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

Annotations already declare readOnlyHint, idempotentHint, non-destructive, and closed-world, so the safety profile is fully covered by structured data. The description adds only 'Returns x,' which is thin behavioral detail and is also redundant with the output schema; no edge-case behavior (e.g., division by zero or non-numeric input) is disclosed.

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?

Three short front-loaded sentences with no padding; the formula and use cases come first. The trailing 'Inputs: a, b, c' sentence is wasted effort since the schema already enumerates the parameters, and it is the source of the naming error.

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 trivial pure-math calculator with full annotation coverage and an output schema, the description covers purpose, formula, and use cases adequately. The gaps are the inaccurate parameter list and lack of any stated numeric preconditions, but neither is critical for this tool class.

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%, so the baseline would be 3, but the description actively mislabels the parameters: it says 'Inputs: a, b, c' while the schema requires 'a', 'b', and 'x'. An agent reading the description for the third operand could supply 'c' and fail validation, so the description is worse than silent here.

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?

It gives a specific verb ('Solve') plus the resource and its formula ('rule of three (cross-multiplication): if a→b, then c→?'), which is enough to distinguish it from neighbors like calculate_rule_of_72 or calculate_ratio_simplify. It does not call out those siblings by name, so an agent must infer the boundary from the math itself.

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?

'Use for proportions, recipe scaling, or unit pricing' gives concrete usage contexts, which is better than nothing. However, there are obvious competing tools (calculate_recipe_scale, calculate_unit_price, calculate_recipe_scaling) and no when-not or alternative-selection guidance is offered; the only cross-reference is list_bundles, which is a discovery tool, not an alternative.

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