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

The groupant beside math/src/deriv.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 source bound model
- **source:** [`math/src/deriv.rs`](https://github.com/ElamurAI/mova-free/blob/main/math/src/deriv.rs)
- **source SHA-256:** `0ea96ef4d7df85aa…`
- **repository folder:** [`math/src/deriv.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/deriv.rs.groupant)
- **repository commit:** `48f2e6f74146`

> **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` |
| **composition** | partial | [composition](#composition) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | executed bounded checks | [tests](#tests) |

## 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) |
| `domain_erasure` | domain_erasure | partial source derived model | [domain_erasure](#domain-erasure) |
| `rule_order` | rule_order | partial source derived model | [rule_order](#rule-order) |
| `sample_metric` | sample_metric | partial source derived model | [sample_metric](#sample-metric) |
| `constant_fiber` | constant_fiber | partial source derived model | [constant_fiber](#constant-fiber) |

## Parts

- [math-deriv-simplification](https://md.groupants.elamur.ai/free/en/mova/math/src/deriv.rs.groupant/simplification.groupant/)
- [math-deriv-rules](https://md.groupants.elamur.ai/free/en/mova/math/src/deriv.rs.groupant/rules.groupant/)
- [math-deriv-numerical-check](https://md.groupants.elamur.ai/free/en/mova/math/src/deriv.rs.groupant/numerical-check.groupant/)

## Model text


### descriptant

#### deriv

simplify recursively folds Q constants/identities including0*x and0/x, with constant power |k|<=64. derive returns0 first if target absent; otherwise applies arithmetic and supported unary chain rules, appends steps and simplifies. Supported calls sin/cos/tan/exp/ln/log/sqrt/asin/acos/atan. check_derivative samples eight fixed points, central difference h=1e-5 max(|p|,1), skips unsupported/nonfinite samples and accepts >=3 usable points with each normalized discrepancy<=1e-5 against max(|df|,1).

Epoch 2026-10-31: complete source read before edits, bounded actual-code tests and source controls. Linsys shape defect was witnessed on old code and repaired; other semantics retained. External receipt name octopus-wave28-mathcore-2026-10-31 includes prospective.md. Registration is partial, not verification.

### approximant

#### Forward and cost

simplify recursively folds Q constants/identities including0*x and0/x, with constant power |k|<=64. derive returns0 first if target absent; otherwise applies arithmetic and supported unary chain rules, appends steps and simplifies. Supported calls sin/cos/tan/exp/ln/log/sqrt/asin/acos/atan. check_derivative samples eight fixed points, central difference h=1e-5 max(|p|,1), skips unsupported/nonfinite samples and accepts >=3 usable points with each normalized discrepancy<=1e-5 against max(|df|,1).

Repeated has/vars scans and dedup, subtree cloning and simplify can be quadratic or output-size dominated, without AST budget. Numerical check uses up to24 evaluations plus cloned envs: O(8*(cost(f)+cost(df)+env size)), with delegated arithmetic and recursion.

No new executable Rust surrogate: exact values, branching, domains and effects require an observation-specific metric before supported 1/2/5/10% profiles. Existing floating diagnostics are not such a profile; no speed claim.

### invariant

#### Domain and invariant

Rules need valid mathematical domains; simplify retains none and0/0 becomes0. i64 MIN abs unchecked at power guard. Steps can append before child failure; errors are not atomic. Expression copying may grow or exhaust stack/resources. Checker clones env and overwrites target; calc::approx subset can leave fewer than3 usable points, which fails. No proof from finite samples.

simplify recursively folds Q constants/identities including0*x and0/x, with constant power |k|<=64. derive returns0 first if target absent; otherwise applies arithmetic and supported unary chain rules, appends steps and simplifies. Supported calls sin/cos/tan/exp/ln/log/sqrt/asin/acos/atan. check_derivative samples eight fixed points, central difference h=1e-5 max(|p|,1), skips unsupported/nonfinite samples and accepts >=3 usable points with each normalized discrepancy<=1e-5 against max(|df|,1).

