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        },
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            "full_id": "ordinary/put_all_resolved",
            "directory_name": "ordinary/put_all_resolved",
            "title": "ordinary/put_all_resolved"
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            "full_id": "controls/harness_arithmetic",
            "directory_name": "controls/harness_arithmetic",
            "title": "controls/harness_arithmetic"
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      "observations": {
        "before": [
          {
            "id": "controls/harness_arithmetic",
            "inputs": "x=1.125; repeat32: x=sqrt(x*1.0001+.03125)+.3",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(1.5624999999999332)"
          },
          {
            "id": "controls/bsm_price",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(25.492089012052705)"
          },
          {
            "id": "controls/bsm_all",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(Greeks { price: 25.492089012052705, delta: 0.7965043257398099, gamma: 0.008292498274462608, theta: -0.019892440655369183, vega: 28.65887403654276, rho: 52.56632255754338, vanna: -0.49419627580829256, volga: 43.68476831073948, charm: 0.0002561413321583294, veta: -0.07227259172863033, color: 9.380022884777405e-6 })"
          },
          {
            "id": "ordinary/put_price",
            "inputs": "PricingInputs { option_type: Put, exercise_style: American, spot: 100.0, strike: 105.0, time_to_expiry: 0.5, rate: 0.03, dividend_yield: 0.01, volatility: 0.25 }; f64_bits=[4059000000000000,405a400000000000,3fe0000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd0000000000000]",
            "units_per_call": 1,
            "control": false,
            "result_debug": "Ok(9.408847753107736)"
          },
          {
            "id": "ordinary/put_all_resolved",
            "inputs": "PricingInputs { option_type: Put, exercise_style: American, spot: 100.0, strike: 105.0, time_to_expiry: 0.5, rate: 0.03, dividend_yield: 0.01, volatility: 0.25 }; f64_bits=[4059000000000000,405a400000000000,3fe0000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd0000000000000]",
            "units_per_call": 1,
            "control": false,
            "result_debug": "Ok(Greeks { price: 9.408847753107736, delta: -0.5613566347702277, gamma: 0.023297610772773925, theta: -0.015998209707057343, vega: 27.568057289001636, rho: -24.78553076444402, vanna: 0.5556457386359057, volga: 6.747767511861635, charm: -0.00043095766461376445, veta: -0.07923581431044605, color: 5.7248165374871185e-5 })"
          },
          {
            "id": "controls/european_iv_baseline",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]; quote_bits=40397df98ba57cc1",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(IvResult { iv: 0.31999999999999934, iterations: 2, used_fallback: false, price_residual: 2.7755575615628914e-17, price_residual_unit: ForwardNormalisedPrice })"
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        ],
        "after": [
          {
            "id": "controls/harness_arithmetic",
            "inputs": "x=1.125; repeat32: x=sqrt(x*1.0001+.03125)+.3",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(1.5624999999999332)"
          },
          {
            "id": "controls/bsm_price",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(25.492089012052705)"
          },
          {
            "id": "controls/bsm_all",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(Greeks { price: 25.492089012052705, delta: 0.7965043257398099, gamma: 0.008292498274462608, theta: -0.019892440655369183, vega: 28.65887403654276, rho: 52.56632255754338, vanna: -0.49419627580829256, volga: 43.68476831073948, charm: 0.0002561413321583294, veta: -0.07227259172863033, color: 9.380022884777405e-6 })"
          },
          {
            "id": "ordinary/put_price",
            "inputs": "PricingInputs { option_type: Put, exercise_style: American, spot: 100.0, strike: 105.0, time_to_expiry: 0.5, rate: 0.03, dividend_yield: 0.01, volatility: 0.25 }; f64_bits=[4059000000000000,405a400000000000,3fe0000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd0000000000000]",
            "units_per_call": 1,
            "control": false,
            "result_debug": "Ok(9.408847753107736)"
          },
          {
            "id": "ordinary/put_all_resolved",
            "inputs": "PricingInputs { option_type: Put, exercise_style: American, spot: 100.0, strike: 105.0, time_to_expiry: 0.5, rate: 0.03, dividend_yield: 0.01, volatility: 0.25 }; f64_bits=[4059000000000000,405a400000000000,3fe0000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd0000000000000]",
            "units_per_call": 1,
            "control": false,
