{
  "capability_id": "math.antilog",
  "tool_id": "anti-log",
  "engine": "antilog",
  "calculation_version": "1.0.5",
  "generated_at": "2026-09-16T22:03:43.777Z",
  "engine_build": "2026-09-10",
  "test_count": 33,
  "passed": 33,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 14,
      "passed": 14
    },
    "boundary": {
      "total": 19,
      "passed": 19
    },
    "property": {
      "total": 0,
      "passed": 0
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/math/anti-log",
  "api": "https://www.calculatorx.com/api/v1/calc/anti-log",
  "schema_input": "https://www.calculatorx.com/schemas/math.antilog.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.antilog.output.json",
  "assumptions": [
    "Real arithmetic; base b > 0 and b ≠ 1.",
    "Result x is positive for real y when b > 0."
  ],
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    "Base must be > 0 and ≠ 1 → INVALID_BASE",
    "Missing y → MISSING_REQUIRED_INPUT; overflow/underflow → RESULT_OVERFLOW / RESULT_UNDERFLOW"
  ],
  "boundary_conditions": [
    "Invalid base (≤ 0 or 1) returns INVALID_BASE.",
    "0 < b < 1 is valid (for example 0.5² = 0.25).",
    "y = 0 returns 1 for every valid base.",
    "Extreme |y| may overflow (RESULT_OVERFLOW) or underflow (RESULT_UNDERFLOW)."
  ],
  "sources": [
    {
      "title": "NIST Digital Library of Mathematical Functions, Chapter 4",
      "section": "Logarithm, Exponential, Powers",
      "url": "https://dlmf.nist.gov/4",
      "supports": "Logarithm and exponential as inverse operations; antilog is exponentiation x = b^y",
      "kind": "reference"
    },
    {
      "title": "NIST DLMF §4.2",
      "section": "Logarithm: definitions and inverse of the exponential",
      "url": "https://dlmf.nist.gov/4.2",
      "supports": "b^(log_b x) = x and log_b(b^y) = y for valid real b and x",
      "kind": "reference"
    },
    {
      "title": "CalculatorX mathematical conventions",
      "section": "Common (base 10), natural (base e), and real bases b > 0, b ≠ 1",
      "supports": "Unspecified antilog is common (base 10); custom bases may be in (0, 1)",
      "kind": "definition"
    }
  ],
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  "fingerprint": "sha256:702267ebeacaaf96d0d5cd571fbad402d9a11466fbb36b528ba29a5a5147f357",
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        "base": "10"
      },
      "expect": 1000,
      "expectWarning": null,
      "actual": 1000,
      "tol": 0
    },
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      "id": "natural-3",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "y": 3,
        "base": "e"
      },
      "expect": 20.085536923187668,
      "expectWarning": null,
      "actual": 20.085536923187668,
      "tol": 1e-12
    },
    {
      "id": "binary-3",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "y": 3,
        "base": "2"
      },
      "expect": 8,
      "expectWarning": null,
      "actual": 8,
      "tol": 0
    },
    {
      "id": "common-neg2",
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      "kind": "golden",
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        "y": -2,
        "base": 10
      },
      "expect": 0.01,
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      "actual": 0.01,
      "tol": 1e-12
    },
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      "id": "custom-8",
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        "b": 8
      },
      "expect": 512,
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      "tol": 0
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      "id": "y-zero",
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        "base": 10
      },
      "expect": 1,
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      "tol": 0
    },
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      "id": "sqrt-10",
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        "y": 0.5,
        "base": 10
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      "expect": 3.1622776601683795,
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      "tol": 1e-12
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      "id": "base-lt-one",
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        "y": 2,
        "b": 0.5
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      "expectWarning": null,
      "actual": 0.25,
      "tol": 0
    },
    {
      "id": "base-lt-one-neg",
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        "b": 0.5
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      "expect": 4,
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      "actual": 4,
      "tol": 0
    },
    {
      "id": "decimal-custom",
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      "kind": "golden",
      "inputs": {
        "y": 2,
        "b": 1.5
      },
      "expect": 2.25,
      "expectWarning": null,
      "actual": 2.25,
      "tol": 1e-12
    },
    {
      "id": "invalid-base-1",
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      "kind": "boundary",
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        "y": 3,
        "b": 1
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      "expectError": "INVALID_BASE",
      "code": "INVALID_BASE",
      "error": "Base must be positive and not equal to 1."
    },
    {
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        "b": 0
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      "expectError": "INVALID_BASE",
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      "error": "Base must be positive and not equal to 1."
    },
    {
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        "b": -2
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      "expectError": "INVALID_BASE",
      "code": "INVALID_BASE",
      "error": "Base must be positive and not equal to 1."
    },
    {
      "id": "empty-y",
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      "code": "MISSING_REQUIRED_INPUT",
      "error": "Enter a numeric log value y."
    },
    {
      "id": "nan-y",
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      "inputs": {
        "y": "n/a",
        "base": 10
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      "expectError": "INVALID_NUMBER",
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      "error": "Enter a numeric log value y."
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    {
      "id": "overflow",
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      "inputs": {
        "y": 400,
        "base": 10
      },
      "expectError": "RESULT_OVERFLOW",
      "code": "RESULT_OVERFLOW",
      "error": "Result overflowed or is undefined for these inputs."
    },
    {
      "id": "underflow",
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      "kind": "boundary",
      "inputs": {
        "y": -400,
        "base": 10
      },
      "expectError": "RESULT_UNDERFLOW",
      "code": "RESULT_UNDERFLOW",
      "error": "Result underflowed to zero for these inputs."
    },
    {
      "id": "near-base-one",
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        "y": 2,
        "b": 1.000000000000001
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      "expect": 1.000000000000002,
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      "actual": 1.0000000000000022,
      "tol": 1e-12
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    {
      "id": "tiny-positive-base",
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        "b": 1e-100
      },
      "expect": 1e-200,
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      "expect": 1.2599210498948732,
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    {
      "id": "large-finite",
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        "base": 10
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      "expect": 1e+308,
      "expectWarning": null,
      "actual": 1e+308,
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    {
      "id": "overflow-309",
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      "inputs": {
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      "expectError": "RESULT_OVERFLOW",
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      "error": "Result overflowed or is undefined for these inputs."
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    {
      "id": "y-infinity",
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      "inputs": {
        "y": "Infinity",
        "base": 10
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      "expectError": "INVALID_NUMBER",
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      "error": "Enter a numeric log value y."
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    {
      "id": "y-nan",
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        "y": "NaN",
        "base": 10
      },
      "expectError": "INVALID_NUMBER",
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      "error": "Enter a numeric log value y."
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    {
      "id": "y-abc",
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        "y": "abc",
        "base": 10
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      "expectError": "INVALID_NUMBER",
      "code": "INVALID_NUMBER",
      "error": "Enter a numeric log value y."
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    {
      "id": "y-whitespace",
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        "y": "   ",
        "base": 10
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      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "Enter a numeric log value y."
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      "id": "y-null",
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