Derivative g admits all supported source trees whose rule expansion simplifies to g. On connected valid domains antiderivatives already differ by additive constants; syntax simplification expands fibers. Unknown target-free calls also map0. Numeric Check constrains only sampled neighborhoods, not a unique antecedent or global identity; steps are partial rule traces, not reversible serialization.

### composition

#### Composition

simplify recursively folds Q constants/identities including0*x and0/x, with constant power |k|<=64. derive returns0 first if target absent; otherwise applies arithmetic and supported unary chain rules, appends steps and simplifies. Supported calls sin/cos/tan/exp/ln/log/sqrt/asin/acos/atan. check_derivative samples eight fixed points, central difference h=1e-5 max(|p|,1), skips unsupported/nonfinite samples and accepts >=3 usable points with each normalized discrepancy<=1e-5 against max(|df|,1).

calc dispatches to comb/nt. poly/linsys consume calc E and stateful Env for constants; deriv consumes E and calc::approx. fcheck consumes separate legacy expr::Expr/units, with no implicit lossless E adapter. Q/Z joins use big. Parent symbolic-computation models these edges; local checks do not certify application wiring. Nested scopes reuse parent syntax, and remaining helpers/types/tests are parent-modeled.

### models

## Typed models

### behavior_complement

For fixed admitted input/state, exclude outputs and effect traces contradicting this actual relation: simplify recursively folds Q constants/identities including0*x and0/x, with constant power |k|<=64. derive returns0 first if target absent; otherwise applies arithmetic and supported unary chain rules, appends steps and simplifies. Supported calls sin/cos/tan/exp/ln/log/sqrt/asin/acos/atan. check_derivative samples eight fixed points, central difference h=1e-5 max(|p|,1), skips unsupported/nonfinite samples and accepts >=3 usable points with each normalized discrepancy<=1e-5 against max(|df|,1). These exclusions are conditional on the stated domain. Unavailable checks, passing residuals and resource limits do not establish global correctness.

### reverse_reconstruction

Derivative g admits all supported source trees whose rule expansion simplifies to g. On connected valid domains antiderivatives already differ by additive constants; syntax simplification expands fibers. Unknown target-free calls also map0. Numeric Check constrains only sampled neighborhoods, not a unique antecedent or global identity; steps are partial rule traces, not reversible serialization.

### domain_erasure

0/x and0*undefined rewrite to0, losing singularity/error effects. Syntax equality does not prove preserved domain.

### rule_order

Target absence precedes unsupported-call rejection; chain derives child first, and rule steps can survive failure.

### sample_metric

Eight fixed points, >=3 usable and normalized error<=1e-5 are finite diagnostics, not supported percent surrogate profiles/global bounds.

### constant_fiber

Every target-free tree maps0, including unsupported calls; reverse recovery needs domain and constant ambiguity.

### tests

#### Actual-code evidence 2026-10-31

Each selected named test passed twice debug/twice release, sorted outcomes identical:

- `test deriv::tests::derivatives_with_checks ... ok`
- `test deriv::wave28::unsupported_constants_and_domain_erasure ... ok`

Compiled source control: control-deriv.patch.txt; compiler exit0, test nonzero, exact source restoration and focused positive exit0. Full logs and numeric exits retained externally in octopus-wave28-mathcore-2026-10-31. Linsys also retains shape-old compile 0 / test 101 witness before shape repair. Seven module controls plus the additional linsys width-guard control; fragment declarations are not extra tests.

Finite synthetic fixtures only; no teacher/API/corpus/GPU/heldout. No allocation/stack faults, huge sizes, deadline proof, or universal numerical bound.

Final validation: eight compiled mutants total (seven module boundaries plus linsys width guard), all compile 0 / test 101 and exact restoration / positive 0. Old-code count mismatch witness compile 0 / test 101 separately. Full-registry structural run reports only ancestor integration bindings; isolated source snapshots validate each owned sidecar. Strict Clippy: dependency invocation blocked in existing global build script; --no-deps reaches math and reports 113 existing library findings, retained externally, no clean lint claim. Added test blocks formatted independently; production layout preserved.