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

Annotations already mark the tool as read-only and idempotent, so the description correctly avoids restating those. It adds behavioral detail by defining the mathematical operation (n-th root of the product) and noting the additional return of the arithmetic mean, which is not visible in the schema.

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 extremely concise: two sentences that front-load the core purpose and immediately follow with the key extra behavior. Every word earns its place, with no filler or redundant restatement of the title.

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 simple calculator with one well-documented parameter and an output schema available, the description covers the essential purpose, input domain, and extra output. It is fully complete for this tool's complexity.

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 schema already fully documents the single parameter, including type, constraints, and the invalidity of negative/zero values. The description only restates that it is a list of positive numbers, adding no new semantic detail, so the baseline 3 is appropriate.

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 begins with a specific verb ('Compute') and explicit resource ('geometric mean'), immediately clarifying what the tool does. It also notes the inclusion of the arithmetic mean, distinguishing it from a pure geometric-mean-only tool and from sibling calculators.

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 states the input requirement ('list of positive numbers') and implies use when a geometric mean is needed. It does not explicitly contrast with siblings like average-calculator, but the added return of arithmetic mean provides context for when this tool might be preferred.

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