R Under development (unstable) (2025-10-25 r88970 ucrt) -- "Unsuffered Consequences" Copyright (C) 2025 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # This file is part of the standard setup for testthat. > # It is recommended that you do not modify it. > # > # Where should you do additional test configuration? > # Learn more about the roles of various files in: > # * https://r-pkgs.org/testing-design.html#sec-tests-files-overview > # * https://testthat.r-lib.org/articles/special-files.html > > library(testthat) > library(StatOpt) > > test_check("StatOpt") --- Running Test: 'Quadratic Function (Exact Alpha) - Convergence and Accuracy' --- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- ✅ PASSED: Quadratic Function (Exact Alpha) - Convergence and Accuracy --- Running Test: 'General Function (Armijo Alpha) - Convergence and Accuracy' --- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- ✅ PASSED: General Function (Armijo Alpha) - Convergence and Accuracy --- Running Test: 'Error Handling - Missing Theta for Exact Alpha' --- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- ✅ PASSED: Error Handling - Missing Theta for Exact Alpha --- Running Test: 'Max Iteration Limit - Non-Convergence' --- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- ✅ PASSED: Max Iteration Limit - Non-Convergence --- Running Test: 'Iteration Data Frame (iter_df) Structure Check' --- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- ✅ PASSED: Iteration Data Frame (iter_df) Structure Check --- Running Test: 'Verbose Output - Code Path Execution' --- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- -------- Using numeric gradient: numDeriv::grad(func = f, x = x, method = 'Richardson') -------- ✅ PASSED: Verbose Output - Code Path Execution --- All Tests Complete --- Iter 1 | a = 0.763932, b = 2.000000 | x1 = 1.236068, f(x1) = 0.055728 | x2 = 1.527864, f(x2) = 0.278640 Iter 2 | a = 0.763932, b = 1.527864 | x1 = 1.055728, f(x1) = 0.003106 | x2 = 1.236068, f(x2) = 0.055728 Iter 3 | a = 0.763932, b = 1.236068 | x1 = 0.944272, f(x1) = 0.003106 | x2 = 1.055728, f(x2) = 0.003106 Iter 4 | a = 0.944272, b = 1.236068 | x1 = 1.055728, f(x1) = 0.003106 | x2 = 1.124612, f(x2) = 0.015528 Iter 5 | a = 0.944272, b = 1.124612 | x1 = 1.013156, f(x1) = 0.000173 | x2 = 1.055728, f(x2) = 0.003106 Iter 6 | a = 0.944272, b = 1.055728 | x1 = 0.986844, f(x1) = 0.000173 | x2 = 1.013156, f(x2) = 0.000173 Iter 7 | a = 0.986844, b = 1.055728 | x1 = 1.013156, f(x1) = 0.000173 | x2 = 1.029417, f(x2) = 0.000865 Iter 8 | a = 0.986844, b = 1.029417 | x1 = 1.003106, f(x1) = 0.000010 | x2 = 1.013156, f(x2) = 0.000173 Iter 9 | a = 0.986844, b = 1.013156 | x1 = 0.996894, f(x1) = 0.000010 | x2 = 1.003106, f(x2) = 0.000010 Iter 10 | a = 0.996894, b = 1.013156 | x1 = 1.003106, f(x1) = 0.000010 | x2 = 1.006944, f(x2) = 0.000048 Iter 11 | a = 0.996894, b = 1.006944 | x1 = 1.000733, f(x1) = 0.000001 | x2 = 1.003106, f(x2) = 0.000010 Iter 12 | a = 0.996894, b = 1.003106 | x1 = 0.999267, f(x1) = 0.000001 | x2 = 1.000733, f(x2) = 0.000001 Iter 13 | a = 0.999267, b = 1.003106 | x1 = 1.000733, f(x1) = 0.000001 | x2 = 1.001639, f(x2) = 0.000003 Iter 14 | a = 0.999267, b = 1.001639 | x1 = 1.000173, f(x1) = 0.000000 | x2 = 1.000733, f(x2) = 0.000001 Iter 15 | a = 0.999267, b = 1.000733 | x1 = 0.999827, f(x1) = 0.000000 | x2 = 1.000173, f(x2) = 0.000000 Iter 16 | a = 0.999827, b = 1.000733 | x1 = 1.000173, f(x1) = 0.000000 | x2 = 1.000387, f(x2) = 0.000000 Iter 17 | a = 0.999827, b = 1.000387 | x1 = 1.000041, f(x1) = 0.000000 | x2 = 1.000173, f(x2) = 0.000000 Iter 18 | a = 0.999827, b = 1.000173 | x1 = 0.999959, f(x1) = 0.000000 | x2 = 1.000041, f(x2) = 0.000000 Iter 19 | a = 0.999959, b = 1.000173 | x1 = 1.000041, f(x1) = 0.000000 | x2 = 1.000091, f(x2) = 0.000000 Iter 20 | a = 0.999959, b = 1.000091 | x1 = 1.000010, f(x1) = 0.000000 | x2 = 1.000041, f(x2) = 0.000000 Iter 21 | a = 0.999959, b = 1.000041 | x1 = 0.999990, f(x1) = 0.000000 | x2 = 1.000010, f(x2) = 0.000000 Iter 22 | a = 0.999990, b = 1.000041 | x1 = 1.000010, f(x1) = 0.000000 | x2 = 1.000022, f(x2) = 0.000000 Iter 23 | a = 0.999990, b = 1.000022 | x1 = 1.000002, f(x1) = 0.000000 | x2 = 1.000010, f(x2) = 0.000000 Iter 24 | a = 0.999990, b = 1.000010 | x1 = 0.999998, f(x1) = 0.000000 | x2 = 1.000002, f(x2) = 0.000000 Iter 25 | a = 0.999990, b = 1.000002 | x1 = 0.999995, f(x1) = 0.000000 | x2 = 0.999998, f(x2) = 0.000000 Iter 26 | a = 0.999995, b = 1.000002 | x1 = 0.999998, f(x1) = 0.000000 | x2 = 1.000000, f(x2) = 0.000000 Iter 27 | a = 0.999998, b = 1.000002 | x1 = 1.000000, f(x1) = 0.000000 | x2 = 1.000000, f(x2) = 0.000000 Iter 28 | a = 0.999998, b = 1.000000 | x1 = 0.999999, f(x1) = 0.000000 | x2 = 1.000000, f(x2) = 0.000000 Iter 29 | a = 0.999999, b = 1.000000 | x1 = 1.000000, f(x1) = 0.000000 | x2 = 1.000000, f(x2) = 0.000000 Iter 30 | a = 1.000000, b = 1.000000 | x1 = 1.000000, f(x1) = 0.000000 | x2 = 1.000000, f(x2) = 0.000000 Minimum at x = 1 with f(x) = 0 Iter 1 | a = 0.7639, b = 2.0000 | x1 = 1.2361, f(x1) = 0.0557 | x2 = 1.5279, f(x2) = 0.2786 Iter 2 | a = 0.7639, b = 1.5279 | x1 = 1.0557, f(x1) = 0.0031 | x2 = 1.2361, f(x2) = 0.0557 Iter 3 | a = 0.7639, b = 1.2361 | x1 = 0.9443, f(x1) = 0.0031 | x2 = 1.0557, f(x2) = 0.0031 Iter 4 | a = 0.9443, b = 1.2361 | x1 = 1.0557, f(x1) = 0.0031 | x2 = 1.1246, f(x2) = 0.0155 Iter 5 | a = 0.9443, b = 1.1246 | x1 = 1.0132, f(x1) = 0.0002 | x2 = 1.0557, f(x2) = 0.0031 Iter 6 | a = 0.9443, b = 1.0557 | x1 = 0.9868, f(x1) = 0.0002 | x2 = 1.0132, f(x2) = 0.0002 Iter 7 | a = 0.9868, b = 1.0557 | x1 = 1.0132, f(x1) = 0.0002 | x2 = 1.0294, f(x2) = 0.0009 Iter 8 | a = 0.9868, b = 1.0294 | x1 = 1.0031, f(x1) = 0.0000 | x2 = 1.0132, f(x2) = 0.0002 Iter 9 | a = 0.9868, b = 1.0132 | x1 = 0.9969, f(x1) = 0.0000 | x2 = 1.0031, f(x2) = 0.0000 Iter 10 | a = 0.9969, b = 1.0132 | x1 = 1.0031, f(x1) = 0.0000 | x2 = 1.0069, f(x2) = 0.0000 Iter 11 | a = 0.9969, b = 1.0069 | x1 = 1.0007, f(x1) = 0.0000 | x2 = 1.0031, f(x2) = 0.0000 Iter 12 | a = 0.9969, b = 1.0031 | x1 = 0.9993, f(x1) = 0.0000 | x2 = 1.0007, f(x2) = 0.0000 Iter 13 | a = 0.9993, b = 1.0031 | x1 = 1.0007, f(x1) = 0.0000 | x2 = 1.0016, f(x2) = 0.0000 Iter 14 | a = 0.9993, b = 1.0016 | x1 = 1.0002, f(x1) = 0.0000 | x2 = 1.0007, f(x2) = 0.0000 Iter 15 | a = 0.9993, b = 1.0007 | x1 = 0.9998, f(x1) = 0.0000 | x2 = 1.0002, f(x2) = 0.0000 Iter 16 | a = 0.9998, b = 1.0007 | x1 = 1.0002, f(x1) = 0.0000 | x2 = 1.0004, f(x2) = 0.0000 Iter 17 | a = 0.9998, b = 1.0004 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0002, f(x2) = 0.0000 Iter 18 | a = 0.9998, b = 1.0002 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 19 | a = 1.0000, b = 1.0002 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0001, f(x2) = 0.0000 Iter 20 | a = 1.0000, b = 1.0001 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 21 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 22 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 23 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 24 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 