Numerical Invariant Property Test Harness Generator

Role: Principal Scientific Computing Quality Engineer specializing in numerical stability and formal invariant testing.

Context

• Target Algorithm Implementation: {{target_algorithm_code}}
• Core Mathematical Invariants: {{mathematical_properties}}
• Absolute and Relative Tolerances: {{precision_tolerance_threshold}}
• Input Domain and Boundary Conditions: {{input_domain_bounds}}
• Property Test Framework: {{target_test_framework}}
• Extreme Distribution Shapes: {{edge_case_distributions}}

Task

Synthesize a complete, executable property-based testing script that mathematically verifies {{target_algorithm_code}} across degenerate, edge, and randomized high-entropy input distributions using {{target_test_framework}}.

Method

1. Analyze {{target_algorithm_code}} to identify arithmetic operations susceptible to catastrophic cancellation, floating-point underflow, overflow, and subnormal representation.
2. Translate {{mathematical_properties}} into strict algebraic invariants (e.g., idempotence, commutativity, symmetry, triangular inequality, conservation laws).
3. Formulate custom input strategy generators parameterized by {{input_domain_bounds}} and {{edge_case_distributions}} targeting branch boundaries, infinities, signed zeros, and NaN boundaries.
4. Design parameterized test assertions enforcing dual relative (rtol) and absolute (atol) tolerances specified in {{precision_tolerance_threshold}}.
5. Implement invariant metamorphic test functions comparing baseline algorithmic steps with mathematically equivalent perturbed formulations.
6. Incorporate automated shrinking heuristics and failure triage reporting to isolate minimal counterexamples for ill-conditioned inputs.
7. Add benchmark performance harnesses measuring floating-point operation overhead and timing variance across test runs.

Constraints

• MUST write 100% executable test scripts compatible with {{target_test_framework}} without unreferenced pseudocode.
• MUST explicitly assert mathematical invariants rather than simple regression snapshot comparisons.
• MUST NOT suppress floating-point runtime warnings (e.g., ZeroDivisionError, RuntimeWarning, invalid value) without explicit exception assertions.
• Include explicit type annotations and docstrings defining mathematical theorem justifications for every test case.

Output format

Provide the complete test script structured in the following sequential order:

1. Dependency Imports and Mathematical Constants Setup
2. Custom Input Strategies and Distribution Generators
3. Invariant Property Test Suite (minimum 5 distinct property tests)
4. Metamorphic and Perturbation Stability Test Suite
5. Test Execution Entrypoint with Detailed Error Diagnostics

Self-review

• Verify that all mathematical invariants from {{mathematical_properties}} have dedicated, executable test functions.
• Ensure tolerance comparisons strictly utilize {{precision_tolerance_threshold}} without hardcoded magic floats.
• Confirm input generators cover all specified boundary edges from {{input_domain_bounds}} and {{edge_case_distributions}}.