check_math

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

No annotations, so the description carries the full disclosure burden. It usefully constrains the accepted input domain to numeric literals and the operators + - * / // % **, which tells the agent what will fail, but it never states the return shape, error behavior for malformed expressions, or numeric precision handling.

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 short sentences, purpose front-loaded, with the operator whitelist as precise supporting detail. Every clause earns its place; nothing is padded or redundant.

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?

For a two-parameter verification tool with no output schema, the description conveys purpose, input constraints, and the intent of the check (catching uncomputed claims), which is enough to call it correctly. The exact response format is only implied rather than stated, which is the one remaining gap.

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, and it does: it names both parameters and defines what `expression` may contain (numeric literals and a specific operator set) and what `claimed_result` is compared against. It could go further on numeric formats or edge cases, but it adds real meaning over the bare schema titles.

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 ('confirm') and resource ('arithmetic expression equals a claimed result'), and the math domain cleanly separates it from the check_quote/check_citation/check_code/check_repo siblings. An agent can route to it without inspecting the schema.

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?

'Catches arithmetic a model asserted without computing' gives a clear triggering context — verifying a numeric claim rather than trusting it. It stops short of explicit when-not-to-use guidance or naming alternatives (e.g. using a real computation tool for symbolic math), so it is clear context without exclusions.

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