25 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 26 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 27 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 28 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 29 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 30 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Iter 31 | a = 1.0000, b = 1.0000 | x1 = 1.0000, f(x1) = 0.0000 | x2 = 1.0000, f(x2) = 0.0000 Minimum at x = 1 with f(x) = 0 x_min: 0, 0 f_min: 0 Iterations: 1 Converged: TRUE Iteration x1 x2 grad_norm f_x 1 0 0 2.828427 0 ------------- Gradient (numDeriv::grad) ------------- Computing numerical gradient using numDeriv::grad ------------- End Gradient ------------- ------------- Line Search (exact along d) ------------- Step size (alpha) will be computed using exact line search along search direction d ------------- End Line Search ------------- ------------- Position Update ------------- Position updated as x <- x + alpha * d ------------- End Position Update ------------- sm.quasi_newton: starting optimization iter grad_norm f(x) alpha ||d|| x (first 4 elements) 1 3.0000e+00 0 0.5 3 0,0 2 1.5000e+00 -2.25 0.2857 1.677 1.5,0 sm.quasi_newton: finished converged: TRUE | iterations: 2 | f_min: -2.57143 ✅ Quadratic Test Passed! x_min = 1.714286, -0.428571 | f_min = -2.571429 ------------- Gradient (numDeriv::grad) ------------- Computing numerical gradient using numDeriv::grad ------------- End Gradient ------------- ------------- Line Search (exact along d) ------------- Step size (alpha) will be computed using exact line search along search direction d ------------- End Line Search ------------- ------------- Position Update ------------- Position updated as x <- x + alpha * d ------------- End Position Update ------------- sm.quasi_newton: starting optimization iter grad_norm f(x) alpha ||d|| x (first 4 elements) 1 1.0000e+01 25 0.5 10 0 sm.quasi_newton: finished converged: TRUE | iterations: 1 | f_min: 0 ✅ 1D Quadratic Test Passed! x_min = 5 | f_min = 0 ------------- Gradient (numDeriv::grad) ------------- Computing numerical gradient using numDeriv::grad ------------- End Gradient ------------- ------------- Line Search (exact along d) ------------- Step size (alpha) will be computed using exact line search along search direction d ------------- End Line Search ------------- ------------- Position Update ------------- Position updated as x <- x + alpha * d ------------- End Position Update ------------- sm.quasi_newton: starting optimization iter grad_norm f(x) alpha ||d|| x (first 4 elements) 1 2.3287e+02 24.2 0.01225 232.9 -1.2,1 2 2.9033e-01 0.194711 0.001285 0.1997 1.441063,2.077985 3 4.4435e-01 0.194685 0.9999 0.008455 1.441157,2.077746 4 4.4494e-01 0.192247 0.2241 1.595 1.438387,2.069758 5 8.2040e+00 0.121219 0.9999 0.1204 1.321134,1.731943 6 7.2877e+00 0.0922382 0.7537 0.1171 1.277538,1.619769 7 2.5626e+00 0.0602155 0.5857 0.3746 1.238883,1.540445 8 3.7107e+00 0.0298148 0.9999 0.08138 1.158853,1.336172 9 4.2046e+00 0.0225431 0.9999 0.1047 1.126707,1.261412 10 2.4195e-01 0.00649316 0.6326 0.1319 1.08056,1.167429 11 1.7158e+00 0.0033848 0.9999 0.03693 1.046341,1.091312 12 9.8297e-01 0.00129595 0.9999 0.03437 1.029735,1.058326 13 1.6424e-01 0.000204173 0.7798 0.0325 1.013956,1.027799 14 3.0124e-01 5.17058e-05 0.8452 0.00476 1.002838,1.005023 15 9.1472e-03 6.52591e-07 0.9976 0.001732 1.000773,1.00157 16 1.4218e-03 1.10757e-09 0.9999 2.128e-05 1.000011,1.000019 17 3.6315e-05 8.45779e-13 0.9999 9.719e-07 1,1.000001 sm.quasi_newton: finished converged: TRUE | iterations: 17 | f_min: 1.04849e-18 ✅ Rosenbrock Test Passed! x_min = 1, 1 | f_min = 0 ------------- Gradient (numDeriv::grad) ------------- Computing numerical gradient using numDeriv::grad ------------- End Gradient ------------- ------------- Line Search (exact along d) ------------- Step size (alpha) will be computed using exact line search along search direction d ------------- End Line Search ------------- ------------- Position Update ------------- Position updated as x <- x + alpha * d ------------- End Position Update ------------- sm.quasi_newton: starting optimization iter grad_norm f(x) alpha ||d|| x (first 4 elements) 1 3.0000e+00 0 0.05 30 0,0 2 1.5000e+00 -2.25 0.02857 16.77 1.5,0 sm.quasi_newton: finished converged: TRUE | iterations: 2 | f_min: -2.57143 ✅ Custom Hessian Test Passed! x_min = 1.714286, -0.428571 | f_min = -2.571429 ------------- Gradient (numDeriv::grad) ------------- Computing numerical gradient using numDeriv::grad ------------- End Gradient ------------- ------------- Line Search (exact along d) ------------- Step size (alpha) will be computed using exact line search along search direction d ------------- End Line Search ------------- ------------- Position Update ------------- Position updated as x <- x + alpha * d ------------- End Position Update ------------- sm.quasi_newton: starting optimization iter grad_norm f(x) alpha ||d|| x (first 4 elements) sm.quasi_newton: finished converged: TRUE | iterations: 0 | f_min: 0 ✅ Flat Function Test Passed! x_min = 0, 0 | f_min = 0 ✅ High-Dimensional Quadratic Test Passed! x_min = 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | f_min = 0 ------------- Gradient (numDeriv::grad) ------------- Gradient will be computed using numDeriv::grad ------------- End Gradient ------------- ------------- Line Search (exact along -grad) ------------- Step size (alpha) will be computed using exact line search if alpha is NULL ------------- End Line Search ------------- ------------- Position Update ------------- x will be updated using x <- x - alpha_k * grad ------------- End Position Update ------------- x_min: 1.714, -0.429 f_min: -2.571 Iterations: 10 Converged: TRUE Iteration x1 x2 grad_norm alpha f_x 1 1.5000 0.0000 3.0000 0.50 -2.2500 2 1.5000 -0.3750 1.5000 0.25 -2.5312 3 1.6875 -0.3750 0.3750 0.50 -2.5664 4 1.6875 -0.4219 0.1875 0.25 -2.5708 5 1.7109 -0.4219 0.0469 0.50 -2.5714 6 1.7109 -0.4277 0.0234 0.25 -2.5714 7 1.7139 -0.4277 0.0059 0.50 -2.5714 8 1.7139 -0.4285 0.0029 0.25 -2.5714 9 1.7142 -0.4285 0.0007 0.50 -2.5714 10 1.7142 -0.4286 0.0004 0.25 -2.5714 ✅ Quadratic Test Passed! x_min = 1.714233, -0.428558 | f_min = -2.571429 ------------- Gradient (numDeriv::grad) ------------- Gradient will be computed using numDeriv::grad ------------- End Gradient ------------- ------------- Line Search (exact along -grad) ------------- Step size (alpha) will be computed using exact line search if alpha is NULL ------------- End Line Search ------------- ------------- Position Update ------------- x will be updated using x <- x - alpha_k * grad ------------- End Position Update ------------- x_min: 5 f_min: 0 Iterations: 1 Converged: TRUE Iteration x1 grad_norm alpha f_x 1 5 10 0.5 0 ✅ 1D Quadratic Test Passed! x_min = 5 | f_min = 0 ------------- Gradient (numDeriv::grad) ------------- Gradient will be computed using numDeriv::grad ------------- End Gradient ------------- ------------- Line Search (exact along -grad) ------------- Step size (alpha) will