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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool calculates without mentioning any behavioral traits like computational complexity, error handling, or output format. For a tool with no annotations, this leaves significant gaps in understanding how it behaves beyond the basic function.

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 description is a single, efficient sentence that directly states the tool's function without unnecessary words. It is appropriately sized for a simple mathematical tool, though it could be more front-loaded by immediately highlighting key details like parameter roles.

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?

Given the tool's complexity (a mathematical function with 3 parameters), no annotations, no output schema, and low schema description coverage, the description is incomplete. It does not explain the return value, error conditions, or practical usage context, making it inadequate for an agent to fully understand how to invoke and interpret results.

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?

The input schema has 3 parameters with 0% description coverage, meaning the schema provides no semantic information. The description does not add any meaning about the parameters (x, mean, std), such as what they represent, their units, or typical values. This fails to compensate for the low schema coverage, leaving parameters undocumented.

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 the tool calculates the probability density function (PDF) of the normal distribution, which clarifies the verb ('calculate') and resource ('PDF of normal distribution'). However, it does not distinguish this from sibling tools like 'normal_cdf' (cumulative distribution function) or 'normal_sample' (sampling from normal distribution), leaving the specific purpose vague relative to alternatives.

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 provides no guidance on when to use this tool versus alternatives. It mentions the domain ('probability') and category ('general'), but this is too generic to help an agent choose between this and other statistical or probability tools in the sibling list, such as 'normal_cdf' or 'exponential_pdf'.

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