---
title: "algorithm-horner-tests — Mova code model"
description: "Mova code model of algorithms/src/horner/tests.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/horner/tests.rs.groupant/"
---
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# algorithm-horner-tests

The groupant beside algorithms/src/horner/tests.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

## Facts

- **kind:** groupant
- **status:** partial descriptive instance
- **source:** [`algorithms/src/horner/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/horner/tests.rs)
- **source SHA-256:** `751f5de9220401ae…`
- **repository folder:** [`algorithms/src/horner/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/horner/tests.rs.groupant)
- **repository commit:** `855da7bd4a7b`

> **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.

## Components

| component | label | where |
|---|---|---|
| **approximant** | partial | [approximant](#approximant) |
| **ast** | partial | `syntax.json` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [approximant](#approximant) |
| **tests** | focused executed full pending | [wave20-evidence](#wave20-evidence) |

## Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

| id | type | label | where |
|---|---|---|---|
| `behavior_complement` | behavior_complement | partial source derived model | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) |
| `oracle_independence` | oracle_independence | partial source derived model | [oracle_independence](#oracle-independence) |
| `mutation_sensitivity` | mutation_sensitivity | partial source derived model | [mutation_sensitivity](#mutation-sensitivity) |
| `finite_scope` | finite_scope | partial source derived model | [finite_scope](#finite-scope) |
| `reference_observation_equivalence` | bitwise_differential_relation | partial source derived model | [reference_observation_equivalence](#reference-observation-equivalence) |

## Model text


### descriptant

#### horner tests.rs

Executable finite checks for horner: power_oracle independently computes powers and differentiated powers, degrees 0..14 over 17 dyadic points; invalid/overflow cases.

Original std-only implementation. Literature: see module-level Clenshaw (1955), Horner (1819), Neumaier (1974), or Lyness (1969) citation as applicable; citations are algorithm references, not copied code.

Epoch 2026-10-30: independent polynomial/basis/integer fixtures and explicit finite-error partitions. Simpson hidden bump demonstrates limits of sampled estimates. An initial correction-denominator mutant survived tight-tolerance tests; a loose-tolerance quartic assertion was added to isolate the correction, and that mutant was then rejected. No speed claim; no percentages inferred from finite observations. Rust syntax projection is partial, without macro expansion, type resolution or semantic proof.

### model

### behavior_complement

For fixed fixtures, complement consists of assertion traces differing from the required exact errors, statuses or tolerance comparisons; implementations agreeing only here remain possible. A passing trace excludes the compiled mutant but not arbitrary bugs outside fixtures.

### reverse_reconstruction

Pass reconstructs the set of implementations consistent with these finite assertions; it does not identify one implementation. Untested inputs remain arbitrary. At x=0 value=c0 and derivative=c1; all higher coefficients remain free. [2,3,7] and [2,3,99] have identical outputs. With fixed degree and x, real fiber is intersection of two affine constraints; dependent constraints and f64 rounding require separate treatment.

### oracle_independence

power_oracle independently computes powers and differentiated powers, coefficient lengths 0..14 over 17 dyadic points; invalid/overflow cases.

### mutation_sensitivity

Replace derivative +value with -value; power_oracle fails

### finite_scope

Finite fixture agreement supplies empirical observations, not a semantic proof or universal error cap. Different implementations with the same fixture outputs remain in the pass fiber.


### reference_observation_equivalence

Compare original per-step and final gates on 133332 combinations (coefficient lengths 0..4, ten values, twelve arguments), two invalid-coefficient cases and derivative-only overflow. Compare both success bit patterns including signed zero, and exact error variants. The shared recurrence reference is complemented by the independent power oracle.

### approximant

#### Forward model and invariant

Three tests combine independent power/derivative observations, boundary/fiber witnesses and full-width comparison with original gate placement. Success bits and error variants remain distinct.

Invariant: 133332 deterministic loop cases compare success bits and exact errors. The missing-derivative-gate mutant must fail W20-HORNER-DERIVATIVE-GATE.

Cost: Fixed corpus: 133332 comparisons with at most four coefficients, 255 independent power-oracle cases of lengths 0..14, and boundaries. Oracle cost is distinct from production.

IEEE-754 assumptions; no universal real accuracy guarantee. Wave20 is exact in its Result observation, not an approximate surrogate.

### tests

#### Evidence

power_oracle independently computes powers and differentiated powers, degrees 0..14 over 17 dyadic points; invalid/overflow cases.

Compiled production negative control: Replace derivative +value with -value; power_oracle fails. Original bytes restored and named positive test rerun. Full algorithms library passes twice debug and twice release with identical sorted test-name/results; receipts bind logs under $MOVA_DATA/runs/octopus-wave19-numeric-2026-10-30. Source projection generated twice and compared before installation. Strict crate all-target Clippy attempted; outcome in receipt.

### wave20-evidence

#### Horner optimization evidence — 2026-10-30

One final finite-pair gate replaces per-coefficient output gates after finite input validation. Under ordinary IEEE-754 arithmetic, nonfinite recurrence states cannot recover to an admitted finite final pair. Successful arithmetic order and Result variants are retained; failure can traverse more coefficients. Root's compiled production mutant rejects; restored code passes four integrated algorithm profiles. Source SHA-256 751f5de9220401aea97bd6d76e421eb99102a06168dd1bb848757d5b8d26f0a5.

[Native receipts](https://md.groupants.elamur.ai/free/en/mova/models/algorithm-library.groupant/#wave20-evidence) and [actual CPU report](https://md.groupants.elamur.ai/free/en/mova/models/algorithm-library.groupant/#wave20-benchmark) distinguish the scoped absorption argument, finite observations and measured work. Historical wave19 measurements remain unchanged.