14-May-2025 10:27:33 circle_monte_carlo_test(): MATLAB/Octave version 6.4.0. Test circle_monte_carlo(). circle01_sample_random_test(): circle01_sample_random() randomly samples the unit circle. Use it to estimate integrals. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 6.28319 0.227159 6.05603 0.00821262 0.218947 5.83708 0.000296915 2 6.28319 1.7083 4.57489 0.747402 0.960895 3.61399 0.357062 4 6.28319 4.75554 1.52764 3.88037 0.875169 0.652474 3.29592 8 6.28319 2.24025 4.04293 0.926559 1.31369 2.72924 0.436389 16 6.28319 3.28275 3.00044 2.36079 0.921965 2.07847 1.86989 32 6.28319 4.11473 2.16845 3.46527 0.649465 1.51899 3.07722 64 6.28319 2.93056 3.35262 2.12438 0.806179 2.54645 1.76693 128 6.28319 2.99457 3.28861 2.20048 0.794091 2.49452 1.81089 256 6.28319 3.08543 3.19776 2.31698 0.768449 2.42931 1.92348 512 6.28319 3.20485 3.07833 2.42577 0.779082 2.29925 2.03869 1024 6.28319 3.27928 3.00391 2.52293 0.756349 2.24756 2.13111 2048 6.28319 3.13163 3.15156 2.33944 0.792184 2.35938 1.94881 4096 6.28319 3.13587 3.14732 2.34732 0.788546 2.35877 1.94962 8192 6.28319 3.14545 3.13773 2.35583 0.78962 2.34811 1.96125 16384 6.28319 3.13709 3.1461 2.34865 0.788435 2.35766 1.95463 32768 6.28319 3.14795 3.13523 2.35821 0.789749 2.34548 1.96343 65536 6.28319 3.14021 3.14297 2.35624 0.783968 2.35901 1.96432 Exact 6.28319 3.14159 3.14159 2.35619 0.785398 2.35619 1.9635 circle01_sample_ergodic_test(): circle01_sample_ergodic() ergodically samples the unit circle. Use it to estimate integrals. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 6.28319 6.28319 0 6.28319 0 0 6.28319 2 6.28319 4.84972 1.43347 4.07032 0.779395 0.654073 3.64655 4 6.28319 3.01837 3.26482 2.25052 0.767845 2.49697 1.90297 8 6.28319 3.04968 3.23351 2.3008 0.748871 2.48464 1.95871 16 6.28319 3.11752 3.16567 2.37908 0.738438 2.42723 2.0164 32 6.28319 3.21906 3.06412 2.43708 0.781985 2.28214 2.04792 64 6.28319 3.16393 3.11926 2.38392 0.78001 2.33925 1.9937 128 6.28319 3.16442 3.11877 2.385 0.779418 2.33935 1.99556 256 6.28319 3.15606 3.12713 2.37107 0.784992 2.34214 1.97789 512 6.28319 3.14012 3.14307 2.3555 0.784619 2.35845 1.96372 1024 6.28319 3.14162 3.14157 2.35699 0.784632 2.35693 1.96467 2048 6.28319 3.14328 3.1399 2.35789 0.785389 2.35451 1.96516 4096 6.28319 3.14146 3.14173 2.35608 0.785374 2.35635 1.96344 8192 6.28319 3.1415 3.14168 2.35615 0.785351 2.35633 1.96351 16384 6.28319 3.14159 3.14159 2.35624 0.78535 2.35624 1.96357 32768 6.28319 3.1417 3.14149 2.3563 0.785398 2.35609 1.9636 65536 6.28319 3.14159 3.1416 2.35619 0.785397 2.3562 1.96349 Exact 6.28319 3.14159 3.14159 2.35619 0.785398 2.35619 1.9635 circle_monte_carlo_test(): Normal end of execution. 14-May-2025 10:27:35