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

Annotations already declare readOnlyHint=true, destructiveHint=false and openWorldHint=false, so safety is covered. The description adds the algorithmic detail (central difference), which is genuine context, but omits accuracy characteristics such as the step-size/precision tradeoff that matter for a numerical method.

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?

A single front-loaded sentence with zero filler. It is efficient, though its terseness is part of why other dimensions have gaps.

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?

An output schema exists, so return values need no explanation, and parameters are fully documented in the schema. Still, for a numerical-approximation tool an agent would benefit from a note on accuracy limits and on when to prefer the symbolic sibling, neither of which is present.

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?

Schema coverage is 100%: all four parameters carry descriptions and examples, including the default step size. The description adds nothing about how h or variable interacts with the approximation, so the baseline 3 applies.

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?

States a specific verb ('Approximate derivative') and resource ('at a point') plus the method ('central difference'), so the operation is unambiguous. It does not, however, distinguish itself from close siblings like calculator_derivative (symbolic) or calculator_second_derivative, leaving that comparison to inference.

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 phrase 'via central difference' implies the numerical/approximation use case versus a symbolic derivative, but no explicit when-to-use, when-not, or named alternative is given. The agent must infer that calculator_derivative is the symbolic counterpart.

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