absolute error = 1.066009502892484e-10 relative error = 2.189627001175452e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.38999999999978 y[1] (closed_form) = -4.867382986601825 y[1] (numeric) = -4.867382986492506 absolute error = 1.093187762535308e-10 relative error = 2.24594564583158e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.39999999999978 y[1] (closed_form) = -4.866309446374962 y[1] (numeric) = -4.866309446262932 absolute error = 1.120303849688753e-10 relative error = 2.302163193759278e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.40999999999977 y[1] (closed_form) = -4.865231873889598 y[1] (numeric) = -4.865231873774859 absolute error = 1.14738440970541e-10 relative error = 2.358334483219836e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.41999999999977 y[1] (closed_form) = -4.864150272394933 y[1] (numeric) = -4.864150272277492 absolute error = 1.174411679016885e-10 relative error = 2.414423102184807e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.42999999999976 y[1] (closed_form) = -4.863064645134939 y[1] (numeric) = -4.863064645014797 absolute error = 1.201421184759965e-10 relative error = 2.4705021882896e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.43999999999976 y[1] (closed_form) = -4.861974995348364 y[1] (numeric) = -4.861974995225528 absolute error = 1.22835963622947e-10 relative error = 2.52646226565272e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.44999999999975 y[1] (closed_form) = -4.860881326268752 y[1] (numeric) = -4.860881326143224 absolute error = 1.255271442346384e-10 relative error = 2.582394751261989e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.45999999999975 y[1] (closed_form) = -4.85978364112445 y[1] (numeric) = -4.859783640996236 absolute error = 1.282138839542313e-10 relative error = 2.638263211334349e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.46999999999974 y[1] (closed_form) = -4.858681943138626 y[1] (numeric) = -4.858681943007729 absolute error = 1.308961827817257e-10 relative error = 2.694067739226597e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.47999999999973 y[1] (closed_form) = -4.857576235529278 y[1] (numeric) = -4.857576235395703 absolute error = 1.335749288955412e-10 relative error = 2.749826712312772e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.48999999999973 y[1] (closed_form) = -4.856466521509244 y[1] (numeric) = -4.856466521372996 absolute error = 1.362483459388386e-10 relative error = 2.805503658583787e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.49999999999972 y[1] (closed_form) = -4.85535280428622 y[1] (numeric) = -4.855352804147302 absolute error = 1.389182102684572e-10 relative error = 2.861135243268474e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.50999999999972 y[1] (closed_form) = -4.85423508706277 y[1] (numeric) = -4.854235086921187 absolute error = 1.415836337059773e-10 relative error = 2.916703273875587e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.51999999999971 y[1] (closed_form) = -4.853113373036336 y[1] (numeric) = -4.853113372892092 absolute error = 1.442446162513988e-10 relative error = 2.972207841935343e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.52999999999971 y[1] (closed_form) = -4.851987665399254 y[1] (numeric) = -4.851987665252354 absolute error = 1.469002697263022e-10 relative error = 3.027630733150561e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.5399999999997 y[1] (closed_form) = -4.850857967338763 y[1] (numeric) = -4.850857967189212 absolute error = 1.495514823091071e-10 relative error = 3.082990335236568e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.5499999999997 y[1] (closed_form) = -4.849724282037021 y[1] (numeric) = -4.849724281884822 absolute error = 1.521991421782332e-10 relative error = 3.138305052556621e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.55999999999969 y[1] (closed_form) = -4.848586612671112 y[1] (numeric) = -4.848586612516269 absolute error = 1.548432493336804e-10 relative error = 3.193574987997924e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.56999999999968 y[1] (closed_form) = -4.847444962413062 y[1] (numeric) = -4.84744496225558 absolute error = 1.574829155970292e-10 relative error = 3.248781921572021e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.57999999999968 y[1] (closed_form) = -4.846299334429852 y[1] (numeric) = -4.846299334269734 absolute error = 1.601181409682795e-10 relative error = 3.303925942641278e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.58999999999967 y[1] (closed_form) = -4.845149731883425 y[1] (numeric) = -4.845149731720674 absolute error = 1.627507018042706e-10 relative error = 3.359043802780592e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.59999999999967 y[1] (closed_form) = -4.843996157930703 y[1] (numeric) = -4.843996157765325 absolute error = 1.653779335697436e-10 relative error = 3.41408060984902e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.60999999999966 y[1] (closed_form) = -4.842838615723596 y[1] (numeric) = -4.842838615555594 absolute error = 1.680016126215378e-10 relative error = 3.469073119142867e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.61999999999966 y[1] (closed_form) = -4.841677108409015 y[1] (numeric) = -4.841677108238394 absolute error = 1.706208507812335e-10 relative error = 3.524003087378535e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.62999999999965 y[1] (closed_form) = -4.840511639128885 y[1] (numeric) = -4.84051163895565 absolute error = 1.732356480488306e-10 relative error = 3.578870602199537e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.63999999999965 y[1] (closed_form) = -4.839342211020154 y[1] (numeric) = -4.839342210844308 absolute error = 1.758460044243293e-10 relative error = 3.633675750888057e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.64999999999964 y[1] (closed_form) = -4.838168827214809 y[1] (numeric) = -4.838168827036355 absolute error = 1.784536962645689e-10 relative error = 3.688455335844479e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.65999999999963 y[1] (closed_form) = -4.836991490839882 y[1] (numeric) = -4.836991490658826 absolute error = 1.810560590342902e-10 relative error = 3.743154383818281e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.66999999999963 y[1] (closed_form) = -4.835810205017467 y[1] (numeric) = -4.835810204833813 absolute error = 1.836539809119131e-10 relative error = 3.797791334353035e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.67999999999962 y[1] (closed_form) = -4.834624972864728 y[1] (numeric) = -4.83462497267848 absolute error = 1.862483500758572e-10 relative error = 3.852384644542487e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.68999999999962 y[1] (closed_form) = -4.833435797493916 y[1] (numeric) = -4.833435797305078 absolute error = 1.888382783477027e-10 relative error = 3.906916037771999e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.69999999999961 y[1] (closed_form) = -4.832242682012373 y[1] (numeric) = -4.832242681820949 absolute error = 1.914237657274498e-10 relative error = 3.961385599278965e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.70999999999961 y[1] (closed_form) = -4.831045629522547 y[1] (numeric) = -4.831045629328543 absolute error = 1.940048122150984e-10 relative error = 4.01579341394612e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.7199999999996 y[1] (closed_form) = -4.829844643122011 y[1] (numeric) = -4.829844642925428 absolute error = 1.965831941674878e-10 relative error = 4.070176345059754e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.7299999999996 y[1] (closed_form) = -4.828639725903459 y[1] (numeric) = -4.828639725704303 absolute error = 1.991562470493591e-10 relative error = 4.124479322426485e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.73999999999959 y[1] (closed_form) = -4.827430880954731 y[1] (numeric) = -4.827430880753004 absolute error = 2.017275235743909e-10 relative error = 4.178776010449991e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.74999999999958 y[1] (closed_form) = -4.826218111358818 y[1] (numeric) = -4.826218111154525 absolute error = 2.042925828504849e-10 relative error = 4.232974518281074e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.75999999999958 y[1] (closed_form) = -4.825001420193876 y[1] (numeric) = -4.825001419987021 absolute error = 2.068540894129001e-10 relative error = 4.287130124918976e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.76999999999957 y[1] (closed_form) = -4.823780810533234 y[1] (numeric) = -4.823780810323823 absolute error = 2.094111550832167e-10 relative error = 4.341224514719769e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.77999999999957 y[1] (closed_form) = -4.822556285445411 y[1] (numeric) = -4.822556285233446 absolute error = 2.119646680398546e-10 relative error = 4.395276187435468e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.78999999999956 y[1] (closed_form) = -4.821327847994121 y[1] (numeric) = -4.821327847779607 absolute error = 2.145146282828136e-10 relative error = 4.449285239377797e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.79999999999956 y[1] (closed_form) = -4.82009550123829 y[1] (numeric) = -4.820095501021228 absolute error = 