            "result_debug": "Ok(Greeks { price: 9.408847753107736, delta: -0.5613566347702277, gamma: 0.023297610772773925, theta: -0.015998209707057343, vega: 27.568057289001636, rho: -24.78553076444402, vanna: 0.5556457386359057, volga: 6.747767511861635, charm: -0.00043095766461376445, veta: -0.07923581431044605, color: 5.7248165374871185e-5 })"
          },
          {
            "id": "controls/european_iv_baseline",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]; quote_bits=40397df98ba57cc1",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(IvResult { iv: 0.31999999999999934, iterations: 2, used_fallback: false, price_residual: 2.7755575615628914e-17, price_residual_unit: ForwardNormalisedPrice })"
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        ]
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          },
          "estimates": {
            "mean": {
              "confidence_interval": {
                "confidence_level": 0.95,
                "lower_bound": 74.72223561721489,
                "upper_bound": 75.32983382775028
              },
              "point_estimate": 75.01253262140457,
              "standard_error": 0.15579920792043606
            },
            "median": {
              "confidence_interval": {
                "confidence_level": 0.95,
                "lower_bound": 74.42841544629387,
                "upper_bound": 74.82946731456863
              },
              "point_estimate": 74.59825334507141,
              "standard_error": 0.1093546762212275
            },
            "median_abs_dev": {
              "confidence_interval": {
                "confidence_level": 0.95,
                "lower_bound": 0.4703806885903469,
                "upper_bound": 1.176290224647065
              },
              "point_estimate": 0.7588911285517078,
              "standard_error": 0.17588125894043882
            },
            "slope": {
              "confidence_interval": {
                "confidence_level": 0.95,
                "lower_bound": 74.4469205161252,
                "upper_bound": 75.24666859709515
              },
              "point_estimate": 74.81072054148183,
              "standard_error": 0.20710976569530642
            },
            "std_dev": {
              "confidence_interval": {
                "confidence_level": 0.95,
                "lower_bound": 0.9272757543836209,
                "upper_bound": 1.434277276699783
              },
              "point_estimate": 1.2135433718352866,
              "standard_error": 0.1295222613499535
            }
          },
          "benchmark": {
            "group_id": "controls",
            "function_id": "harness_arithmetic",
            "value_str": null,
            "throughput": {
              "Elements": 1
            },
            "full_id": "controls/harness_arithmetic",
            "directory_name": "controls/harness_arithmetic",
            "title": "controls/harness_arithmetic"
          }
        }
      },
      "observations": {
        "before": [
          {
            "id": "controls/harness_arithmetic",
            "inputs": "x=1.125; repeat32: x=sqrt(x*1.0001+.03125)+.3",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(1.5624999999999332)"
          },
          {
            "id": "controls/bsm_price",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(25.492089012052705)"
          },
          {
            "id": "controls/bsm_all",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(Greeks { price: 25.492089012052705, delta: 0.7965043257398099, gamma: 0.008292498274462608, theta: -0.019892440655369183, vega: 28.65887403654276, rho: 52.56632255754338, vanna: -0.49419627580829256, volga: 43.68476831073948, charm: 0.0002561413321583294, veta: -0.07227259172863033, color: 9.380022884777405e-6 })"
          },
          {
            "id": "ordinary/put_price",
            "inputs": "PricingInputs { option_type: Put, exercise_style: American, spot: 100.0, strike: 105.0, time_to_expiry: 0.5, rate: 0.03, dividend_yield: 0.01, volatility: 0.25 }; f64_bits=[4059000000000000,405a400000000000,3fe0000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd0000000000000]",
            "units_per_call": 1,
            "control": false,
            "result_debug": "Ok(9.408847753107736)"
          },
          {
            "id": "ordinary/put_all_resolved",
            "inputs": "PricingInputs { option_type: Put, exercise_style: American, spot: 100.0, strike: 105.0, time_to_expiry: 0.5, rate: 0.03, dividend_yield: 0.01, volatility: 0.25 }; f64_bits=[4059000000000000,405a400000000000,3fe0000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd0000000000000]",
            "units_per_call": 1,
            "control": false,
