derivative_backward

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

No annotations are provided, so the description carries full burden. It mentions the calculation method but doesn't disclose important behavioral traits: what precision to expect, error characteristics of backward difference, whether it handles symbolic functions or only numeric evaluation, what happens with invalid inputs, or what the output format is. For a mathematical computation tool with zero annotation coverage, this leaves significant gaps in understanding how the tool behaves.

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 appropriately concise with a single sentence that states the core purpose. The domain/category information ('Domain: calculus, Category: general') is somewhat redundant but not wasteful. However, it could be more front-loaded by immediately explaining key parameters or usage context.

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's mathematical complexity, zero annotation coverage, 0% schema description coverage, and no output schema, the description is insufficient. It doesn't explain the mathematical method in detail, parameter requirements, output format, error handling, or precision considerations. For a derivative calculation tool that likely produces numeric results, more context is needed to use it effectively.

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 description coverage is 0%, so the description must compensate but doesn't. It mentions no parameters at all, while the schema shows three parameters (func, x, h). The description doesn't explain what 'func' should contain (e.g., mathematical expression syntax), what 'x' represents (evaluation point), or what 'h' is (step size, with default shown in schema but not described). With 0% schema coverage and no parameter information in the description, this is inadequate.

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's purpose: 'Calculate numeric derivative using backward difference method'. It specifies the verb ('calculate'), resource ('numeric derivative'), and method ('backward difference'), with domain/category context. However, it doesn't differentiate from sibling tools like 'derivative_central' or 'derivative_forward', which are presumably alternative differentiation methods.

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 provides no guidance on when to use this tool versus alternatives. While it mentions the method ('backward difference'), it doesn't explain when this method is appropriate compared to forward or central difference methods (which appear as sibling tools). There are no usage prerequisites, exclusions, or comparisons to help the agent choose correctly.

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