finite_differences

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

No annotations are provided, so the description carries the transparency burden. It discloses the computational methods, the comparison against exact SymPy derivative, and the return type, but omits edge cases, failure modes, or dependency details such as SymPy being required.

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 well-structured: a clear one-sentence intro, a method summary, Args, and Returns. No filler or redundant wording is present, though it could be slightly more compact.

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?

Given the tool has 4 parameters, no output schema, and no annotations, the description adequately covers purpose, input semantics, algorithm, and return shape. It lacks examples or error handling details but is sufficient for basic invocation.

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?

With 0% schema description coverage, the Args section meaningfully explains all four parameters: func_str (math expression), x_val (evaluation point), h (small positive step size), and precision (rounding digits). This compensates well for the lack of schema-level descriptions.

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 clearly states the tool approximates first and second derivatives of f(x) using finite differences, with a specific verb and resource. It distinguishes itself from sibling numerical method tools by focusing on differentiation.

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?

The description explains what the tool computes (forward, backward, central differences and comparison to SymPy) but offers no explicit guidance on when to use it versus alternatives. Usage is implied but no exclusions or alternative references are provided.

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