            "result_debug": "Ok(Greeks { price: 9.408847753107736, delta: -0.5613566347702277, gamma: 0.023297610772773925, theta: -0.015998209707057343, vega: 27.568057289001636, rho: -24.78553076444402, vanna: 0.5556457386359057, volga: 6.747767511861635, charm: -0.00043095766461376445, veta: -0.07923581431044605, color: 5.7248165374871185e-5 })"
          },
          {
            "id": "controls/european_iv_baseline",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]; quote_bits=40397df98ba57cc1",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(IvResult { iv: 0.31999999999999934, iterations: 2, used_fallback: false, price_residual: 2.7755575615628914e-17, price_residual_unit: ForwardNormalisedPrice })"
          }
        ],
        "after": [
          {
            "id": "controls/harness_arithmetic",
            "inputs": "x=1.125; repeat32: x=sqrt(x*1.0001+.03125)+.3",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(1.5624999999999332)"
          },
          {
            "id": "controls/bsm_price",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(25.492089012052705)"
          },
          {
            "id": "controls/bsm_all",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(Greeks { price: 25.492089012052705, delta: 0.7965043257398099, gamma: 0.008292498274462608, theta: -0.019892440655369183, vega: 28.65887403654276, rho: 52.56632255754338, vanna: -0.49419627580829256, volga: 43.68476831073948, charm: 0.0002561413321583294, veta: -0.07227259172863033, color: 9.380022884777405e-6 })"
          },
          {
            "id": "ordinary/put_price",
            "inputs": "PricingInputs { option_type: Put, exercise_style: American, spot: 100.0, strike: 105.0, time_to_expiry: 0.5, rate: 0.03, dividend_yield: 0.01, volatility: 0.25 }; f64_bits=[4059000000000000,405a400000000000,3fe0000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd0000000000000]",
            "units_per_call": 1,
            "control": false,
            "result_debug": "Ok(9.408847753107736)"
          },
          {
            "id": "ordinary/put_all_resolved",
            "inputs": "PricingInputs { option_type: Put, exercise_style: American, spot: 100.0, strike: 105.0, time_to_expiry: 0.5, rate: 0.03, dividend_yield: 0.01, volatility: 0.25 }; f64_bits=[4059000000000000,405a400000000000,3fe0000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd0000000000000]",
            "units_per_call": 1,
            "control": false,
            "result_debug": "Ok(Greeks { price: 9.408847753107736, delta: -0.5613566347702277, gamma: 0.023297610772773925, theta: -0.015998209707057343, vega: 27.568057289001636, rho: -24.78553076444402, vanna: 0.5556457386359057, volga: 6.747767511861635, charm: -0.00043095766461376445, veta: -0.07923581431044605, color: 5.7248165374871185e-5 })"
          },
          {
            "id": "controls/european_iv_baseline",
            "inputs": "PricingInputs { option_type: Call, exercise_style: European, spot: 120.0, strike: 100.0, time_to_expiry: 0.75, rate: 0.03, dividend_yield: 0.01, volatility: 0.32 }; f64_bits=[405e000000000000,4059000000000000,3fe8000000000000,3f9eb851eb851eb8,3f847ae147ae147b,3fd47ae147ae147b]; quote_bits=40397df98ba57cc1",
            "units_per_call": 1,
            "control": true,
            "result_debug": "Ok(IvResult { iv: 0.31999999999999934, iterations: 2, used_fallback: false, price_residual: 2.7755575615628914e-17, price_residual_unit: ForwardNormalisedPrice })"
          }
        ]
      }
    }
  },
  "quantlib": {
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      "version": "1.41",
      "python": "3.14.7 (main, Aug  5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]",
      "platform": "macOS-26.6.2-arm64-arm-64bit-Mach-O",
      "wheel_metadata": "Wheel-Version: 1.0\nGenerator: setuptools (75.3.2)\nRoot-Is-Purelib: false\nTag: cp38-abi3-macosx_11_0_arm64\n\n",
      "binary_sha256": "65de4ccb730b8135f0c67fbe97327057b726766d3a2d3aebb91857338812c320",
      "evaluation_date": "2026-09-09",
      "day_counter": "Actual/360",
      "inputs": {
        "european": {
          "option": "Call",
          "spot": 120.0,
          "strike": 100.0,
          "days": 270,
          "years": 0.75,
          "rate": 0.03,
          "yield_rate": 0.01,
          "volatility": 0.32,
          "maturity": "2027-06-06",
          "f64_bits": {
            "spot": "405e000000000000",
            "strike": "4059000000000000",
            "years": "3fe8000000000000",
            "rate": "3f9eb851eb851eb8",
            "yield_rate": "3f847ae147ae147b",
            "volatility": "3fd47ae147ae147b"
          }
        },
        "american": {
          "option": "Put",
          "spot": 100.0,
          "strike": 105.0,
          "days": 180,
          "years": 0.5,
          "rate": 0.03,
          "yield_rate": 0.01,
          "volatility": 0.25,
