Tue Oct 19 11:24:13 2021 ball_monte_carlo_test(): Python version: 3.6.9 Estimate integrals over the interior of the unit ball using the Monte Carlo method. N 1 X^2 Y^2 Z^2 X^4 X^2Y^2 Z^4 1 4.18879 1.19622 1.27937 0.000104392 0.341611 0.365357 2.60164e-09 2 4.18879 2.43011 0.225013 0.373615 1.42105 0.12271 0.0621478 4 4.18879 0.648632 0.777116 0.931638 0.181324 0.173602 0.454445 8 4.18879 0.986889 0.673249 0.861241 0.518894 0.0964666 0.266223 16 4.18879 0.71694 0.875493 0.827052 0.305969 0.0886703 0.379652 32 4.18879 0.984441 0.927778 0.811326 0.385707 0.169072 0.351994 64 4.18879 1.02849 0.819155 0.732341 0.472723 0.126023 0.282648 128 4.18879 0.870033 0.793607 0.817151 0.369942 0.108469 0.34647 256 4.18879 0.883379 0.858978 0.83016 0.37031 0.127889 0.338938 512 4.18879 0.819374 0.859239 0.790201 0.348513 0.118405 0.326508 1024 4.18879 0.832821 0.84103 0.828353 0.34811 0.117414 0.353129 2048 4.18879 0.841017 0.821685 0.825062 0.357949 0.123552 0.351051 4096 4.18879 0.835894 0.85122 0.826352 0.359569 0.120127 0.356285 8192 4.18879 0.843195 0.822316 0.846144 0.366164 0.118198 0.362077 16384 4.18879 0.846603 0.821573 0.846229 0.364366 0.119784 0.363426 32768 4.18879 0.839813 0.837373 0.835579 0.359541 0.119644 0.357055 65536 4.18879 0.840921 0.837634 0.8326 0.359805 0.119913 0.355573 Exact 4.18879 0.837758 0.837758 0.837758 0.359039 0.11968 0.359039 Tue Oct 19 11:24:15 2021