be computed using exact line search if alpha is NULL ------------- End Line Search ------------- ------------- Position Update ------------- x will be updated using x <- x - alpha_k * grad ------------- End Position Update ------------- x_min: 1.323, 1.751 f_min: 0.104 Iterations: 1000 Converged: FALSE Iteration x1 x2 grad_norm alpha f_x 1 1.4411 2.0780 232.8677 0.0122 0.1947 2 1.4329 2.0600 0.2903 0.0681 0.1919 3 1.4346 2.0592 3.2424 0.0005 0.1890 4 1.4313 2.0532 0.2894 0.0237 0.1880 5 1.4323 2.0527 1.8910 0.0006 0.1870 6 1.4282 2.0446 0.2875 0.0313 0.1857 7 1.4293 2.0441 2.1571 0.0006 0.1844 8 1.4267 2.0396 0.2879 0.0181 0.1837 9 1.4276 2.0391 1.6307 0.0006 0.1829 10 1.4266 2.0379 0.2996 0.0050 0.1827 11 1.4271 2.0376 0.8517 0.0006 0.1825 12 1.4263 2.0368 0.3065 0.0036 0.1823 13 1.4267 2.0365 0.7219 0.0007 0.1822 14 1.4260 2.0357 0.3091 0.0033 0.1820 15 1.4263 2.0354 0.6960 0.0007 0.1818 16 1.4256 2.0347 0.3104 0.0032 0.1817 17 1.4259 2.0344 0.6790 0.0007 0.1815 18 1.4253 2.0337 0.3114 0.0030 0.1814 19 1.4256 2.0334 0.6665 0.0007 0.1813 20 1.4249 2.0328 0.3122 0.0030 0.1811 21 1.4253 2.0324 0.6568 0.0007 0.1810 22 1.4246 2.0318 0.3129 0.0029 0.1808 23 1.4249 2.0315 0.6490 0.0007 0.1807 24 1.4243 2.0309 0.3134 0.0028 0.1805 25 1.4246 2.0306 0.6426 0.0007 0.1804 26 1.4240 2.0300 0.3138 0.0028 0.1803 27 1.4243 2.0296 0.6371 0.0007 0.1801 28 1.4236 2.0290 0.3142 0.0028 0.1800 29 1.4240 2.0287 0.6325 0.0007 0.1799 30 1.4234 2.0282 0.3168 0.0026 0.1797 31 1.4237 2.0279 0.6068 0.0007 0.1796 32 1.4231 2.0273 0.3196 0.0024 0.1795 33 1.4234 2.0270 0.5858 0.0007 0.1794 34 1.4228 2.0266 0.3224 0.0023 0.1792 35 1.4231 2.0262 0.5682 0.0007 0.1791 36 1.4226 2.0258 0.3250 0.0021 0.1790 37 1.4228 2.0255 0.5528 0.0007 0.1789 38 1.4223 2.0250 0.3276 0.0020 0.1788 39 1.4226 2.0247 0.5395 0.0008 0.1787 40 1.4221 2.0243 0.3301 0.0020 0.1786 41 1.4223 2.0240 0.5276 0.0008 0.1785 42 1.4218 2.0236 0.3325 0.0019 0.1784 43 1.4221 2.0233 0.5170 0.0008 0.1782 44 1.4216 2.0229 0.3350 0.0018 0.1781 45 1.4218 2.0226 0.5073 0.0008 0.1780 46 1.4214 2.0223 0.3373 0.0018 0.1779 47 1.4216 2.0219 0.4984 0.0008 0.1778 48 1.4211 2.0216 0.3397 0.0017 0.1777 49 1.4214 2.0213 0.4901 0.0008 0.1776 50 1.4209 2.0209 0.3421 0.0016 0.1776 51 1.4211 2.0206 0.4824 0.0008 0.1775 52 1.4207 2.0203 0.3445 0.0016 0.1774 53 1.4209 2.0200 0.4752 0.0008 0.1773 54 1.4205 2.0197 0.3469 0.0015 0.1772 55 1.4207 2.0193 0.4657 0.0009 0.1771 56 1.4203 2.0190 0.3504 0.0015 0.1770 57 1.4205 2.0187 0.4566 0.0009 0.1769 58 1.4200 2.0184 0.3541 0.0014 0.1768 59 1.4203 2.0181 0.4477 0.0009 0.1767 60 1.4198 2.0178 0.3581 0.0014 0.1766 61 1.4201 2.0175 0.4390 0.0009 0.1765 62 1.4196 2.0172 0.3624 0.0014 0.1764 63 1.4198 2.0169 0.4434 0.0009 0.1764 64 1.4194 2.0166 0.3598 0.0014 0.1763 65 1.4196 2.0163 0.4347 0.0009 0.1762 66 1.4192 2.0160 0.3643 0.0014 0.1761 67 1.4194 2.0157 0.4393 0.0009 0.1760 68 1.4190 2.0154 0.3615 0.0014 0.1759 69 1.4192 2.0151 0.4438 0.0009 0.1758 70 1.4188 2.0148 0.3590 0.0014 0.1757 71 1.4190 2.0145 0.4351 0.0009 0.1756 72 1.4186 2.0142 0.3634 0.0014 0.1756 73 1.4188 2.0139 0.4397 0.0009 0.1755 74 1.4184 2.0136 0.3607 0.0014 0.1754 75 1.4186 2.0133 0.4441 0.0009 0.1753 76 1.4181 2.0130 0.3581 0.0014 0.1752 77 1.4184 2.0127 0.4354 0.0009 0.1751 78 1.4179 2.0124 0.3626 0.0014 0.1750 79 1.4181 2.0121 0.4400 0.0009 0.1749 80 1.4177 2.0118 0.3598 0.0014 0.1748 81 1.4179 2.0115 0.4443 0.0009 0.1748 82 1.4175 2.0112 0.3574 0.0014 0.1747 83 1.4177 2.0109 0.4357 0.0009 0.1746 84 1.4173 2.0106 0.3617 0.0014 0.1745 85 1.4175 2.0103 0.4402 0.0009 0.1744 86 1.4171 2.0100 0.3590 0.0014 0.1743 87 1.4173 2.0096 0.4446 0.0009 0.1742 88 1.4169 2.0094 0.3566 0.0014 0.1741 89 1.4171 2.0090 0.4360 0.0009 0.1740 90 1.4167 2.0088 0.3609 0.0014 0.1740 91 1.4169 2.0084 0.4405 0.0009 0.1739 92 1.4164 2.0082 0.3583 0.0014 0.1738 93 1.4167 2.0078 0.4319 0.0009 0.1737 94 1.4162 2.0076 0.3627 0.0014 0.1736 95 1.4164 2.0072 0.4365 0.0009 0.1735 96 1.4160 2.0070 0.3599 0.0014 0.1734 97 1.4162 2.0066 0.4409 0.0009 0.1733 98 1.4158 2.0064 0.3573 0.0014 0.1732 99 1.4160 2.0060 0.4324 0.0009 0.1732 100 1.4156 2.0058 0.3617 0.0014 0.1731 101 1.4158 2.0054 0.4370 0.0009 0.1730 102 1.4154 2.0052 0.3590 0.0014 0.1729 103 1.4156 2.0048 0.4414 0.0009 0.1728 104 1.4152 2.0046 0.3564 0.0014 0.1727 105 1.4154 2.0042 0.4329 0.0009 0.1726 106 1.4150 2.0040 0.3608 0.0014 0.1725 107 1.4152 2.0036 0.4374 0.0009 0.1725 108 1.4147 2.0034 0.3581 0.0014 0.1724 109 1.4150 2.0030 0.4418 0.0009 0.1723 110 1.4145 2.0028 0.3556 0.0014 0.1722 111 1.4147 2.0024 0.4333 0.0009 0.1721 112 1.4143 2.0022 0.3599 0.0014 0.1720 113 1.4145 2.0018 0.4378 0.0009 0.1719 114 1.4141 2.0016 0.3572 0.0014 0.1718 115 1.4143 2.0012 0.4293 0.0009 0.1717 116 1.4139 2.0010 0.3617 0.0014 0.1717 117 1.4141 2.0006 0.4340 0.0009 0.1716 118 1.4137 2.0004 0.3588 0.0014 0.1715 119 1.4139 2.0000 0.4384 0.0009 0.1714 120 1.4135 1.9998 0.3562 0.0014 0.1713 121 1.4137 1.9994 0.4300 0.0009 0.1712 122 1.4133 1.9992 0.3606 0.0014 0.1711 123 1.4135 1.9988 0.4346 0.0009 0.1710 124 1.4130 1.9986 0.3578 0.0014 0.1710 125 1.4133 1.9982 0.4390 0.0009 0.1709 126 1.4128 1.9980 0.3552 0.0014 0.1708 127 1.4131 1.9976 0.4306 0.0009 0.1707 128 1.4126 1.9974 0.3596 0.0014 0.1706 129 1.4128 1.9970 0.4351 0.0009 0.1705 130 1.4124 1.9968 0.3568 0.0014 0.1704 131 1.4126 1.9964 0.4267 0.0010 0.1703 132 1.4122 1.9962 0.3634 0.0013 0.1703 133 1.4124 1.9958 0.4281 0.0010 0.1702 134 1.4120 1.9956 0.3603 0.0014 0.1701 135 1.4122 1.9952 0.4327 0.0009 0.1700 136 1.4118 1.9950 0.3574 0.0014 0.1699 137 1.4120 1.9946 0.4372 0.0009 0.1698 138 1.4116 1.9944 0.3548 0.0014 0.1697 139 1.4118 1.9940 0.4288 0.0009 0.1696 140 1.4114 1.9938 0.3592 0.0014 0.1696 141 1.4116 1.9934 0.4334 0.0009 0.1695 142 1.4112 1.9932 0.3564 0.0014 0.1694 143 1.4114 1.9928 0.4251 0.0010 0.1693 144 1.4109 1.9926 0.3629 0.0013 0.1692 145 1.4112 1.9923 0.4265 0.0010 0.1691 146 1.4107 1.9920 0.3619 0.0013 0.1690 147 1.4109 1.9917 0.4278 0.0010 0.1690 148 1.4105 1.9914 0.3588 0.0014 0.1689 149 1.4107 1.9911 0.4324 0.0009 0.1688 150 1.4103 1.9908 0.3560 0.0014 0.1687 151 1.4105 1.9905 0.4241 0.0010 0.1686 152 1.4101 1.9902 0.3625 0.0013 0.1685 153 1.4103 1.9899 0.4256 0.0010 0.1684 154 1.4099 1.9896 0.3615 0.0013 0.1684 155 1.4101 1.9893 0.4270 0.0010 0.1683 156 1.4097 1.9890 0.3584 0.0014 0.1682 157 1.4099 1.9887 0.4316 0.0009 0.1681 158 1.4095 1.9884 0.3556 0.0014 0.1680 159 1.4097 1.9881 0.4233 0.0010 0.1679 160 1.4093 1.9879 0.3621 0.0013 0.1678 161 1.4095 1.9875 0.4248 0.0010 0.1677 162 1.4091 1.9873 0.3610 0.0013 0.1677 163 1.4093 1.9869 0.4262 0.0010 0.1676 164 1.4088 1.9867 0.3579 0.0014 0.1675 165 1.4090 1.9863 0.4308 0.0009 0.1674 166 1.4086 1.9861 0.3551 0.0014 0.1673 167 1.4088 1.9857 0.4225 0.0010 0.1672 168 1.4084 1.9855 0.3616 0.0013 0.1671 169 1.4086 1.9851 0.4241 0.0010 0.1671 170 1.4082 1.9849 0.3605 0.0013 0.1670 171 1.4084 1.9845 0.4255 0.0010 0.1669 172 1.4080 1.9843 0.3594 0.0013 0.1668 173 1.4082 1.9840 0.4267 0.0010 0.1667 174 1.4078 1.9837 0.3565 0.0014 0.1666 175 1.4080 1.9834 0.4313 0.0009 