chain_rule

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It only restates the operation and does not describe return values, output form, simplification behavior, or edge cases such as non-composite inputs.

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 earns its place by clarifying the target domain ('composite functions'), even though it closely mirrors the tool name.

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 schema covers all input parameters, and the description is enough to identify the tool's purpose. However, with no output schema and no behavioral detail, the agent is left to infer the return value and when not to use this tool, making the definition minimally viable but not complete.

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 100%, with each parameter having descriptions and examples or defaults. The tool description adds no additional parameter-level meaning, so the baseline score of 3 is appropriate.

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 uses a specific verb ('Apply') and identifies the resource ('composite functions') and technique ('chain rule'). It is distinguishable from siblings like gradient_vector and implicit_differentiation, though it does not explicitly state that it returns a derivative.

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 'for composite functions' implies when the tool should be used, but there is no explicit guidance about when to choose chain_rule over differentiate_symbolic or differentiate_numerical, and no exclusions or alternative routing.

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