---
title: "math-deriv-rules — 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/rules.groupant/"
---
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# math-deriv-rules

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_fragment
- **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…`
- **covers:** derive checks target absence then arithmetic/chain rules. Steps append during recursion and survive errors. Inverse fibers remain nonunique/domain-dependent. Repeated has/simplify/clones dominate work, no integration or bounded output size guarantee. (bytes 2437–6714)
- **part of:** [math-deriv](https://md.groupants.elamur.ai/free/en/mova/math/src/deriv.rs.groupant/)
- **repository folder:** [`math/src/deriv.rs.groupant/rules.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/deriv.rs.groupant/rules.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` |
| **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) |
| `product_quotient` | product_quotient | partial source derived model | [product_quotient](#product-quotient) |
| `power_cases` | power_cases | partial source derived model | [power_cases](#power-cases) |
| `chain_dispatch` | chain_dispatch | partial source derived model | [chain_dispatch](#chain-dispatch) |
| `step_prefix` | step_prefix | partial source derived model | [step_prefix](#step-prefix) |

## Model text


### descriptant

#### math-deriv-rules

derive checks target absence then arithmetic/chain rules. Steps append during recursion and survive errors. Inverse fibers remain nonunique/domain-dependent. Repeated has/simplify/clones dominate work, no integration or bounded output size guarantee.

Epoch 2026-10-31: complete source read, parent AST reused; partial finite evidence only.

### approximant

#### Scoped forward and cost

derive checks target absence then arithmetic/chain rules. Steps append during recursion and survive errors. Inverse fibers remain nonunique/domain-dependent. Repeated has/simplify/clones dominate work, no integration or bounded output size guarantee.

No executable percent surrogate claimed.

### invariant

#### Scoped invariant

derive checks target absence then arithmetic/chain rules. Steps append during recursion and survive errors. Inverse fibers remain nonunique/domain-dependent. Repeated has/simplify/clones dominate work, no integration or bounded output size guarantee.

Source range[2437,6714) bound by manifest digest. Parent domain applies, not arbitrary public states.

### models

## Source-scoped typed relations

### behavior_complement

A target-dependent unsupported call excludes Ok; the same unknown call without target excludes Err and returns0 because absence test wins. Rule construction never consults a numeric sample to decide supportedness.

### reverse_reconstruction

Derivative1 admits x+c for any target-free constant expression c on admitted domains. Returned simplified tree and steps do not recover c, original syntax or lost domain conditions.

### product_quotient

Constant factor branches derive only variable-dependent operand. General product is a'*b+a*b'; quotient uses(a'*b-a*b')/b² unless denominator is target-free, then a'/b.

### power_cases

Target-free exponent uses k*a^(k-1)*a'; target-free base uses a^b*ln(a)*b'; otherwise a^b*(b'*ln(a)+b*a'/a). Validity depends on mathematical domain not stored in E.

### chain_dispatch

For one-argument call derive inner first, then select supported outer derivative. Unsupported outer can error after inner steps. Multiple-argument calls reject unless target absence already returned0.

### step_prefix

Sum/product/power steps append before recursive child work, and no rollback occurs on Err. A step list is a prefix trace, not proof that every displayed rule completed successfully.

### tests

#### Evidence

See ../tests.md for actual checks and source mutant; this fragment adds no runtime test.

derive checks target absence then arithmetic/chain rules. Steps append during recursion and survive errors. Inverse fibers remain nonunique/domain-dependent. Repeated has/simplify/clones dominate work, no integration or bounded output size guarantee.