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

Annotations already carry readOnly/idempotent/no-destructive safety, so the description wisely focuses on other behavior: it discloses the return format (decimal string past 15 digits) and the paid x402/Solana pricing model plus an HTTPS fallback endpoint. These are non-obvious operational traits an agent needs and cannot get from annotations.

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?

Front-loads the definition and base cases, then constraints, then output format, then pricing/endpoint. Every sentence adds distinct, useful information with no filler.

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 compensates by explaining the return value (integer until 15 digits, then decimal string). Ranges, pricing, and endpoint make it essentially complete for a simple two-param math 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 0%, so the description must carry parameter meaning; it does so by stating n runs 0–32 and x runs -1000–1000, matching both required params. It implies n is the order and x the evaluation point but doesn't explicitly label them, a minor gap.

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+resource: computes the probabilist Hermite polynomial He(n,x) at integer x, with concrete base cases (He(0,x)=1, He(1,x)=x, He(2,1)=0) that pin down the exact variant. It distinguishes itself from the physicist variant via 'probabilist' but never names the sibling 'hermite' tool as the contrast.

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 worked examples and the domain constraints, giving an agent a sense of when the tool applies. However, it never states when to prefer this over the sibling 'hermite' (physicist) tool or any related polynomial tool, leaving the alternative-selection decision to inference.

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