{ "capability_id": "math.percent_error", "tool_id": "percent-error", "engine": "percent-error", "calculation_version": "1.1.5", "generated_at": "2026-10-22T08:54:35.071Z", "engine_build": "2026-10-22", "test_count": 14, "passed": 14, "failed": 0, "tests_summary": { "golden": { "passed": 10, "total": 10 }, "boundary": { "passed": 4, "total": 4 }, "property": { "passed": 0, "total": 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/percent-error", "api": "https://www.calculatorx.com/api/v1/calc/percent-error", "schema_input": "https://www.calculatorx.com/schemas/math.percent_error.input.json", "schema_output": "https://www.calculatorx.com/schemas/math.percent_error.output.json", "assumptions": [ "Interactive evaluation runs locally in the browser. Shared URLs and REST may evaluate the same versioned engine on the server (query SSR).", "Accepted value T ≠ 0.", "Default formula uses absolute value so % error ≥ 0.", "Two active fields solve the selected third; all three supplied values check consistency before solving, even with explicit solve_for. Consistency allows8 ULP for same-sign nonzero P and strict zero.", "Inverse P is the requested percentage. Candidates are rounded to binary64, so achieved_percent_error and resolution_limited disclose any discrepancy; two mathematical branches may round to the same float.", "All aliases must agree. Unknown inputs and invalid absolute/signed policies are rejected." ], "limitations": [ "T must be nonzero; quantities need the same ratio-scale unit.", "Private CPython Fraction reference covers sampled binary64 domains; no measurement uncertainty or exhaustive real-domain proof.", "Every valid branch/secondary result must fit binary64; NUMERIC_RANGE requires rescaling.", "Inverse P is requested; achieved P and resolution_limited describe candidate rounding; strict-zero8ULP triple consistency." ], "boundary_conditions": [ "T = 0 → TRUE_VALUE_ZERO (undefined)", "Fewer than two inputs → MISSING_REQUIRED_INPUT", "Invalid solve_for → INVALID_SOLVE_FOR", "Negative P in absolute mode → INVALID_PERCENT", "O = 0, P = 100%, absolute, solve T → INFINITELY_MANY (any T ≠ 0)", "O = 0, P ≠ 100%, absolute, solve T → NO_REAL_SOLUTION", "O ≠ 0, P = 100%, absolute, solve T → T = O/2; the 1 − P/100 branch is omitted (not a full calculation error)", "O = 0, P = −100%, signed, solve T → INFINITELY_MANY (any T ≠ 0)", "O = 0, P ≠ −100%, signed, solve T → NO_REAL_SOLUTION", "O ≠ 0, P = −100%, signed, solve T → NO_REAL_SOLUTION", "Solving from P may yield two candidates (±) when absolute mode is on", "All three supplied values not consistent within8 ULP and strict zero → INCONSISTENT_INPUTS, including explicit solve_for", "NUMERIC_RANGE rejects nonzero text/output underflow or overflow, including secondary fields and any valid inverse branch", "Invalid number/type, conflicting aliases, unknown field, or invalid absolute policy → explicit recoverable error" ], "sources": [ { "title": "JCGM 200:2012 — International vocabulary of metrology (VIM)", "section": "§2.16 measurement error", "url": "https://www.bipm.org/en/committees/jc/jcgm/publications", "supports": "Defines measurement error as measured quantity value minus a reference quantity value (ε = O − T). Does not define relative error — VIM §2.18 is measurement bias, not relative error. Does not prescribe a percent-error ×100% laboratory convention.", "kind": "reference", "accessed": "2026-08-28" }, { "title": "NIST Dataplot PERCERR", "section": "Percent error of a true/accepted value vs an observed value", "url": "https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/percerr.htm", "supports": "Documents percent error from an accepted (true) value and an observed value, and notes that some conventions take the absolute value. Instantly readable page — not the frameset handbook root.", "kind": "reference", "accessed": "2026-08-28", "publisher": "National Institute of Standards and Technology" }, { "title": "NIST Dataplot RELERR", "section": "Relative error of a true/accepted value vs an observed value", "url": "https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/relerr.htm", "supports": "Documents relative error (Xt − Xo)/Xt. Notes that some sources take the absolute value, and some reverse numerator order — those change sign, not magnitude.", "kind": "reference", "accessed": "2026-08-28" }, { "title": "CalculatorX laboratory convention", "section": "Absolute-value percent error, signed opt-in, and reverse-solve states", "supports": "Default % error = |O−T|/|T|×100% so the result is ≥ 0; signed (O−T)/T×100% is opt-in. Displayed absolute error is |ε|, the magnitude of VIM measurement error — not a separate VIM term. Absolute reverse-solves publish both ± candidates, omit a zero-denominator branch, and publish INFINITELY_MANY when every T ≠ 0 works. Signed P = −100% with O ≠ 0 is NO_REAL_SOLUTION.", "kind": "definition" } ], "methods": [], "fingerprint": "sha256:cc181c268aff9f75fe00900ab63528357899fb64397d05b1af05d931a22c0777", "tier": "engine_tested", "verification": { "tests": { "passed": 14, "total": 14, "golden": 10, "boundary": 4, "property": 0 }, "contract_checks": { "passed": 6, "total": 6 } }, "evidence_core_generated_at": "2026-10-22T02:58:22.527Z", "rendered_at": "2026-10-22T08:54:35.071Z", "release_integrity": { "status": "verified", "scope": "workspace", "production_attestation_required": true, "calculation_version": "1.1.5", "artifacts": { "engine": "1.1.5", "page": "1.1.5", "capability": "1.1.5", "evidence": "1.1.5", "input_schema": "1.1.5", "output_schema": "1.1.5", "mcp_contract": "1.1.5" }, "digests": { "input_schema_sha256": "d45595a4c7095395487d1ba2ba9972b5d9c8322f128b8291a4d10694a58d771d", "output_schema_sha256": "7dd6f7845c5c4200d83bdcbce30df5d6076babac04054264f38a7ee30819e5c7", "evidence_sha256": "67c53720d73cf33f01dab347216965cd2ff26e42b57bba51d7c8ae21ecebf697", "evidence_core_sha256": "67c53720d73cf33f01dab347216965cd2ff26e42b57bba51d7c8ae21ecebf697", "capability_sha256": "8bc7ec7e68681b2f75257724ba64c62d0575c9a0e490cb3f7840ae54e1829aa7", "engine_sha256": "a664ae25cd2134de7de43a99352933043215473589aec38c9416508150cb1008", "mcp_contract_sha256": "a1a8617719bef45391ee6917dc1783a01de2eedf297e7596b3cb5017cd0e1560" }, "contract_checks": { "total": 6, "passed": 6, "failed": 0, "items": [ { "id": "release-artifacts-aligned", "status": "pass", "detail": "1.1.5" }, { "id": "schema-output-required-declared", "status": "pass" }, { "id": "schema-valid-input-executes", "status": "pass" }, { "id": "engine-success-output-validates-schema", "status": "pass" }, { "id": "schema-rejects-incomplete-input", "status": "pass" }, { "id": "rest-success-payload-validates-schema", "status": "pass" } ] }, "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json" }, "tests": [], "disclosure": { "policy": "calculatorx-public-evidence-v1", "full_validation": "private", "representation": "summary" } }