Cody

# Problem 2908. Approximation of Pi

Solution 1747603

Submitted on 11 Mar 2019 by Gasper Umbreht
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### Test Suite

Test Status Code Input and Output
1   Pass
n = 1; y_correct = -0.858407346410207; assert(abs(pi_approx(n)-y_correct)<(100*eps))

x = 0 x1 = 1 x = 1 y = -0.8584

2   Pass
n = 2; y_correct = 0.474925986923126; assert(abs(pi_approx(n)-y_correct)<(100*eps))

x = 0 x1 = 1 x = 1 x1 = -0.3333 x = 0.6667 y = 0.4749

3   Pass
n = 4; y_correct = 0.246354558351698; assert(abs(pi_approx(n)-y_correct)<(100*eps))

x = 0 x1 = 1 x = 1 x1 = -0.3333 x = 0.6667 x1 = 0.2000 x = 0.8667 x1 = -0.1429 x = 0.7238 y = 0.2464

4   Pass
n = 7; y_correct = -0.142145830148691; assert(abs(pi_approx(n)-y_correct)<(100*eps))

x = 0 x1 = 1 x = 1 x1 = -0.3333 x = 0.6667 x1 = 0.2000 x = 0.8667 x1 = -0.1429 x = 0.7238 x1 = 0.1111 x = 0.8349 x1 = -0.0909 x = 0.7440 x1 = 0.0769 x = 0.8209 y = -0.1421

5   Pass
n = 10; y_correct = 0.099753034660390; assert(abs(pi_approx(n)-y_correct)<(100*eps))

x = 0 x1 = 1 x = 1 x1 = -0.3333 x = 0.6667 x1 = 0.2000 x = 0.8667 x1 = -0.1429 x = 0.7238 x1 = 0.1111 x = 0.8349 x1 = -0.0909 x = 0.7440 x1 = 0.0769 x = 0.8209 x1 = -0.0667 x = 0.7543 x1 = 0.0588 x = 0.8131 x1 = -0.0526 x = 0.7605 y = 0.0998

6   Pass
n = 14; y_correct = 0.071338035810608; assert(abs(pi_approx(n)-y_correct)<(100*eps))

x = 0 x1 = 1 x = 1 x1 = -0.3333 x = 0.6667 x1 = 0.2000 x = 0.8667 x1 = -0.1429 x = 0.7238 x1 = 0.1111 x = 0.8349 x1 = -0.0909 x = 0.7440 x1 = 0.0769 x = 0.8209 x1 = -0.0667 x = 0.7543 x1 = 0.0588 x = 0.8131 x1 = -0.0526 x = 0.7605 x1 = 0.0476 x = 0.8081 x1 = -0.0435 x = 0.7646 x1 = 0.0400 x = 0.8046 x1 = -0.0370 x = 0.7676 y = 0.0713

7   Pass
n = 17; y_correct = -0.058772861819756; assert(abs(pi_approx(n)-y_correct)<(100*eps))

x = 0 x1 = 1 x = 1 x1 = -0.3333 x = 0.6667 x1 = 0.2000 x = 0.8667 x1 = -0.1429 x = 0.7238 x1 = 0.1111 x = 0.8349 x1 = -0.0909 x = 0.7440 x1 = 0.0769 x = 0.8209 x1 = -0.0667 x = 0.7543 x1 = 0.0588 x = 0.8131 x1 = -0.0526 x = 0.7605 x1 = 0.0476 x = 0.8081 x1 = -0.0435 x = 0.7646 x1 = 0.0400 x = 0.8046 x1 = -0.0370 x = 0.7676 x1 = 0.0345 x = 0.8020 x1 = -0.0323 x = 0.7698 x1 = 0.0303 x = 0.8001 y = -0.0588

8   Pass
n = 20; y_correct = 0.049968846921953; assert(abs(pi_approx(n)-y_correct)<(100*eps))

x = 0 x1 = 1 x = 1 x1 = -0.3333 x = 0.6667 x1 = 0.2000 x = 0.8667 x1 = -0.1429 x = 0.7238 x1 = 0.1111 x = 0.8349 x1 = -0.0909 x = 0.7440 x1 = 0.0769 x = 0.8209 x1 = -0.0667 x = 0.7543 x1 = 0.0588 x = 0.8131 x1 = -0.0526 x = 0.7605 x1 = 0.0476 x = 0.8081 x1 = -0.0435 x = 0.7646 x1 = 0.0400 x = 0.8046 x1 = -0.0370 x = 0.7676 x1 = 0.0345 x = 0.8020 x1 = -0.0323 x = 0.7698 x1 = 0.0303 x = 0.8001 x1 = -0.0286 x = 0.7715 x1 = 0.0270 x = 0.7985 x1 = -0.0256 x = 0.7729 y = 0.0500

9   Pass
n = 25; y_correct = -0.039984031845239; assert(abs(pi_approx(n)-y_correct)<(100*eps))

x = 0 x1 = 1 x = 1 x1 = -0.3333 x = 0.6667 x1 = 0.2000 x = 0.8667 x1 = -0.1429 x = 0.7238 x1 = 0.1111 x = 0.8349 x1 = -0.0909 x = 0.7440 x1 = 0.0769 x = 0.8209 x1 = -0.0667 x = 0.7543 x1 = 0.0588 x = 0.8131 x1 = -0.0526 x = 0.7605 x1 = 0.0476 x = 0.8081 x1 = -0.0435 x = 0.7646 x1 = 0.0400 x = 0.8046 x1 = -0.0370 x = 0.7676 x1 = 0.0345 x = 0.8020 x1 = -0.0323 x = 0.7698 x1 = 0.0303 x = 0.8001 x1 = -0.0286 x = 0.7715 x1 = 0.0270 x = 0.7985 x1 = -0.0256 x = 0.7729 x1 = 0.0244 x = 0.7973 x1 = -0.0233 x = 0.7740 x1 = 0.0222 x = 0.7963 x1 = -0.0213 x = 0.7750 x1 = 0.0204 x = 0.7954 y = -0.0400