08-Oct-2025 16:44:48 sphere_monte_carlo_test(): MATLAB/Octave version 6.4.0 Test sphere_monte_carlo(). TEST01 Use SPHERE01_SAMPLE to estimate integrals over the surface of the unit sphere. N 1 X^2 Y^2 Z^2 X^4 X^2Y^2 Z^4 1 12.566371 5.247930 2.494882 4.823558 2.191625 1.041905 1.851506 2 12.566371 5.232553 3.346485 3.987333 3.674392 0.568031 1.565488 4 12.566371 2.522893 8.019003 2.024475 0.946790 0.880063 0.517925 8 12.566371 6.443215 3.094694 3.028462 5.088533 0.691091 1.471277 16 12.566371 4.329965 2.346719 5.889687 2.908760 0.706090 4.422243 32 12.566371 3.289213 4.425257 4.851901 1.776495 0.745257 2.776061 64 12.566371 4.152556 4.240464 4.173351 2.693398 0.821772 2.579336 128 12.566371 4.264705 4.061679 4.239987 2.532144 0.863403 2.567062 256 12.566371 4.294387 4.196703 4.075281 2.702665 0.840584 2.529948 512 12.566371 4.175342 4.200765 4.190264 2.530400 0.840471 2.541359 1024 12.566371 4.115407 4.209477 4.241486 2.456598 0.807135 2.557606 2048 12.566371 4.090316 4.508443 3.967612 2.412038 0.861589 2.275499 4096 12.566371 4.085803 4.261585 4.218983 2.435289 0.834892 2.562759 8192 12.566371 4.188971 4.176788 4.200611 2.518973 0.834298 2.524681 16384 12.566371 4.142861 4.253500 4.170009 2.464726 0.840675 2.487247 32768 12.566371 4.217275 4.167012 4.182084 2.544331 0.833096 2.508402 65536 12.566371 4.173091 4.195565 4.197714 2.493457 0.839124 2.518929 Exact 12.566371 4.188790 4.188790 4.188790 2.513274 0.837758 2.513274 sphere_monte_carlo_test(): Normal end of execution. 08-Oct-2025 16:44:48