0.1665 176 1.4076 1.9831 0.3537 0.0014 0.1665 177 1.4078 1.9828 0.4231 0.0010 0.1664 178 1.4074 1.9825 0.3601 0.0013 0.1663 179 1.4076 1.9822 0.4245 0.0010 0.1662 180 1.4072 1.9819 0.3591 0.0013 0.1661 181 1.4074 1.9816 0.4258 0.0010 0.1660 182 1.4069 1.9813 0.3561 0.0014 0.1659 183 1.4071 1.9810 0.4304 0.0009 0.1659 184 1.4067 1.9807 0.3533 0.0014 0.1658 185 1.4069 1.9804 0.4222 0.0010 0.1657 186 1.4065 1.9801 0.3597 0.0013 0.1656 187 1.4067 1.9798 0.4237 0.0010 0.1655 188 1.4063 1.9795 0.3586 0.0013 0.1654 189 1.4065 1.9792 0.4250 0.0010 0.1653 190 1.4061 1.9790 0.3556 0.0014 0.1653 191 1.4063 1.9786 0.4296 0.0009 0.1652 192 1.4059 1.9784 0.3528 0.0014 0.1651 193 1.4061 1.9780 0.4214 0.0010 0.1650 194 1.4057 1.9778 0.3592 0.0013 0.1649 195 1.4059 1.9774 0.4229 0.0010 0.1648 196 1.4055 1.9772 0.3581 0.0013 0.1647 197 1.4057 1.9768 0.4243 0.0010 0.1647 198 1.4053 1.9766 0.3571 0.0014 0.1646 199 1.4055 1.9762 0.4255 0.0010 0.1645 200 1.4050 1.9760 0.3542 0.0014 0.1644 201 1.4053 1.9756 0.4300 0.0009 0.1643 202 1.4048 1.9754 0.3515 0.0014 0.1642 203 1.4050 1.9750 0.4219 0.0010 0.1641 204 1.4046 1.9748 0.3578 0.0013 0.1641 205 1.4048 1.9745 0.4233 0.0010 0.1640 206 1.4044 1.9742 0.3567 0.0014 0.1639 207 1.4046 1.9739 0.4245 0.0010 0.1638 208 1.4042 1.9736 0.3538 0.0014 0.1637 209 1.4044 1.9733 0.4291 0.0009 0.1636 210 1.4040 1.9730 0.3511 0.0014 0.1635 211 1.4042 1.9727 0.4210 0.0010 0.1635 212 1.4038 1.9724 0.3573 0.0013 0.1634 213 1.4040 1.9721 0.4224 0.0010 0.1633 214 1.4036 1.9718 0.3563 0.0014 0.1632 215 1.4038 1.9715 0.4237 0.0010 0.1631 216 1.4034 1.9712 0.3554 0.0014 0.1630 217 1.4036 1.9709 0.4248 0.0010 0.1629 218 1.4032 1.9707 0.3525 0.0014 0.1629 219 1.4034 1.9703 0.4168 0.0010 0.1628 220 1.4029 1.9701 0.3588 0.0013 0.1627 221 1.4032 1.9697 0.4186 0.0010 0.1626 222 1.4027 1.9695 0.3575 0.0013 0.1625 223 1.4029 1.9691 0.4202 0.0010 0.1624 224 1.4025 1.9689 0.3564 0.0013 0.1624 225 1.4027 1.9685 0.4216 0.0010 0.1623 226 1.4023 1.9683 0.3554 0.0014 0.1622 227 1.4025 1.9679 0.4229 0.0010 0.1621 228 1.4021 1.9677 0.3544 0.0014 0.1620 229 1.4023 1.9674 0.4240 0.0010 0.1619 230 1.4019 1.9671 0.3515 0.0014 0.1618 231 1.4021 1.9668 0.4160 0.0010 0.1618 232 1.4017 1.9665 0.3578 0.0013 0.1617 233 1.4019 1.9662 0.4178 0.0010 0.1616 234 1.4015 1.9659 0.3566 0.0013 0.1615 235 1.4017 1.9656 0.4194 0.0010 0.1614 236 1.4013 1.9653 0.3554 0.0014 0.1613 237 1.4015 1.9650 0.4208 0.0010 0.1613 238 1.4011 1.9648 0.3544 0.0014 0.1612 239 1.4013 1.9644 0.4221 0.0010 0.1611 240 1.4008 1.9642 0.3535 0.0014 0.1610 241 1.4010 1.9638 0.4233 0.0010 0.1609 242 1.4006 1.9636 0.3506 0.0014 0.1608 243 1.4008 1.9632 0.4153 0.0010 0.1607 244 1.4004 1.9630 0.3568 0.0013 0.1607 245 1.4006 1.9626 0.4171 0.0010 0.1606 246 1.4002 1.9624 0.3556 0.0013 0.1605 247 1.4004 1.9621 0.4187 0.0010 0.1604 248 1.4000 1.9618 0.3544 0.0014 0.1603 249 1.4002 1.9615 0.4201 0.0010 0.1602 250 1.3998 1.9612 0.3534 0.0014 0.1602 251 1.4000 1.9609 0.4214 0.0010 0.1601 252 1.3996 1.9606 0.3525 0.0014 0.1600 253 1.3998 1.9603 0.4225 0.0010 0.1599 254 1.3994 1.9600 0.3496 0.0014 0.1598 255 1.3996 1.9597 0.4146 0.0010 0.1597 256 1.3992 1.9595 0.3558 0.0013 0.1597 257 1.3994 1.9591 0.4164 0.0010 0.1596 258 1.3989 1.9589 0.3546 0.0013 0.1595 259 1.3992 1.9585 0.4180 0.0010 0.1594 260 1.3987 1.9583 0.3534 0.0014 0.1593 261 1.3989 1.9579 0.4194 0.0010 0.1592 262 1.3985 1.9577 0.3524 0.0014 0.1592 263 1.3987 1.9573 0.4206 0.0010 0.1591 264 1.3983 1.9571 0.3515 0.0014 0.1590 265 1.3985 1.9567 0.4218 0.0010 0.1589 266 1.3981 1.9565 0.3486 0.0014 0.1588 267 1.3983 1.9562 0.4139 0.0010 0.1587 268 1.3979 1.9559 0.3548 0.0013 0.1586 269 1.3981 1.9556 0.4157 0.0010 0.1586 270 1.3977 1.9553 0.3535 0.0014 0.1585 271 1.3979 1.9550 0.4173 0.0010 0.1584 272 1.3975 1.9547 0.3524 0.0014 0.1583 273 1.3977 1.9544 0.4187 0.0010 0.1582 274 1.3973 1.9542 0.3514 0.0014 0.1581 275 1.3975 1.9538 0.4199 0.0010 0.1581 276 1.3971 1.9536 0.3505 0.0013 0.1580 277 1.3973 1.9532 0.4087 0.0010 0.1579 278 1.3969 1.9530 0.3568 0.0013 0.1578 279 1.3971 1.9526 0.4108 0.0010 0.1577 280 1.3966 1.9524 0.3552 0.0013 0.1576 281 1.3968 1.9520 0.4128 0.0010 0.1576 282 1.3964 1.9518 0.3538 0.0013 0.1575 283 1.3966 1.9515 0.4145 0.0010 0.1574 284 1.3962 1.9512 0.3526 0.0014 0.1573 285 1.3964 1.9509 0.4161 0.0010 0.1572 286 1.3960 1.9506 0.3514 0.0014 0.1571 287 1.3962 1.9503 0.4176 0.0010 0.1571 288 1.3958 1.9500 0.3504 0.0014 0.1570 289 1.3960 1.9497 0.4188 0.0010 0.1569 290 1.3956 1.9495 0.3495 0.0013 0.1568 291 1.3958 1.9491 0.4076 0.0010 0.1567 292 1.3954 1.9489 0.3557 0.0013 0.1566 293 1.3956 1.9485 0.4098 0.0010 0.1566 294 1.3952 1.9483 0.3542 0.0013 0.1565 295 1.3954 1.9479 0.4118 0.0010 0.1564 296 1.3950 1.9477 0.3528 0.0013 0.1563 297 1.3952 1.9474 0.4135 0.0010 0.1562 298 1.3948 1.9471 0.3515 0.0014 0.1561 299 1.3950 1.9468 0.4151 0.0010 0.1561 300 1.3945 1.9465 0.3503 0.0014 0.1560 301 1.3947 1.9462 0.4166 0.0010 0.1559 302 1.3943 1.9460 0.3493 0.0013 0.1558 303 1.3945 1.9456 0.4055 0.0010 0.1557 304 1.3941 1.9454 0.3556 0.0013 0.1557 305 1.3943 1.9450 0.4078 0.0010 0.1556 306 1.3939 1.9448 0.3539 0.0013 0.1555 307 1.3941 1.9444 0.4099 0.0010 0.1554 308 1.3937 1.9442 0.3524 0.0013 0.1553 309 1.3939 1.9439 0.4117 0.0010 0.1552 310 1.3935 1.9436 0.3511 0.0014 0.1552 311 1.3937 1.9433 0.4134 0.0010 0.1551 312 1.3933 1.9430 0.3499 0.0014 0.1550 313 1.3935 1.9427 0.4150 0.0010 0.1549 314 1.3931 1.9425 0.3488 0.0013 0.1548 315 1.3933 1.9421 0.4040 0.0010 0.1547 316 1.3929 1.9419 0.3550 0.0013 0.1547 317 1.3931 1.9415 0.4064 0.0010 0.1546 318 1.3927 1.9413 0.3533 0.0013 0.1545 319 1.3929 1.9409 0.4085 0.0010 0.1544 320 1.3925 1.9407 0.3518 0.0013 0.1543 321 1.3927 1.9404 0.4104 0.0010 0.1543 322 1.3922 1.9401 0.3505 0.0014 0.1542 323 1.3924 1.9398 0.4121 0.0010 0.1541 324 1.3920 1.9395 0.3492 0.0014 0.1540 325 1.3922 1.9392 0.4137 0.0010 0.1539 326 1.3918 1.9390 0.3481 0.0013 0.1538 327 1.3920 1.9386 0.4029 0.0010 0.1538 328 1.3916 1.9384 0.3543 0.0013 0.1537 329 1.3918 1.9380 0.4052 0.0010 0.1536 330 1.3914 1.9378 0.3526 0.0013 0.1535 331 1.3916 1.9374 0.4074 0.0010 0.1534 332 1.3912 1.9372 0.3510 0.0013 0.1534 333 1.3914 1.9369 0.4093 0.0010 0.1533 334 1.3910 1.9366 0.3497 0.0014 0.1532 335 1.3912 1.9363 0.4111 0.0010 0.1531 336 1.3908 1.9360 0.3484 0.0014 0.1530 337 1.3910 1.9357 0.4127 0.0010 0.1529 338 1.3906 1.9355 0.3473 0.0013 0.1529 339 1.3908 1.9351 0.4019 0.0010 0.1528 340 1.3904 1.9349 0.3534 0.0013 0.1527 341 1.3906 1.9345 0.4043 0.0010 0.1526 342 1.3902 1.9343 0.3517 0.0013 0.1525 343 1.3904 1.9339 0.4064 0.0010 0.1525 344 1.3899 1.9337 0.3502 0.0013 0.1524 345 1.3901 1.9334 0.4084 0.0010 0.1523 346 1.3897 1.9331 0.3488 0.0014 0.1522 347 1.3899 1.9328 0.4102 0.0010 0.1521 348 1.3895 1.9325 0.3475 0.0013 0.1520 349 1.3897 1.9322 0.3996 0.0010 0.1520 350 1.3893 1.9320 0.3537 0.0013 0.1519 351 1.3895 1.9316 0.4021 0.0010 0.1518 352 1.3891 1.9314 0.3519 0.0013 0.1517 353 1.3893 1.9310 0.4044 0.0010 0.1516 354 1.3889 1.9308 0.3502 0.0013 0.1516 355 1.3891 1.9305 0.4064 0.0010 0.1515 356 1.3887 1.9302 0.3487 0.0014 0.1514 357 1.3889 1.9299 0.4083 0.0010 0.1513 358 1.3885 1.9296 0.3474 0.0014 0.1512 359 1.3887 1.9293 0.4100 0.0010 0.1511 360 1.3883 1.9291 0.3462 0.0013 0.1511 361 1.3885 1.9287 0.3995 0.0010 0.1510 362 1.3881 1.9285 0.3523 0.0013 0.1509 363 1.3883 1.9281 0.4019 0.0010 0.1508 364 1.3879 1.9279 0.3505 0.0013 0.1507 365 1.3881 1.9276 0.4041 0.0010 0.1507 366 1.3876 1.9273 0.3489 0.0013 0.1506 367 1.3878 1.9270 0.4062 0.0010 0.1505 368 1.3874 1.9267 0.3474 0.0014 0.1504 369 1.3876 1.9264 0.4080 0.0010 0.1503 370 1.3872 1.9262 0.3461 0.0013 0.1503 371 1.3874 1.9258 0.3976 0.0010 0.1502 372 1.3870 1.9256 0.3523 0.0013 0.1501 373 1.3872 1.9252 0.4001 0.0010 0.1500 374 1.3868 1.9250 0.3504 0.0013 0.1499 375 1.3870 1.9247 0.4024 0.0010 0.1499 376 1.3866 1.9244 0.3487 0.0013 0.1498 377 1.3868 1.9241 0.4045 0.0010 0.1497 378 1.3864 1.9238 0.3472 0.0014 0.1496 379 1.3866 1.9235 0.4065 0.0010 0.1495 380 1.3862 1.9233 0.3458 0.0013 0.1494 381 1.3864 1.9229 0.3961 0.0010 0.1494 382 1.3860 1.9227 0.3520 0.0013 0.1493 383 1.3862 1.9223 0.3987 0.0010 0.1492 384 1.3858 1.9221 0.3500 0.0013 0.1491 385 1.3860 1.9218 0.4011 0.0010 0.1490 386 1.3856 1.9215 0.3483 0.0013 0.1490 387 1.3858 1.9212 0.4033 0.0010 0.1489 388 1.3854 1.9210 0.3468 0.0014 0.1488 389 1.3856 1.9206 0.4052 0.0010 0.1487 390 1.3852 1.9204 0.3454 0.0013 0.1486 391 1.3853 1.9200 0.3950 0.0010 0.1486 392 1.3849 1.9198 0.3515 0.0013 0.1485 393 1.3851 1.9194 0.3976 0.0010 0.1484 394 1.3847 1.9192 0.3495 0.0013 0.1483 395 1.3849 1.9189 0.4000 0.0010 0.1482 396 1.3845 1.9186 0.3478 0.0013 0.1482 397 1.3847 1.9183 0.4022 0.0010 0.1481 398 1.3843 1.9181 0.3462 0.0014 0.1480 399 1.3845 1.9177 0.4042 0.0010 0.1479 400 1.3841 1.9175 0.3447 0.0013 0.1478 401 1.3843 1.9171 0.3940 0.0010 0.1478 402 1.3839 1.9169 0.3508 0.0013 0.1477 403 1.3841 1.9166 0.3967 0.0010 0.1476 404 1.3837 1.9163 0.3489 0.0013 0.1475 405 1.3839 1.9160 0.3991 0.0010 0.1474 406 1.3835 1.9158 0.3471 0.0013 0.1474 407 1.3837 1.9154 0.4013 0.0010 0.1473 408 1.3833 1.9152 0.3455 0.0014 0.1472 409 1.3835 1.9148 0.4034 0.0010 0.1471 410 1.3831 1.9146 0.3441 0.0013 0.1470 411 1.3833 1.9142 0.3932 0.0010 0.1470 412 1.3829 1.9140 0.3501 0.0013 0.1469 413 1.3831 1.9137 0.3959 0.0010 0.1468 414 1.3826 1.9135 0.3481 0.0013 0.1467 415 1.3828 1.9131 0.3983 0.0010 0.1466 416 1.3824 1.9129 0.3463 0.0013 0.1466 417 1.3826 1.9125 0.4005 0.0010 0.1465 418 1.3822 1.9123 0.3447 0.0014 0.1464 419 1.3824 1.9119 0.4026 0.0010 0.1463 420 1.3820 1.9117 0.3433 0.0013 0.1462 421 1.3822 1.9114 0.3925 0.0010 0.1462 422 1.3818 1.9111 0.3493 0.0013 0.1461 423 1.3820 1.9108 0.3951 0.0010 0.1460 424 1.3816 1.9106 0.3473 0.0013 0.1459 425 1.3818 1.9102 0.3976 0.0010 0.1458 426 1.3814 1.9100 0.3456 0.0014 0.1458 427 1.3816 1.9096 0.3998 0.0010 0.1457 428 1.3812 1.9094 0.3440 0.0013 0.1456 429 1.3814 1.9091 0.3899 0.0010 0.1455 430 1.3810 1.9088 0.3500 0.0013 0.1454 431 1.3812 1.9085 0.3927 0.0010 0.1454 432 1.3808 1.9083 0.3479 0.0013 0.1453 433 1.3810 1.9079 0.3953 0.0010 0.1452 434 1.3806 1.9077 0.3460 0.0013 0.1451 435 1.3808 1.9073 0.3977 0.0010 0.1451 436 1.3804 1.9071 0.3443 0.0014 0.1450 437 1.3806 1.9068 0.3998 0.0010 0.1449 438 1.3802 1.9065 0.3427 0.0013 0.1448 439 1.3804 1.9062 0.3899 0.0010 0.1447 440 1.3799 1.9060 0.3488 0.0013 0.1447 441 1.3801 1.9056 0.3927 0.0010 0.1446 442 1.3797 1.9054 0.3467 0.0013 0.1445 443 1.3799 1.9050 0.3952 0.0010 0.1444 444 1.3795 1.9048 0.3448 0.0013 0.1443 445 1.3797 1.9045 0.3975 0.0010 0.1443 446 1.3793 1.9043 0.3432 0.0013 0.1442 447 1.3795 1.9039 0.3878 0.0011 0.1441 448 1.3791 1.9037 0.3492 0.0013 0.1440 449 1.3793 1.9033 0.3906 0.0010 0.1439 450 1.3789 1.9031 0.3470 0.0013 0.1439 451 1.3791 1.9028 0.3933 0.0010 0.1438 452 1.3787 1.9025 0.3451 0.0013 0.1437 453 1.3789 1.9022 0.3957 0.0010 0.1436 454 1.3785 1.9020 0.3433 0.0014 0.1436 455 1.3787 1.9016 0.3979 0.0010 0.1435 456 1.3783 1.9014 0.3417 0.0013 0.1434 457 1.3785 1.9010 0.3881 0.0010 0.1433 458 1.3781 1.9008 0.3477 0.0013 0.1432 459 1.3783 1.9005 0.3909 0.0010 0.1432 460 1.3779 1.9002 0.3456 0.0013 0.1431 461 1.3781 1.8999 0.3935 0.0010 0.1430 462 1.3777 1.8997 0.3437 0.0014 0.1429 463 1.3779 1.8993 0.3959 0.0010 0.1428 464 1.3775 1.8991 0.3420 0.0013 0.1428 465 1.3777 1.8987 0.3862 0.0011 0.1427 466 1.3772 1.8985 0.3480 0.0013 0.1426 467 1.3774 1.8982 0.3891 0.0010 0.1425 468 1.3770 1.8979 0.3458 0.0013 0.1425 469 1.3772 1.8976 0.3917 0.0010 0.1424 470 1.3768 1.8974 0.3438 0.0013 0.1423 471 1.3770 1.8970 0.3942 0.0010 0.1422 472 1.3766 1.8968 0.3420 0.0013 0.1421 473 1.3768 1.8964 0.3846 0.0011 0.1421 474 1.3764 1.8962 0.3480 0.0013 0.1420 475 1.3766 1.8959 0.3876 0.0010 0.1419 476 1.3762 1.8957 0.3458 0.0013 0.1418 477 1.3764 1.8953 0.3903 0.0010 0.1417 478 1.3760 1.8951 0.3437 0.0013 0.1417 479 1.3762 1.8947 0.3928 0.0010 0.1416 480 1.3758 1.8945 0.3419 0.0013 0.1415 481 1.3760 1.8942 0.3833 0.0011 0.1414 482 1.3756 1.8940 0.3479 0.0013 0.1414 483 1.3758 1.8936 0.3863 0.0011 0.1413 484 1.3754 1.8934 0.3456 0.0013 0.1412 485 1.3756 1.8930 0.3891 0.0010 0.1411 486 1.3752 1.8928 0.3435 0.0013 0.1410 487 1.3754 1.8925 0.3917 0.0010 0.1410 488 1.3750 1.8922 0.3416 0.0013 0.1409 489 1.3752 1.8919 0.3823 0.0011 0.1408 490 1.3748 1.8917 0.3476 0.0013 0.1407 491 1.3750 1.8913 0.3853 0.0011 0.1407 492 1.3746 1.8911 0.3453 0.0013 0.1406 493 1.3747 1.8907 0.3881 0.0010 0.1405 494 1.3743 1.8905 0.3431 0.0013 0.1404 495 1.3745 1.8902 0.3907 0.0010 0.1403 496 1.3741 1.8900 0.3412 0.0013 0.1403 497 1.3743 1.8896 0.3813 0.0011 0.1402 498 1.3739 1.8894 0.3472 0.0013 0.1401 499 1.3741 1.8890 0.3844 0.0011 0.1400 500 1.3737 1.8888 0.3448 0.0013 0.1400 501 1.3739 1.8885 0.3872 0.0010 0.1399 502 1.3735 1.8883 0.3427 0.0013 0.1398 503 1.3737 1.8879 0.3899 0.0010 0.1397 504 1.3733 1.8877 0.3408 0.0013 0.1396 505 1.3735 1.8873 0.3805 0.0011 0.1396 506 1.3731 1.8871 0.3468 0.0013 0.1395 507 1.3733 1.8868 0.3836 0.0011 0.1394 508 1.3729 1.8865 0.3444 0.0013 0.1393 509 1.3731 1.8862 0.3865 0.0010 0.1393 510 1.3727 1.8860 0.3422 0.0013 0.1392 511 1.3729 1.8856 0.3891 0.0010 0.1391 512 1.3725 1.8854 0.3402 0.0013 0.1390 513 1.3727 1.8851 0.3798 0.0011 0.1390 514 1.3723 1.8848 0.3462 0.0013 0.1389 515 1.3725 1.8845 0.3829 0.0011 0.1388 516 1.3721 1.8843 0.3438 0.0013 0.1387 517 1.3723 1.8839 0.3858 0.0010 0.1386 518 1.3719 1.8837 0.3416 0.0013 0.1386 519 1.3721 1.8834 0.3884 0.0010 0.1385 520 1.3717 1.8831 0.3397 0.0013 0.1384 521 1.3719 1.8828 0.3792 0.0011 0.1383 522 1.3715 1.8826 0.3456 0.0013 0.1383 523 1.3716 1.8822 0.3823 0.0011 0.1382 524 1.3712 1.8820 0.3432 0.0013 0.1381 525 1.3714 1.8816 0.3851 0.0010 0.1380 526 1.3710 1.8814 0.3410 0.0013 0.1380 527 1.3712 1.8811 0.3878 0.0010 0.1379 528 1.3708 1.8809 0.3391 0.0013 0.1378 529 1.3710 1.8805 0.3786 0.0011 0.1377 530 1.3706 1.8803 0.3450 0.0013 0.1376 531 1.3708 1.8799 0.3817 0.0011 0.1376 532 1.3704 1.8797 0.3426 0.0013 0.1375 533 1.3706 1.8794 0.3846 0.0010 0.1374 534 1.3702 1.8792 0.3404 0.0013 0.1373 535 1.3704 1.8788 0.3872 0.0010 0.1373 536 1.3700 1.8786 0.3384 0.0013 0.1372 537 1.3702 1.8782 