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

Annotations already establish that this is a read-only, idempotent, non-destructive computation, so the safety profile is covered. The description adds genuinely non-obvious behavior beyond that: the return type changes to a decimal string once the value exceeds 15 digits, and each successful call costs $0.001 via x402 on Solana with an HTTPS mirror. Those are things an agent could not infer from the schema or 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?

The definition and examples are front-loaded, which is the right ordering, and every clause carries information. The pricing and endpoint sentences are boilerplate for this server but still actionable for the agent, so they earn a place, though the paragraph is somewhat dense rather than crisply segmented.

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 single-integer computation with no output schema, the description supplies everything needed to call it correctly: the mathematical semantics, the valid input range, the return-type switch at 15 digits, and the cost/transport details. An agent would not need to guess anything material.

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 the meaning of 'n', and it does — n is the upper bound of the k! product, with worked examples at n=1, 3, and 4 showing the mapping. The 1..20 bound is repeated from the schema rather than added, so the description is nearly but not fully compensating for the bare 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 states a specific mathematical object and its exact definition ('the product of k! for k from 1 through n'), then grounds it with concrete example values (sf(1)=1, sf(3)=12, sf(4)=288). Against a dense sibling set containing factorial, alt_factorial, double_factorial, and primorial, the product-of-factorials formula is enough for an agent to tell exactly which one this is.

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 domain constraint ('n runs from 1 to 20') and the payment terms tell the agent when the call is valid and what it costs, which is real usage guidance. However, nothing routes the agent relative to near-neighbors like factorial, alt_factorial, or primorial — there is no 'use X instead if you want a single factorial' statement, so usage is implied rather than directed.

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