2.170619239905136e-10 relative error = 4.50327019318912e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.80999999999955 y[1] (closed_form) = -4.81885924823206 y[1] (numeric) = -4.818859248012457 absolute error = 2.196030024492757e-10 relative error = 4.557157433677762e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.81999999999955 y[1] (closed_form) = -4.817619092024811 y[1] (numeric) = -4.817619091802669 absolute error = 2.221414163727786e-10 relative error = 4.611020757961464e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.82999999999954 y[1] (closed_form) = -4.816375035661159 y[1] (numeric) = -4.816375035436484 absolute error = 2.246753894041831e-10 relative error = 4.664823393956097e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.83999999999953 y[1] (closed_form) = -4.815127082180979 y[1] (numeric) = -4.815127081953773 absolute error = 2.272058097219087e-10 relative error = 4.718583867967144e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.84999999999953 y[1] (closed_form) = -4.813875234619408 y[1] (numeric) = -4.813875234389675 absolute error = 2.297326773259556e-10 relative error = 4.772302274762188e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.85999999999952 y[1] (closed_form) = -4.81261949600686 y[1] (numeric) = -4.812619495774604 absolute error = 2.322559922163236e-10 relative error = 4.8259787088722e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.86999999999952 y[1] (closed_form) = -4.811359869369038 y[1] (numeric) = -4.811359869134263 absolute error = 2.347748662145932e-10 relative error = 4.879594804563676e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.87999999999951 y[1] (closed_form) = -4.810096357726939 y[1] (numeric) = -4.810096357489649 absolute error = 2.37290187499184e-10 relative error = 4.933169106228007e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.88999999999951 y[1] (closed_form) = -4.808828964096874 y[1] (numeric) = -4.808828963857072 absolute error = 2.398010678916762e-10 relative error = 4.986683237895367e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.8999999999995 y[1] (closed_form) = -4.807557691490468 y[1] (numeric) = -4.807557691248159 absolute error = 2.423083955704897e-10 relative error = 5.040155753084011e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.9099999999995 y[1] (closed_form) = -4.806282542914682 y[1] (numeric) = -4.806282542669872 absolute error = 2.448095060003652e-10 relative error = 5.09353130646175e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.91999999999949 y[1] (closed_form) = -4.805003521371816 y[1] (numeric) = -4.805003521124506 absolute error = 2.473097282518211e-10 relative error = 5.146920853477643e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.92999999999948 y[1] (closed_form) = -4.803720629859524 y[1] (numeric) = -4.80372062960972 absolute error = 2.49803733254339e-10 relative error = 5.200213594886846e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.93999999999948 y[1] (closed_form) = -4.802433871370821 y[1] (numeric) = -4.802433871118526 absolute error = 2.522950737215979e-10 relative error = 5.253483556028268e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.94999999999947 y[1] (closed_form) = -4.801143248894099 y[1] (numeric) = -4.801143248639317 absolute error = 2.547819732967582e-10 relative error = 5.306693845376203e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.95999999999947 y[1] (closed_form) = -4.799848765413132 y[1] (numeric) = -4.799848765155867 absolute error = 2.572644319798201e-10 relative error = 5.359844539970143e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.96999999999946 y[1] (closed_form) = -4.79855042390709 y[1] (numeric) = -4.798550423647346 absolute error = 2.597442261276228e-10 relative error = 5.412972735131396e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.97999999999946 y[1] (closed_form) = -4.797248227350551 y[1] (numeric) = -4.797248227088332 absolute error = 2.622195793833271e-10 relative error = 5.466041508720241e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.98999999999945 y[1] (closed_form) = -4.795942178713508 y[1] (numeric) = -4.795942178448817 absolute error = 2.646913799253525e-10 relative error = 5.519069456261771e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 10.99999999999945 y[1] (closed_form) = -4.794632280961381 y[1] (numeric) = -4.794632280694221 absolute error = 2.671605159321189e-10 relative error = 5.572075193189789e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.001 Finished! diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 1001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %