{
  "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"
    }
  }
}
