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

Annotations already declare readOnly=true, idempotent=true, destructive=false and closed-world, so safety is covered. The description adds real behavioral context beyond that: answers are numerically verified, unverifiable problems are refused (a disclosed failure mode), and the response includes steps, checks and a page link. It stops short of anything like limits on problem size or latency.

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 compact clauses, front-loaded with the capability and supported problem types, followed by the verification/refusal guarantee and the return shape. There is no filler and no repetition of the title or annotations.

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?

With an output schema present, the description need not document return values, and indeed it only sketches them. It covers scope, verification, refusal behavior and domain, so an agent can call it correctly; the only gaps are guidance about input length/language and when to route to a sibling tool.

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 67%, so the baseline is 3. The description's list of problem kinds partially maps onto the 'type' enum (equation, derivative, integral, limit, simplify, trigonometry) and clarifies what each mode means, but it says nothing about 'lang' or the 300-character problem limit, both of which are left to the schema.

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 names a specific verb (solve) and a bounded resource domain (algebra, trigonometry, calculus) and enumerates the concrete problem kinds handled: equations, systems, derivatives, integrals, limits, simplify/factor. That scope enumeration implicitly separates it from run_calculator and convert_units, but it never names a sibling or states the boundary explicitly, so it falls short of the top score.

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?

Usage is only implied: the agent can infer this is the tool for step-by-step symbolic math. The description adds one useful constraint ('unverifiable problems are refused'), but it never says when to prefer run_calculator or convert_units, nor what input form is expected beyond the schema's own hint.

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