math

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

With no annotations, the description must carry disclosure. It discloses the required discovery-before-call behavior and dynamic dispatch, but it does not state failure modes, validation behavior, or side effects. This is minimally adequate but not rich.

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?

Two sentences, with the core action first and the discovery workflow second. No filler; every clause contributes to correct invocation.

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 description covers discovery, parameter lookup, and invocation, and an output schema exists for return values. It is complete for the main execution path, though it leaves unknown-tool errors and the batch sibling unaddressed.

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%, so parameters are already documented. The description adds that tool names and parameters can be discovered via math_man and math_ls, which is useful routing information rather than new semantic detail about the parameters themselves.

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 ('Execute') and a clear resource ('a math tool by name'), presenting the tool as a dispatcher rather than a single math operation. It also distinguishes itself from its discovery siblings by listing the preceding math_ls and math_man steps.

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?

It explicitly instructs the agent to call math_ls first)Skip earlier? It tells the agent when to use this tool: after discovering tool names and parameters. It does not mention math_batch as an alternative for batched execution, so the guidance is not complete.

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