{
"benchmark": "Monte Carlo Pi Estimation",
"version": "1.0.0",
"timestamp": "2024-12-12T00:00:00Z",
"hardware": {
"cpu": "AMD Ryzen 9 5950X",
"cores": 16,
"ram_gb": 64,
"os": "Linux 6.8"
},
"results": {
"pi_estimate_1k": {
"metric": "estimation_error",
"sample_size": 100,
"n_samples": 1000,
"mean": 0.028,
"std": 0.015,
"ci_lower": 0.025,
"ci_upper": 0.031,
"confidence_level": 0.95,
"expected_error": 0.032,
"within_expected": true
},
"pi_estimate_10k": {
"metric": "estimation_error",
"sample_size": 100,
"n_samples": 10000,
"mean": 0.0089,
"std": 0.0048,
"ci_lower": 0.0080,
"ci_upper": 0.0098,
"confidence_level": 0.95,
"expected_error": 0.010,
"within_expected": true
},
"pi_estimate_100k": {
"metric": "estimation_error",
"sample_size": 100,
"n_samples": 100000,
"mean": 0.0028,
"std": 0.0015,
"ci_lower": 0.0025,
"ci_upper": 0.0031,
"confidence_level": 0.95,
"expected_error": 0.0032,
"within_expected": true
},
"execution_time_10k": {
"metric": "execution_time_ns",
"sample_size": 100,
"mean": 567890,
"std": 23456,
"ci_lower": 563289,
"ci_upper": 572491,
"confidence_level": 0.95
}
},
"convergence_analysis": {
"convergence_rate": {
"theoretical": "O(1/sqrt(n))",
"empirical_exponent": -0.498,
"ci_lower": -0.512,
"ci_upper": -0.484,
"matches_theory": true
},
"variance_reduction": {
"baseline_variance": 0.0015,
"antithetic_variance": 0.0008,
"reduction_percent": 46.7,
"p_value": 0.0001
}
},
"effect_sizes": {
"10k_vs_1k": {
"cohens_d": 1.87,
"interpretation": "large",
"practical_significance": "10x samples gives ~3x accuracy improvement"
}
}
}