Public evidence

math.percent_error

Machine-checked verification for calculation version 1.1.4 · tier engine_tested

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

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· T≠0; solve_for p|o|t; all three fields verify; absolute reverse-solves are multi-valued · Protocol · Schema · Production report

Declared partition coverage: PASS · 5/5 declared partitions (forward, inverse-observed, inverse-true, verify, invalid-domain)
Versions: Calculation 1.1.4 · CVP protocol 1.0.0-proposed
CVP identity: 3/3 property · digest 620c0f56d567

Verification

Legacy regression suite: 14/14 calculation tests · Production surface contract 3/3

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.

This calculator CURRENT · Public schema 1.1.4 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Calculation version 1.1.4. CVP 1.0.0-proposed. 6/6 golden · 4/4 CVP boundary · 4/4 invalid · 3/3 property · 1/1 metamorphic · 7/7 round-trip · 1/1 cross-interface · 1/1 CVP contract. digest 620c0f56d567.

Golden (oracle-backed) 6 / 6
CVP boundary 4 / 4
Invalid input 4 / 4
Property 3 / 3
Metamorphic 1 / 1
Round-trip 7 / 7
Cross-interface 1 / 1
CVP contract 1 / 1
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Assurance Engineering

release artifacts aligned PASS
schema valid input executes PASS
engine success output validates schema PASS

Fingerprint sha256:783cd14e12cb9811044d6bc3fce9d6c1f6fd3cf96201ae81a3916d8ad4aad9f1

Input schema sha256:9e03727ba37a3e2ed408e1b5848d278926befd7c7560784f476b13b239ba0ac9 · Output schema sha256:1ffdaff2555960cc04fef346c1146c38f6a8feb12995a9fdb488e220d00a439c · 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: 2026-09-10
Evidence core: 2026-09-10T22:48:17.762Z
Rendered: 2026-09-16T22:03:43.775Z
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.
Exactly two fields are inputs. Explicit solve_for selects the output. If all three are supplied without solve_for, they are checked for consistency rather than overwritten.

Limitations

T = 0 → TRUE_VALUE_ZERO
Inconsistent triples may return status inconsistent
Reverse solve edge cases → NO_REAL_SOLUTION / INFINITELY_MANY

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.

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`basic`	golden	pass	Expected 1.5 · Actual value=1.5 · solve_for=p · observed=101.5 · true=100 · percent_error=1.5 · absolute_error=1.5 · relative_error=0.015 · signed_percent_error=1.5
`approx`	golden	pass	Expected 8.7217417812505 · Actual value=8.7217417812505 · solve_for=p · observed=56.891 · true=62.327 · percent_error=8.7217417812505 · absolute_error=5.436 · relative_error=0.08721741781250501 · signed_percent_error=-8.7217417812505
`exact`	golden	pass	Expected 0 · Actual value=0 · solve_for=p · observed=5 · true=5 · percent_error=0 · absolute_error=0 · relative_error=0 · signed_percent_error=0
`share-ot`	golden	pass	Expected percent_error=2 · absolute_error=2 · relative_error=0.02 · Actual value=2 · solve_for=p · observed=98 · true=100 · percent_error=2 · absolute_error=2 · relative_error=0.02 · signed_percent_error=-2
`signed`	golden	pass	Expected percent_error=-22.22222222222222 · Actual value=-22.22222222222222 · solve_for=p · observed=7 · true=9 · percent_error=-22.22222222222222 · absolute_error=2 · relative_error=0.2222222222222222 · signed_percent_error=-22.22222222222222
`reverse-o-abs`	golden	pass	Expected value=98 · solve_for=o · solution_type=two · status=success · Actual value=98 · solve_for=o · true=100 · percent_error=2 · absolute_error=2 · relative_error=0.02 · signed_percent_error=-2 · absolute=true
`zero-true`	boundary	pass	Expected TRUE_VALUE_ZERO · Actual TRUE_VALUE_ZERO
`inconsistent`	golden	pass	Expected status=inconsistent · code=INCONSISTENT_INPUTS · percent_error=2 · Actual value=2 · solve_for=p · observed=98 · true=100 · percent_error=2 · entered_percent_error=20 · absolute_error=2 · relative_error=0.02
`infinite-t`	golden	pass	Expected status=infinite · code=INFINITELY_MANY · constraint=T != 0 · solution_type=infinite · Actual solve_for=t · observed=0 · percent_error=100 · relative_error=1 · absolute=true · status=infinite · code=INFINITELY_MANY · solution_type=infinite
`no-sol-t`	boundary	pass	Expected NO_REAL_SOLUTION · Actual NO_REAL_SOLUTION
`solve-t-p100`	golden	pass	Expected value=25 · solve_for=t · true=25 · solution_type=unique · Actual value=25 · solve_for=t · observed=50 · true=25 · percent_error=100 · absolute_error=25 · relative_error=1 · signed_percent_error=100
`infinite-t-signed`	golden	pass	Expected status=infinite · code=INFINITELY_MANY · constraint=T != 0 · solution_type=infinite · Actual solve_for=t · observed=0 · percent_error=-100 · relative_error=1 · signed_percent_error=-100 · absolute=false · status=infinite · code=INFINITELY_MANY
`no-sol-t-signed-p`	boundary	pass	Expected NO_REAL_SOLUTION · Actual NO_REAL_SOLUTION
`no-sol-t-signed-o0`	boundary	pass	Expected NO_REAL_SOLUTION · Actual NO_REAL_SOLUTION