Public evidence

math.percent_error

Machine-checked verification for calculation version 1.1.5 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest Reproduce MCP Review policy

CVP status

All p/o/t directions, absolute/signed and strict-zero8ULP triple consistency; exact binary64-rational arithmetic, complete inverse branches with individual diagnostics, exact infinite endpoints and explicit range/rounding limits

Declared partition coverage: PASS · 5/5 declared partitions (forward, inverse-observed, inverse-true, verify, invalid-domain)
Versions: Calculation 1.1.5 · CVP protocol 1.0.0-proposed · Evidence 2026-10-22.percent-error-complete-contract-v3
Verification revision: 2026-10-22.percent-error-complete-contract-v3 · 3/3 property · digest 6f7189188a89

Verification

Legacy regression suite: 14/14 calculation tests · Production surface contract 6/6

Three distinct suites: educational examples on the calculator page, this legacy regression count (14/14 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

STALE · Build schema 1.1.5 matches page · production binding STALE · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-22.percent-error-complete-contract-v3. Calculation version 1.1.5. CVP 1.0.0-proposed. 151/151 golden · 4/4 CVP boundary · 37/37 invalid · 3/3 property · 1/1 metamorphic · 7/7 round-trip · 26/26 cross-interface · 3/3 cross-calculator · 6/6 CVP contract. digest 6f7189188a89. Private independent CPython Fraction/float checks complete primary, secondary and inverse branch sets on sampled normalized binary64 inputs; arithmetic comparison0 ULP, triple consistency8 ULP for same-sign nonzero percentages with strict zero. Public disclosure is summary-only, not the private full corpus.

Golden (oracle-backed) 151 / 151
CVP boundary 4 / 4
Invalid input 37 / 37
Property 3 / 3
Metamorphic 1 / 1
Round-trip 7 / 7
Cross-interface 26 / 26
Cross-calculator 3 / 3
CVP contract 6 / 6
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 4/4 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Assurance Engineering

release artifacts aligned PASS
schema output required declared PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS
rest success payload validates schema PASS

Fingerprint sha256:cc181c268aff9f75fe00900ab63528357899fb64397d05b1af05d931a22c0777

Input schema sha256:d45595a4c7095395487d1ba2ba9972b5d9c8322f128b8291a4d10694a58d771d · Output schema sha256:7dd6f7845c5c4200d83bdcbce30df5d6076babac04054264f38a7ee30819e5c7 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: percent-error
Engine: percent-error
Engine build: 2026-10-22
Evidence core: 2026-10-22T02:58:22.527Z
Rendered: 2026-10-22T08:54:35.071Z
Last reviewed: —

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.

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

JCGM 200:2012 — International vocabulary of metrology (VIM) — §2.16 measurement error
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.
NIST Dataplot PERCERR — Percent error of a true/accepted value vs an observed value
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.
NIST Dataplot RELERR — Relative error of a true/accepted value vs an observed value
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.
CalculatorX laboratory convention — 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.

Verification disclosure

Aggregate outcomes, scope and artifact commitments are public. Complete test inputs, expected values, execution records and oracle infrastructure are retained privately. This summary does not independently reproduce the full verification run.