differentiate_numerical

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations provided, the description carries the full burden of behavioral disclosure, but it only restates the computation method. It does not explain whether the result is a scalar, vector, or Hessian matrix, nor what constraints apply to the function definition. The return shape and derivative-order behavior are left to schema and inference.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is a single, front-loaded sentence with no filler. It places the primary action first and lets the schema handle parameter detail. This is appropriately concise for a straightforward computational tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

The tool sits among five overlapping siblings and has no annotations or output schema, so the description needs to disambiguate and set expectations. It does neither: no output form, no mention of the Hessian option via 'order', and no guidance for choosing numerical vs symbolic differentiation. An agent could easily select the wrong sibling without opening schemas.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema documents all three parameters with 100% coverage, including the default for 'order' and an example for 'function_def', so the baseline is 3. The description adds no additional parameter-level meaning beyond naming autograd. A higher score would require supplementary semantic detail not already present in the schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description states a clear verb-resource pair ('Compute numerical derivatives') and identifies the implementation ('using autograd'), which visibly distinguishes it from differentiate_symbolic. It does not explicitly mention evaluating at a point, but the 'point' parameter supports that. Overall the core action is unambiguous.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance is given for when to prefer this tool over differentiate_symbolic, partial_derivatives, gradient_vector, or the other siblings. The word 'numerical' implies a use case, but there is no explicit context, exclusions, or alternatives. An agent must infer the selection criteria from sibling names alone.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.