0.3780 0.0011 0.1371 538 1.3698 1.8780 0.3443 0.0013 0.1370 539 1.3700 1.8777 0.3811 0.0011 0.1370 540 1.3696 1.8775 0.3419 0.0013 0.1369 541 1.3698 1.8771 0.3840 0.0010 0.1368 542 1.3694 1.8769 0.3397 0.0013 0.1367 543 1.3696 1.8765 0.3867 0.0010 0.1367 544 1.3692 1.8763 0.3378 0.0013 0.1366 545 1.3694 1.8760 0.3775 0.0011 0.1365 546 1.3690 1.8758 0.3436 0.0013 0.1364 547 1.3692 1.8754 0.3806 0.0011 0.1363 548 1.3688 1.8752 0.3412 0.0013 0.1363 549 1.3690 1.8748 0.3835 0.0010 0.1362 550 1.3686 1.8746 0.3391 0.0013 0.1361 551 1.3688 1.8743 0.3745 0.0011 0.1360 552 1.3684 1.8741 0.3451 0.0013 0.1360 553 1.3685 1.8737 0.3777 0.0011 0.1359 554 1.3681 1.8735 0.3424 0.0013 0.1358 555 1.3683 1.8731 0.3808 0.0011 0.1357 556 1.3679 1.8729 0.3401 0.0013 0.1357 557 1.3681 1.8726 0.3836 0.0010 0.1356 558 1.3677 1.8724 0.3380 0.0013 0.1355 559 1.3679 1.8720 0.3746 0.0011 0.1354 560 1.3675 1.8718 0.3439 0.0013 0.1354 561 1.3677 1.8714 0.3778 0.0011 0.1353 562 1.3673 1.8712 0.3413 0.0013 0.1352 563 1.3675 1.8709 0.3808 0.0011 0.1351 564 1.3671 1.8707 0.3390 0.0013 0.1351 565 1.3673 1.8703 0.3836 0.0010 0.1350 566 1.3669 1.8701 0.3370 0.0013 0.1349 567 1.3671 1.8697 0.3746 0.0011 0.1348 568 1.3667 1.8695 0.3428 0.0013 0.1347 569 1.3669 1.8692 0.3778 0.0011 0.1347 570 1.3665 1.8690 0.3403 0.0013 0.1346 571 1.3667 1.8686 0.3807 0.0011 0.1345 572 1.3663 1.8684 0.3381 0.0013 0.1344 573 1.3665 1.8681 0.3719 0.0011 0.1344 574 1.3661 1.8679 0.3440 0.0013 0.1343 575 1.3663 1.8675 0.3752 0.0011 0.1342 576 1.3659 1.8673 0.3414 0.0013 0.1341 577 1.3661 1.8669 0.3783 0.0011 0.1341 578 1.3657 1.8667 0.3389 0.0013 0.1340 579 1.3659 1.8664 0.3812 0.0011 0.1339 580 1.3655 1.8662 0.3368 0.0013 0.1338 581 1.3657 1.8658 0.3723 0.0011 0.1338 582 1.3653 1.8656 0.3426 0.0013 0.1337 583 1.3655 1.8652 0.3756 0.0011 0.1336 584 1.3651 1.8650 0.3400 0.0013 0.1335 585 1.3652 1.8647 0.3786 0.0011 0.1335 586 1.3648 1.8645 0.3377 0.0013 0.1334 587 1.3650 1.8641 0.3814 0.0010 0.1333 588 1.3646 1.8639 0.3356 0.0013 0.1332 589 1.3648 1.8635 0.3726 0.0011 0.1332 590 1.3644 1.8633 0.3414 0.0013 0.1331 591 1.3646 1.8630 0.3758 0.0011 0.1330 592 1.3642 1.8628 0.3388 0.0013 0.1329 593 1.3644 1.8624 0.3788 0.0011 0.1329 594 1.3640 1.8622 0.3366 0.0013 0.1328 595 1.3642 1.8619 0.3701 0.0011 0.1327 596 1.3638 1.8617 0.3425 0.0013 0.1326 597 1.3640 1.8613 0.3734 0.0011 0.1326 598 1.3636 1.8611 0.3398 0.0013 0.1325 599 1.3638 1.8607 0.3765 0.0011 0.1324 600 1.3634 1.8605 0.3373 0.0013 0.1323 601 1.3636 1.8602 0.3794 0.0011 0.1323 602 1.3632 1.8600 0.3351 0.0013 0.1322 603 1.3634 1.8596 0.3706 0.0011 0.1321 604 1.3630 1.8594 0.3409 0.0013 0.1320 605 1.3632 1.8590 0.3739 0.0011 0.1320 606 1.3628 1.8588 0.3383 0.0013 0.1319 607 1.3630 1.8585 0.3769 0.0011 0.1318 608 1.3626 1.8583 0.3360 0.0013 0.1317 609 1.3628 1.8579 0.3683 0.0011 0.1317 610 1.3624 1.8577 0.3419 0.0013 0.1316 611 1.3626 1.8574 0.3717 0.0011 0.1315 612 1.3622 1.8572 0.3391 0.0013 0.1314 613 1.3624 1.8568 0.3748 0.0011 0.1314 614 1.3620 1.8566 0.3367 0.0013 0.1313 615 1.3621 1.8562 0.3778 0.0011 0.1312 616 1.3618 1.8560 0.3344 0.0013 0.1311 617 1.3619 1.8557 0.3691 0.0011 0.1311 618 1.3616 1.8555 0.3402 0.0013 0.1310 619 1.3617 1.8551 0.3724 0.0011 0.1309 620 1.3613 1.8549 0.3376 0.0013 0.1308 621 1.3615 1.8546 0.3755 0.0011 0.1308 622 1.3611 1.8543 0.3352 0.0013 0.1307 623 1.3613 1.8540 0.3669 0.0011 0.1306 624 1.3609 1.8538 0.3410 0.0013 0.1305 625 1.3611 1.8534 0.3703 0.0011 0.1305 626 1.3607 1.8532 0.3383 0.0013 0.1304 627 1.3609 1.8529 0.3735 0.0011 0.1303 628 1.3605 1.8527 0.3358 0.0013 0.1302 629 1.3607 1.8523 0.3650 0.0011 0.1302 630 1.3603 1.8521 0.3417 0.0013 0.1301 631 1.3605 1.8518 0.3685 0.0011 0.1300 632 1.3601 1.8516 0.3388 0.0013 0.1300 633 1.3603 1.8512 0.3717 0.0011 0.1299 634 1.3599 1.8510 0.3362 0.0013 0.1298 635 1.3601 1.8506 0.3748 0.0011 0.1297 636 1.3597 1.8504 0.3338 0.0013 0.1297 637 1.3599 1.8501 0.3663 0.0011 0.1296 638 1.3595 1.8499 0.3396 0.0013 0.1295 639 1.3597 1.8495 0.3696 0.0011 0.1294 640 1.3593 1.8493 0.3369 0.0013 0.1294 641 1.3595 1.8490 0.3728 0.0011 0.1293 642 1.3591 1.8488 0.3344 0.0013 0.1292 643 1.3593 1.8484 0.3644 0.0011 0.1291 644 1.3589 1.8482 0.3403 0.0013 0.1291 645 1.3591 1.8478 0.3678 0.0011 0.1290 646 1.3587 1.8476 0.3374 0.0013 0.1289 647 1.3589 1.8473 0.3710 0.0011 0.1288 648 1.3585 1.8471 0.3348 0.0013 0.1288 649 1.3587 1.8467 0.3627 0.0011 0.1287 650 1.3583 1.8465 0.3408 0.0013 0.1286 651 1.3585 1.8462 0.3662 0.0011 0.1285 652 1.3581 1.8460 0.3378 0.0013 0.1285 653 1.3582 1.8456 0.3695 0.0011 0.1284 654 1.3579 1.8454 0.3351 0.0013 0.1283 655 1.3580 1.8450 0.3726 0.0011 0.1283 656 1.3577 1.8448 0.3327 0.0013 0.1282 657 1.3578 1.8445 0.3642 0.0011 0.1281 658 1.3574 1.8443 0.3385 0.0013 0.1280 659 1.3576 1.8439 0.3676 0.0011 0.1280 660 1.3572 1.8437 0.3357 0.0013 0.1279 661 1.3574 1.8434 0.3708 0.0011 0.1278 662 1.3570 1.8432 0.3332 0.0013 0.1277 663 1.3572 1.8428 0.3625 0.0011 0.1277 664 1.3568 1.8426 0.3390 0.0013 0.1276 665 1.3570 1.8423 0.3659 0.0011 0.1275 666 1.3566 1.8421 0.3361 0.0013 0.1274 667 1.3568 1.8417 0.3692 0.0011 0.1274 668 1.3564 1.8415 0.3335 0.0013 0.1273 669 1.3566 1.8411 0.3610 0.0011 0.1272 670 1.3562 1.8409 0.3394 0.0013 0.1272 671 1.3564 1.8406 0.3645 0.0011 0.1271 672 1.3560 1.8404 0.3364 0.0013 0.1270 673 1.3562 1.8400 0.3678 0.0011 0.1269 674 1.3558 1.8398 0.3337 0.0013 0.1269 675 1.3560 1.8395 0.3596 0.0011 0.1268 676 1.3556 1.8393 0.3396 0.0013 0.1267 677 1.3558 1.8389 0.3632 0.0011 0.1266 678 1.3554 1.8387 0.3365 0.0013 0.1266 679 1.3556 1.8384 0.3665 0.0011 0.1265 680 1.3552 1.8382 0.3338 0.0013 0.1264 681 1.3554 1.8378 0.3697 0.0011 0.1263 682 1.3550 1.8376 0.3313 0.0013 0.1263 683 1.3552 1.8372 0.3615 0.0011 0.1262 684 1.3548 1.8370 0.3370 0.0013 0.1261 685 1.3550 1.8367 0.3649 0.0011 0.1261 686 1.3546 1.8365 0.3342 0.0013 0.1260 687 1.3548 1.8361 0.3681 0.0011 0.1259 688 1.3544 1.8359 0.3316 0.0013 0.1258 689 1.3546 1.8356 0.3600 0.0011 0.1258 690 1.3542 1.8354 0.3374 0.0013 0.1257 691 1.3543 1.8350 0.3635 0.0011 0.1256 692 1.3540 1.8348 0.3344 0.0013 0.1255 693 1.3541 1.8345 0.3668 0.0011 0.1255 694 1.3538 1.8343 0.3318 0.0013 0.1254 695 1.3539 1.8339 0.3586 0.0011 0.1253 696 1.3536 1.8337 0.3376 0.0013 0.1253 697 1.3537 1.8334 0.3622 0.0011 0.1252 698 1.3533 1.8332 0.3346 0.0013 0.1251 699 1.3535 1.8328 0.3655 0.0011 0.1250 700 1.3531 1.8326 0.3318 0.0013 0.1250 701 1.3533 1.8322 0.3575 0.0011 0.1249 702 1.3529 1.8320 0.3377 0.0013 0.1248 703 1.3531 1.8317 0.3610 0.0011 0.1248 704 1.3527 1.8315 0.3346 0.0013 0.1247 705 1.3529 1.8311 0.3644 0.0011 0.1246 706 1.3525 1.8309 0.3318 0.0013 0.1245 707 1.3527 1.8306 0.3564 0.0011 0.1245 708 1.3523 1.8304 0.3377 0.0013 0.1244 709 1.3525 1.8300 0.3600 0.0011 0.1243 710 1.3521 1.8298 0.3346 0.0013 0.1242 711 1.3523 1.8295 0.3634 0.0011 0.1242 712 1.3519 1.8293 0.3318 0.0013 0.1241 713 1.3521 1.8289 0.3554 0.0011 0.1240 714 1.3517 1.8287 0.3376 0.0013 0.1240 715 1.3519 1.8284 0.3591 0.0011 0.1239 716 1.3515 1.8282 0.3345 0.0013 0.1238 717 1.3517 1.8278 0.3625 0.0011 0.1237 718 1.3513 