          "maturity": "2027-03-08",
          "f64_bits": {
            "spot": "4059000000000000",
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            "years": "3fe0000000000000",
            "rate": "3f9eb851eb851eb8",
            "yield_rate": "3f847ae147ae147b",
            "volatility": "3fd0000000000000"
          }
        }
      },
      "iv_quote_bits": "40397df98ba57cc1",
      "iv_solver": {
        "accuracy": 1e-10,
        "max_evaluations": 100,
        "min_vol": 1e-07,
        "max_vol": 4.0
      },
      "greek_order": [
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        "vega",
        "theta_per_365_day",
        "rho"
      ],
      "before": {
        "european_price": 25.49208901205275,
        "european_iv": 0.3199999999999976,
        "european_greeks": [
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        "american_price": 9.377807299465326,
        "american_greeks": [
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      "samples": {
        "european_price": {
          "iterations": 25944,
          "elapsed_ns": [
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          "median_ns": 1792.3837688868332
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        "european_iv": {
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          "elapsed_ns": [
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          "median_ns": 9645.73801472051
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        "european_greeks": {
          "iterations": 16151,
          "elapsed_ns": [
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          "median_ns": 3108.0144573091447
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        "american_price": {
          "iterations": 20708,
          "elapsed_ns": [
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          "median_ns": 2417.366887193355
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        "american_greeks": {
          "iterations": 13380,
          "elapsed_ns": [
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          "median_ns": 3738.378176382661
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      },
      "after": {
        "european_price": 25.49208901205275,
        "european_iv": 0.3199999999999976,
        "european_greeks": [
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        "american_price": 9.377807299465326,
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      }
    },
    "Q2": {
      "version": "1.41",
      "python": "3.14.7 (main, Aug  5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]",
      "platform": "macOS-26.6.2-arm64-arm-64bit-Mach-O",
      "wheel_metadata": "Wheel-Version: 1.0\nGenerator: setuptools (75.3.2)\nRoot-Is-Purelib: false\nTag: cp38-abi3-macosx_11_0_arm64\n\n",
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      "evaluation_date": "2026-09-09",
      "day_counter": "Actual/360",
      "inputs": {
        "european": {
          "option": "Call",
          "spot": 120.0,
          "strike": 100.0,
          "days": 270,
          "years": 0.75,
          "rate": 0.03,
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          "volatility": 0.32,
          "maturity": "2027-06-06",
          "f64_bits": {
            "spot": "405e000000000000",
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            "volatility": "3fd47ae147ae147b"
          }
        },
        "american": {
          "option": "Put",
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          "strike": 105.0,
          "days": 180,
          "years": 0.5,
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          "yield_rate": 0.01,
          "volatility": 0.25,
          "maturity": "2027-03-08",
          "f64_bits": {
            "spot": "4059000000000000",
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            "rate": "3f9eb851eb851eb8",
            "yield_rate": "3f847ae147ae147b",
            "volatility": "3fd0000000000000"
          }
        }
      },
      "iv_quote_bits": "40397df98ba57cc1",
      "iv_solver": {
        "accuracy": 1e-10,
        "max_evaluations": 100,
        "min_vol": 1e-07,
        "max_vol": 4.0
      },
      "greek_order": [
        "delta",
        "gamma",
        "vega",
        "theta_per_365_day",
        "rho"
      ],
      "before": {
        "european_price": 25.49208901205275,
        "european_iv": 0.3199999999999976,
        "european_greeks": [
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          0.008292498274462611,
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    "passed": true,
    "american": "Different approximations; finite outputs retained, no equality or accuracy-ranking claim."
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}
