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

Annotations already declare readOnly/idempotent/non-destructive, but the description adds the economically critical facts the agent cannot get elsewhere: a $0.001 USDC charge per successful call over x402 on Solana, plus an equivalent HTTPS endpoint. The 'per successful call' phrasing also clarifies failure isn't billed.

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 sentences, front-loaded with the definition and result format, followed by domain, price, and endpoint. Every sentence carries information, though the endpoint URL is long and the range restatement duplicates the schema constraints.

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 no output schema, the description correctly supplies the return form ('reduced fraction') and concrete value examples. Input domain, cost model, payment context, and transport alternative are all covered, leaving nothing essential for a correct invocation unstated.

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 carry the load, and it does give the valid ranges and clarify that x is an integer input. The worked examples (L(n,0)=1, L(1,1)=0, L(2,1)=-1/2) additionally pin down the reduced-fraction return convention, though a plain-language gloss of what n means (polynomial order) and out-of-range behavior is absent.

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 the exact mathematical object (Laguerre polynomial L(n, x)), states the output form ('as a reduced fraction'), and pins the domain. No sibling tool computes Laguerre polynomials, so nothing is ambiguous even without an explicit sibling callout.

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 implied by the mathematical definition and the stated bounds (n 0-32, x -1000..1000), which implicitly tells the agent when the tool is valid. However, there is no guidance about alternatives, such as pointing to legendre_pol, hermite, or chebyshev_t for other orthogonal polynomials, and no advice on what to do outside the supported range.

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