1.8276 0.3316 0.0013 0.1237 719 1.3515 1.8273 0.3546 0.0011 0.1236 720 1.3511 1.8271 0.3375 0.0013 0.1235 721 1.3513 1.8267 0.3582 0.0011 0.1235 722 1.3509 1.8265 0.3343 0.0013 0.1234 723 1.3511 1.8262 0.3617 0.0011 0.1233 724 1.3507 1.8260 0.3314 0.0013 0.1232 725 1.3509 1.8256 0.3538 0.0011 0.1232 726 1.3505 1.8254 0.3373 0.0013 0.1231 727 1.3507 1.8250 0.3574 0.0011 0.1230 728 1.3503 1.8249 0.3341 0.0013 0.1230 729 1.3505 1.8245 0.3609 0.0011 0.1229 730 1.3501 1.8243 0.3312 0.0013 0.1228 731 1.3503 1.8239 0.3530 0.0012 0.1227 732 1.3499 1.8237 0.3371 0.0013 0.1227 733 1.3501 1.8234 0.3567 0.0011 0.1226 734 1.3497 1.8232 0.3338 0.0013 0.1225 735 1.3498 1.8228 0.3602 0.0011 0.1224 736 1.3495 1.8226 0.3309 0.0013 0.1224 737 1.3496 1.8223 0.3524 0.0012 0.1223 738 1.3493 1.8221 0.3368 0.0013 0.1222 739 1.3494 1.8217 0.3561 0.0011 0.1222 740 1.3491 1.8215 0.3335 0.0013 0.1221 741 1.3492 1.8212 0.3596 0.0011 0.1220 742 1.3489 1.8210 0.3305 0.0013 0.1219 743 1.3490 1.8206 0.3518 0.0012 0.1219 744 1.3486 1.8204 0.3364 0.0013 0.1218 745 1.3488 1.8201 0.3555 0.0011 0.1217 746 1.3484 1.8199 0.3331 0.0013 0.1217 747 1.3486 1.8195 0.3590 0.0011 0.1216 748 1.3482 1.8193 0.3302 0.0013 0.1215 749 1.3484 1.8190 0.3512 0.0012 0.1215 750 1.3480 1.8188 0.3360 0.0013 0.1214 751 1.3482 1.8184 0.3549 0.0011 0.1213 752 1.3478 1.8182 0.3327 0.0013 0.1212 753 1.3480 1.8179 0.3584 0.0011 0.1212 754 1.3476 1.8177 0.3298 0.0013 0.1211 755 1.3478 1.8173 0.3507 0.0012 0.1210 756 1.3474 1.8171 0.3356 0.0013 0.1210 757 1.3476 1.8168 0.3544 0.0011 0.1209 758 1.3472 1.8166 0.3323 0.0013 0.1208 759 1.3474 1.8162 0.3579 0.0011 0.1207 760 1.3470 1.8160 0.3293 0.0013 0.1207 761 1.3472 1.8157 0.3502 0.0012 0.1206 762 1.3468 1.8155 0.3352 0.0013 0.1205 763 1.3470 1.8151 0.3539 0.0011 0.1205 764 1.3466 1.8149 0.3319 0.0013 0.1204 765 1.3468 1.8146 0.3574 0.0011 0.1203 766 1.3464 1.8144 0.3289 0.0013 0.1202 767 1.3466 1.8140 0.3497 0.0012 0.1202 768 1.3462 1.8138 0.3347 0.0013 0.1201 769 1.3464 1.8135 0.3534 0.0011 0.1200 770 1.3460 1.8133 0.3314 0.0013 0.1200 771 1.3462 1.8129 0.3569 0.0011 0.1199 772 1.3458 1.8127 0.3284 0.0013 0.1198 773 1.3460 1.8124 0.3493 0.0012 0.1197 774 1.3456 1.8122 0.3342 0.0013 0.1197 775 1.3458 1.8118 0.3530 0.0011 0.1196 776 1.3454 1.8116 0.3309 0.0013 0.1195 777 1.3456 1.8113 0.3565 0.0011 0.1195 778 1.3452 1.8111 0.3279 0.0013 0.1194 779 1.3454 1.8107 0.3489 0.0012 0.1193 780 1.3450 1.8105 0.3337 0.0013 0.1193 781 1.3452 1.8102 0.3525 0.0011 0.1192 782 1.3448 1.8100 0.3304 0.0013 0.1191 783 1.3449 1.8096 0.3561 0.0011 0.1190 784 1.3446 1.8094 0.3274 0.0013 0.1190 785 1.3447 1.8091 0.3485 0.0012 0.1189 786 1.3444 1.8089 0.3332 0.0013 0.1188 787 1.3445 1.8085 0.3522 0.0011 0.1188 788 1.3442 1.8083 0.3299 0.0013 0.1187 789 1.3443 1.8080 0.3557 0.0011 0.1186 790 1.3440 1.8078 0.3269 0.0013 0.1186 791 1.3441 1.8074 0.3481 0.0012 0.1185 792 1.3438 1.8072 0.3326 0.0013 0.1184 793 1.3439 1.8069 0.3518 0.0011 0.1183 794 1.3435 1.8067 0.3293 0.0013 0.1183 795 1.3437 1.8063 0.3553 0.0011 0.1182 796 1.3433 1.8061 0.3264 0.0013 0.1181 797 1.3435 1.8058 0.3477 0.0012 0.1181 798 1.3431 1.8056 0.3320 0.0013 0.1180 799 1.3433 1.8052 0.3514 0.0011 0.1179 800 1.3429 1.8050 0.3288 0.0013 0.1179 801 1.3431 1.8047 0.3549 0.0011 0.1178 802 1.3427 1.8045 0.3258 0.0013 0.1177 803 1.3429 1.8041 0.3474 0.0012 0.1176 804 1.3425 1.8039 0.3315 0.0013 0.1176 805 1.3427 1.8036 0.3511 0.0011 0.1175 806 1.3423 1.8034 0.3282 0.0013 0.1174 807 1.3425 1.8030 0.3436 0.0012 0.1174 808 1.3421 1.8029 0.3341 0.0013 0.1173 809 1.3423 1.8025 0.3474 0.0012 0.1172 810 1.3419 1.8023 0.3305 0.0013 0.1172 811 1.3421 1.8020 0.3511 0.0011 0.1171 812 1.3417 1.8018 0.3273 0.0013 0.1170 813 1.3419 1.8014 0.3437 0.0012 0.1169 814 1.3415 1.8012 0.3332 0.0013 0.1169 815 1.3417 1.8009 0.3475 0.0012 0.1168 816 1.3413 1.8007 0.3297 0.0013 0.1167 817 1.3415 1.8003 0.3511 0.0011 0.1167 818 1.3411 1.8001 0.3265 0.0013 0.1166 819 1.3413 1.7998 0.3437 0.0012 0.1165 820 1.3409 1.7996 0.3323 0.0013 0.1165 821 1.3411 1.7992 0.3475 0.0012 0.1164 822 1.3407 1.7990 0.3288 0.0013 0.1163 823 1.3409 1.7987 0.3511 0.0011 0.1162 824 1.3405 1.7985 0.3257 0.0013 0.1162 825 1.3407 1.7981 0.3437 0.0012 0.1161 826 1.3403 1.7979 0.3314 0.0013 0.1160 827 1.3405 1.7976 0.3475 0.0012 0.1160 828 1.3401 1.7974 0.3279 0.0013 0.1159 829 1.3403 1.7970 0.3511 0.0011 0.1158 830 1.3399 1.7968 0.3249 0.0013 0.1158 831 1.3401 1.7965 0.3437 0.0012 0.1157 832 1.3397 1.7963 0.3305 0.0013 0.1156 833 1.3399 1.7959 0.3475 0.0012 0.1156 834 1.3395 1.7958 0.3271 0.0013 0.1155 835 1.3397 1.7954 0.3402 0.0012 0.1154 836 1.3393 1.7952 0.3330 0.0013 0.1153 837 1.3395 1.7948 0.3440 0.0012 0.1153 838 1.3391 1.7947 0.3294 0.0013 0.1152 839 1.3392 1.7943 0.3477 0.0011 0.1151 840 1.3389 1.7941 0.3260 0.0013 0.1151 841 1.3390 1.7938 0.3405 0.0012 0.1150 842 1.3387 1.7936 0.3319 0.0013 0.1149 843 1.3388 1.7932 0.3443 0.0012 0.1149 844 1.3385 1.7930 0.3283 0.0013 0.1148 845 1.3386 1.7927 0.3480 0.0011 0.1147 846 1.3383 1.7925 0.3250 0.0013 0.1147 847 1.3384 1.7921 0.3407 0.0012 0.1146 848 1.3381 1.7919 0.3308 0.0013 0.1145 849 1.3382 1.7916 0.3445 0.0012 0.1145 850 1.3378 1.7914 0.3272 0.0013 0.1144 851 1.3380 1.7910 0.3482 0.0011 0.1143 852 1.3377 1.7909 0.3240 0.0013 0.1142 853 1.3378 1.7905 0.3409 0.0012 0.1142 854 1.3374 1.7903 0.3297 0.0013 0.1141 855 1.3376 1.7900 0.3447 0.0012 0.1140 856 1.3373 1.7898 0.3262 0.0013 0.1140 857 1.3374 1.7894 0.3375 0.0012 0.1139 858 1.3370 1.7892 0.3321 0.0013 0.1138 859 1.3372 1.7889 0.3414 0.0012 0.1138 860 1.3368 1.7887 0.3284 0.0013 0.1137 861 1.3370 1.7883 0.3452 0.0012 0.1136 862 1.3366 1.7881 0.3250 0.0013 0.1136 863 1.3368 1.7878 0.3380 0.0012 0.1135 864 1.3364 1.7876 0.3308 0.0013 0.1134 865 1.3366 1.7872 0.3419 0.0012 0.1134 866 1.3362 1.7871 0.3271 0.0013 0.1133 867 1.3364 1.7867 0.3456 0.0012 0.1132 868 1.3360 1.7865 0.3238 0.0013 0.1132 869 1.3362 1.7861 0.3384 0.0012 0.1131 870 1.3358 1.7860 0.3295 0.0013 0.1130 871 1.3360 1.7856 0.3423 0.0012 0.1129 872 1.3356 1.7854 0.3259 0.0013 0.1129 873 1.3358 1.7851 0.3460 0.0011 0.1128 874 1.3354 1.7849 0.3227 0.0013 0.1127 875 1.3356 1.7845 0.3388 0.0012 0.1127 876 1.3352 1.7843 0.3283 0.0013 0.1126 877 1.3354 1.7840 0.3426 0.0012 0.1125 878 1.3350 1.7838 0.3248 0.0013 0.1125 879 1.3352 1.7834 0.3355 0.0012 0.1124 880 1.3348 1.7833 0.3307 0.0013 0.1123 881 1.3350 1.7829 0.3394 0.0012 0.1123 882 1.3346 1.7827 0.3269 0.0013 0.1122 883 1.3348 1.7824 0.3432 0.0012 0.1121 884 1.3344 1.7822 0.3234 0.0013 0.1121 885 1.3346 1.7818 0.3361 0.0012 0.1120 886 1.3342 1.7816 0.3292 0.0013 0.1119 887 1.3344 1.7813 0.3400 0.0012 0.1119 888 1.3340 1.7811 0.3255 0.0013 0.1118 889 1.3342 1.7807 0.3437 0.0012 0.1117 890 1.3338 1.7805 0.3222 0.0013 0.1117 891 1.3340 1.7802 0.3366 0.0012 0.1116 892 1.3336 1.7800 0.3278 0.0013 0.1115 893 1.3338 1.7796 0.3405 0.0012 0.1115 894 1.3334 1.7795 0.3242 0.0013 0.1114 895 1.3336 1.7791 0.3335 0.0012 0.1113 896 1.3332 1.7789 0.3301 0.0013 0.1112 897 1.3334 1.7786 0.3374 0.0012 0.1112 898 1.3330 1.7784 0.3262 0.0013 0.1111 899 