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

No annotations are provided, so the description carries the burden, but for a deterministic math function the behavioral surface is small and the description does disclose that output is a density value for the given parameters. It adds the '5 free trial calls per signed wallet' detail, which is genuinely useful billing context, though it never states auth mechanics or return format.

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?

A single front-loaded sentence that names the operation before the marketing emoji and trial clause. No redundancy or padding, though the trial/pricing tail is filler for a selection decision.

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 and no annotations, the description should say what comes back (a number or numeric string) and whether any error behavior exists for invalid sd. It correctly conveys the core computation but leaves return shape and the meaning of the string-typed inputs unaddressed, so it is only just adequate.

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% and there are three parameters, so the description must compensate. It does name all three in prose (x, mean, standard deviation), but gives no type, range, or unit guidance — notable since the schema types all three as strings, which is counterintuitive for numeric inputs.

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 and resource: 'Returns the normal probability density at x for a given mean and standard deviation'. An agent knows exactly what is computed. It does not distinguish itself from close siblings such as x402-normal-cdf, x402-normal-quantile, or x402-standard-normal-cdf, which is the only thing holding it below a 5.

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?

There is no when-to-use guidance and no routing to alternatives, despite several near-identical siblings (normal-cdf, normal-quantile, uniform-pdf, exponential-pdf). The only usage-adjacent content is the trial-call note, which concerns payment rather than selection.

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