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

Annotations already declare readOnlyHint, idempotentHint, non-destructive behavior, and openWorldHint, so the safety profile is covered. The description adds valuable context beyond annotations: pricing ($0.001 USDC per successful call), payment protocol, and the output format switch to a decimal string past 15 digits.

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?

The definition and examples are front-loaded, followed by domain constraints and practical payment/endpoint details. It is compact for the amount of useful information conveyed, though the pricing and HTTPS endpoint sentences could be separated more clearly from the mathematical definition.

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?

There is no output schema, so the description usefully states that results past 15 digits are returned as decimal strings and implies numeric output otherwise. It covers valid domains and pricing; only error behavior for invalid inputs such as k > n is left 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 parameter meaning. It gives valid ranges for both n and k, adds the non-schema constraint that k must not exceed n, and illustrates valid values through examples like L(5, 2)=240 and L(6, 3)=1200.

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 states a specific mathematical object and function form ("The unsigned Lah number L(n, k)") with base cases and examples, so the agent knows exactly what is computed. It does not explicitly distinguish itself from the sibling lah_row, which may compute an entire row, leaving some ambiguity about when to choose this single-value tool.

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?

The description gives constraints (n and k from 0 to 20, k must not pass n) and examples, which imply valid use. However, it never states when to use this tool instead of lah_row or other Lah-related siblings, and gives no explicit exclusions or invalid-input guidance beyond the domain constraint.

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