1.3332 1.7780 0.3412 0.0012 0.1110 900 1.3328 1.7778 0.3228 0.0013 0.1110 901 1.3330 1.7775 0.3342 0.0012 0.1109 902 1.3326 1.7773 0.3285 0.0013 0.1108 903 1.3328 1.7769 0.3381 0.0012 0.1108 904 1.3324 1.7768 0.3248 0.0013 0.1107 905 1.3326 1.7764 0.3419 0.0012 0.1106 906 1.3322 1.7762 0.3214 0.0013 0.1106 907 1.3324 1.7759 0.3349 0.0012 0.1105 908 1.3320 1.7757 0.3270 0.0013 0.1104 909 1.3321 1.7753 0.3387 0.0012 0.1104 910 1.3318 1.7751 0.3234 0.0013 0.1103 911 1.3319 1.7748 0.3318 0.0012 0.1102 912 1.3316 1.7746 0.3293 0.0013 0.1102 913 1.3317 1.7742 0.3358 0.0012 0.1101 914 1.3314 1.7741 0.3253 0.0013 0.1100 915 1.3315 1.7737 0.3396 0.0012 0.1100 916 1.3312 1.7735 0.3218 0.0013 0.1099 917 1.3313 1.7732 0.3326 0.0012 0.1098 918 1.3310 1.7730 0.3276 0.0013 0.1098 919 1.3311 1.7726 0.3365 0.0012 0.1097 920 1.3308 1.7724 0.3238 0.0013 0.1096 921 1.3309 1.7721 0.3297 0.0012 0.1096 922 1.3306 1.7719 0.3297 0.0013 0.1095 923 1.3307 1.7715 0.3337 0.0012 0.1094 924 1.3304 1.7714 0.3257 0.0013 0.1094 925 1.3305 1.7710 0.3375 0.0012 0.1093 926 1.3302 1.7708 0.3221 0.0013 0.1092 927 1.3303 1.7705 0.3306 0.0012 0.1092 928 1.3300 1.7703 0.3279 0.0013 0.1091 929 1.3301 1.7699 0.3346 0.0012 0.1090 930 1.3297 1.7697 0.3240 0.0013 0.1090 931 1.3299 1.7694 0.3384 0.0012 0.1089 932 1.3296 1.7692 0.3205 0.0013 0.1088 933 1.3297 1.7688 0.3315 0.0012 0.1088 934 1.3293 1.7687 0.3261 0.0013 0.1087 935 1.3295 1.7683 0.3354 0.0012 0.1086 936 1.3292 1.7681 0.3224 0.0013 0.1086 937 1.3293 1.7678 0.3286 0.0012 0.1085 938 1.3289 1.7676 0.3283 0.0013 0.1084 939 1.3291 1.7672 0.3326 0.0012 0.1084 940 1.3287 1.7671 0.3242 0.0013 0.1083 941 1.3289 1.7667 0.3365 0.0012 0.1082 942 1.3285 1.7665 0.3206 0.0013 0.1082 943 1.3287 1.7662 0.3297 0.0012 0.1081 944 1.3283 1.7660 0.3263 0.0013 0.1080 945 1.3285 1.7656 0.3336 0.0012 0.1080 946 1.3281 1.7654 0.3225 0.0013 0.1079 947 1.3283 1.7651 0.3268 0.0012 0.1078 948 1.3279 1.7649 0.3284 0.0012 0.1078 949 1.3281 1.7645 0.3309 0.0012 0.1077 950 1.3277 1.7644 0.3243 0.0013 0.1076 951 1.3279 1.7640 0.3347 0.0012 0.1076 952 1.3275 1.7638 0.3206 0.0013 0.1075 953 1.3277 1.7635 0.3280 0.0012 0.1074 954 1.3273 1.7633 0.3264 0.0013 0.1074 955 1.3275 1.7629 0.3320 0.0012 0.1073 956 1.3271 1.7628 0.3224 0.0013 0.1072 957 1.3273 1.7624 0.3252 0.0013 0.1072 958 1.3269 1.7622 0.3284 0.0012 0.1071 959 1.3271 1.7619 0.3293 0.0012 0.1070 960 1.3267 1.7617 0.3242 0.0013 0.1070 961 1.3269 1.7613 0.3332 0.0012 0.1069 962 1.3265 1.7612 0.3205 0.0013 0.1068 963 1.3267 1.7608 0.3265 0.0012 0.1068 964 1.3263 1.7606 0.3263 0.0013 0.1067 965 1.3265 1.7603 0.3305 0.0012 0.1066 966 1.3261 1.7601 0.3222 0.0013 0.1066 967 1.3263 1.7597 0.3343 0.0012 0.1065 968 1.3259 1.7595 0.3186 0.0013 0.1064 969 1.3261 1.7592 0.3276 0.0012 0.1064 970 1.3257 1.7590 0.3243 0.0013 0.1063 971 1.3259 1.7586 0.3316 0.0012 0.1062 972 1.3255 1.7585 0.3204 0.0013 0.1062 973 1.3257 1.7581 0.3249 0.0012 0.1061 974 1.3253 1.7579 0.3262 0.0013 0.1060 975 1.3255 1.7576 0.3289 0.0012 0.1060 976 1.3251 1.7574 0.3221 0.0013 0.1059 977 1.3253 1.7570 0.3328 0.0012 0.1059 978 1.3249 1.7569 0.3184 0.0013 0.1058 979 1.3251 1.7565 0.3261 0.0012 0.1057 980 1.3247 1.7563 0.3241 0.0013 0.1057 981 1.3249 1.7560 0.3301 0.0012 0.1056 982 1.3245 1.7558 0.3202 0.0013 0.1055 983 1.3247 1.7554 0.3235 0.0013 0.1055 984 1.3243 1.7553 0.3261 0.0013 0.1054 985 1.3245 1.7549 0.3275 0.0012 0.1053 986 1.3241 1.7547 0.3219 0.0013 0.1053 987 1.3243 1.7544 0.3314 0.0012 0.1052 988 1.3239 1.7542 0.3181 0.0013 0.1051 989 1.3241 1.7538 0.3248 0.0012 0.1051 990 1.3237 1.7537 0.3238 0.0013 0.1050 991 1.3239 1.7533 0.3288 0.0012 0.1049 992 1.3235 1.7531 0.3198 0.0013 0.1049 993 1.3237 1.7528 0.3222 0.0013 0.1048 994 1.3233 1.7526 0.3257 0.0012 0.1047 995 1.3235 1.7522 0.3263 0.0012 0.1047 996 1.3231 1.7521 0.3215 0.0013 0.1046 997 1.3233 1.7517 0.3302 0.0012 0.1045 998 1.3229 1.7515 0.3177 0.0013 0.1045 999 1.3231 1.7512 0.3236 0.0012 0.1044 1000 1.3227 1.7510 0.3234 0.0013 0.1043 ❌ Rosenbrock Test Failed! x_min = 1.322688, 1.750986 | f_min = 0.104347 ✅ High-Dimensional Quadratic Test Passed! x_min ~ 0 | f_min = 0 ------------- Gradient (numDeriv::grad) ------------- Gradient will be computed using numDeriv::grad ------------- End Gradient ------------- ------------- Line Search (exact along -grad) ------------- Step size (alpha) will be computed using exact line search if alpha is NULL ------------- End Line Search ------------- ------------- Position Update ------------- x will be updated using x <- x - alpha_k * grad ------------- End Position Update ------------- x_min: 1.714, -0.429 f_min: -2.571 Iterations: 60 Converged: TRUE Iteration x1 x2 grad_norm alpha f_x 1 0.3000 0.0000 3.0000 0.1 -0.8100 2 0.5400 -0.0300 2.4187 0.1 -1.3428 3 0.7350 -0.0720 1.9947 0.1 -1.7073 4 0.8952 -0.1167 1.6632 0.1 -1.9614 5 1.0278 -0.1595 1.3938 0.1 -2.1401 6 1.1382 -0.1985 1.1706 0.1 -2.2662 7 1.2304 -0.2329 0.9842 0.1 -2.3554 8 1.3076 -0.2628 0.8278 0.1 -2.4185 9 1.3724 -0.2884 0.6965 0.1 -2.4632 10 1.4268 -0.3103 0.5860 0.1 -2.4948 11 1.4724 -0.3289 0.4930 0.1 -2.5172 12 1.5108 -0.3446 0.4148 0.1 -2.5330 13 1.5431 -0.3578 0.3491 0.1 -2.5442 14 1.5703 -0.3690 0.2937 0.1 -2.5522 15 1.5931 -0.3784 0.2471 0.1 -2.5578 16 1.6123 -0.3864 0.2079 0.1 -2.5618 17 1.6285 -0.3931 0.1750 0.1 -2.5646 18 1.6421 -0.3987 0.1472 0.1 -2.5666 19 1.6536 -0.4034 0.1239 0.1 -2.5680 20 1.6632 -0.4074 0.1042 0.1 -2.5690 21 1.6713 -0.4108 0.0877 0.1 -2.5697 22 1.6781 -0.4136 0.0738 0.1 -2.5702 23 1.6838 -0.4160 0.0621 0.1 -2.5706 24 1.6887 -0.4180 0.0522 0.1 -2.5708 25 1.6927 -0.4196 0.0440 0.1 -2.5710 26 1.6962 -0.4211 0.0370 0.1 -2.5711 27 1.6990 -0.4223 0.0311 0.1 -2.5712 28 1.7014 -0.4233 0.0262 0.1 -2.5713 29 1.7035 -0.4241 0.0220 0.1 -2.5713 30 1.7052 -0.4248 0.0185 0.1 -2.5714 31 1.7066 -0.4254 0.0156 0.1 -2.5714 32 1.7079 -0.4259 0.0131 0.1 -2.5714 33 1.7089 -0.4263 0.0110 0.1 -2.5714 34 1.7097 -0.4267 0.0093 0.1 -2.5714 35 1.7105 -0.4270 0.0078 0.1 -2.5714 36 1.7111 -0.4272 0.0066 0.1 -2.5714 37 1.7116 -0.4274 0.0055 0.1 -2.5714 38 1.7120 -0.4276 0.0047 0.1 -2.5714 39 1.7124 -0.4278 0.0039 0.1 -2.5714 40 1.7127 -0.4279 0.0033 0.1 -2.5714 41 1.7129 -0.4280 0.0028 0.1 -2.5714 42 1.7131 -0.4281 0.0023 0.1 -2.5714 43 1.7133 -0.4282 0.0020 0.1 -2.5714 44 1.7135 -0.4282 0.0017 0.1 -2.5714 45 1.7136 -0.4283 0.0014 0.1 -2.5714 46 1.7137 -0.4283 0.0012 0.1 -2.5714 47 1.7138 -0.4284 0.0010 0.1 -2.5714 48 1.7139 -0.4284 0.0008 0.1 -2.5714 49 1.7139 -0.4284 0.0007 0.1 -2.5714 50 1.7140 -0.4285 0.0006 0.1 -2.5714 51 1.7140 -0.4285 0.0005 0.1 -2.5714 52 1.7141 -0.4285 0.0004 0.1 -2.5714 53 1.7141 -0.4285 0.0003 0.1 -2.5714 54 1.7141 -0.4285 0.0003 0.1 -2.5714 55 1.7142 -0.4285 0.0002 0.1 -2.5714 56 1.7142 -0.4285 0.0002 0.1 -2.5714 57 1.7142 -0.4285 0.0002 0.1 -2.5714 58 1.7142 -0.4285 0.0001 0.1 -2.5714 59 1.7142 -0.4285 0.0001 0.1 -2.5714 60 1.7142 -0.4286 0.0001 0.1 -2.5714 ✅ Fixed Step Size Test Passed! x_min = 1.714235, -0.42855 | f_min = -2.571429 [ FAIL 0 | WARN 0 | SKIP 0 | PASS 34 ] > > proc.time() user system elapsed 1.70 0.21 1.92