Wed Oct 8 07:43:48 2025 disk_monte_carlo_test(): python version: 3.10.12 numpy version: 1.26.4 Test disk_monte_carlo(). disk_area_test(): disk_area() returns the area of the unit disk. ( CX CY ) R Area ( 0.981885,-2.007634) 0.042309 0.005624 ( 1.499219,-4.975785) 0.707059 1.570583 ( 3.524601,-0.123399) 0.383939 0.463099 ( 0.734458,-4.097139) 0.803740 2.029463 ( 2.363545,-0.701952) 0.151196 0.071818 ( 4.936611,-0.710858) 0.135410 0.057604 (-4.438214,-1.259235) 0.367248 0.423709 ( 4.604364, 0.410877) 0.710622 1.586453 ( 1.178899, 4.169439) 0.690465 1.497729 (-2.021240,-2.415205) 0.231846 0.168868 disk_sample_test(): disk_sample() estimates integrals in the disk with center (0,0) and radius 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 1.77889 0.633508 1.00728 0.358716 0.127748 0.570358 2 3.14159 2.3629 0.337515 1.78127 0.25052 0.0390075 1.34585 4 3.14159 0.551978 0.82892 0.10439 0.153481 0.326703 0.0209642 8 3.14159 0.917736 0.833802 0.3813 0.235587 0.384073 0.186544 16 3.14159 0.567066 1.03883 0.208081 0.156145 0.590439 0.0991415 32 3.14159 0.686195 0.719906 0.33928 0.119993 0.297377 0.227453 64 3.14159 0.674894 0.789474 0.29062 0.120574 0.404823 0.156223 128 3.14159 0.721064 0.857387 0.355137 0.123105 0.483267 0.224604 256 3.14159 0.75939 0.739208 0.391057 0.117636 0.369139 0.252042 512 3.14159 0.77531 0.782866 0.388941 0.13018 0.391094 0.242324 1024 3.14159 0.792316 0.74766 0.405656 0.120402 0.364045 0.256413 2048 3.14159 0.763957 0.802611 0.375194 0.129138 0.406836 0.23111 4096 3.14159 0.788338 0.771054 0.391152 0.129189 0.381015 0.240919 8192 3.14159 0.793554 0.775357 0.398636 0.130154 0.3891 0.248646 16384 3.14159 0.788131 0.780849 0.394487 0.128706 0.390503 0.246178 32768 3.14159 0.786011 0.785778 0.393468 0.1308 0.393491 0.246443 65536 3.14159 0.787172 0.781363 0.394795 0.129819 0.390295 0.246794 Exact 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 disk_sample_test(): disk_sample() estimates integrals in the disk with center (1,0) and radius 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 3.87454 0.209929 4.7785 0.258906 0.0140279 5.89335 2 3.14159 8.76474 1.30824 25.9024 3.09012 0.760907 80.354 4 3.14159 1.94574 0.389614 2.36383 0.346791 0.120944 2.99543 8 3.14159 3.16227 1.04287 6.80858 1.00004 0.464765 18.2251 16 3.14159 3.62468 0.700197 7.00341 0.820691 0.320864 15.456 32 3.14159 3.69442 0.736553 8.02992 1.04537 0.374056 21.873 64 3.14159 3.68386 0.734123 7.50954 0.857315 0.362515 18.0499 128 3.14159 3.82122 0.806592 7.98267 0.889523 0.395384 20.6759 256 3.14159 3.83956 0.749921 8.11788 0.826982 0.378783 20.8356 512 3.14159 3.76893 0.823534 7.69345 0.944877 0.423497 19.4548 1024 3.14159 3.89704 0.819298 8.07905 0.949539 0.413504 20.4299 2048 3.14159 4.02992 0.772445 8.51037 0.895766 0.381516 21.8005 4096 3.14159 3.86646 0.795488 8.08868 0.912577 0.40161 20.7258 8192 3.14159 3.92942 0.795727 8.20416 0.927432 0.401734 20.8466 16384 3.14159 3.94078 0.785371 8.29184 0.922475 0.391345 21.2157 32768 3.14159 3.93589 0.789222 8.24243 0.921342 0.395414 20.9859 65536 3.14159 3.92195 0.788259 8.2421 0.915985 0.39491 21.0618 disk_sample_test(): disk_sample() estimates integrals in the disk with center (1,2) and radius 3 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 28.2743 112.128 647.861 444.67 2569.24 14844.7 1763.44 2 28.2743 148.246 26.7329 848.395 97.8667 50.431 5194.04 4 28.2743 71.2207 136.116 610.141 25.8268 2206.58 5628.59 8 28.2743 109.222 216.26 885.172 534.072 3608.32 8374.48 16 28.2743 103.048 90.9651 739.694 154.564 626.188 6360.21 32 28.2743 76.9081 149.202 464.086 440.45 1662.75 3494.15 64 28.2743 92.1247 190.795 790.469 592.138 2463.33 8486.98 128 28.2743 98.6362 185.085 735.383 633.598 2287.59 6893.78 256 28.2743 97.1288 183.916 706.037 564.001 2395.3 6441.43 512 28.2743 88.5192 175.378 682.371 506.764 2317.63 6946.72 1024 28.2743 93.1093 179.618 707.405 572.311 2309.07 6973.02 2048 28.2743 95.5299 176.648 735.604 561.04 2284.17 7339.67 4096 28.2743 93.2822 171.664 710.972 534.426 2158 7023.12 8192 28.2743 91.3307 175.303 686.72 507.987 2241.98 6739.96 16384 28.2743 91.7889 174.785 702.283 518.978 2223.71 7003.3 32768 28.2743 91.6763 177.444 693.051 524.763 2279.21 6847.52 65536 28.2743 92.2707 177.088 699.648 530.806 2272.41 6926.69 disk_monte_carlo_test(): Normal end of execution. Wed Oct 8 07:43:52 2025