prime_counting_sieve

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

No annotations are provided, so the description carries the full burden. It discloses the method ('optimized sieve') and output format ('returns count, not list'), which are useful behavioral traits. However, it does not mention performance characteristics, memory usage, error handling, or limitations (e.g., maximum limit), leaving gaps in behavioral understanding.

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 highly concise and front-loaded, with a single sentence that efficiently conveys the tool's purpose, method, and output. The parenthetical domain and category annotations add useful context without redundancy, making every word earn its place.

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 moderate complexity (algorithmic prime counting), no annotations, no output schema, and low schema coverage, the description is minimally adequate. It covers the basic purpose and output but lacks details on performance, error conditions, or example usage, which would be helpful for an AI agent to invoke it correctly in varied contexts.

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 description adds meaning by specifying that the 'limit' parameter is used to count primes up to that value, which clarifies the parameter's purpose beyond the schema's basic type definition. With 0% schema description coverage and only one parameter, this compensates adequately, though it could provide more detail (e.g., valid range or constraints).

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 clearly states the specific action ('Count primes up to limit'), the method ('using optimized sieve'), and the output ('returns count, not list'), distinguishing it from sibling tools like 'prime_count' or 'sieve_of_eratosthenes' that might return lists or use different methods. The domain and category annotations further clarify its algorithmic nature.

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 implies usage for counting primes with an optimized sieve method, but does not explicitly state when to use this tool versus alternatives like 'prime_count' or 'sieve_of_eratosthenes' (which are siblings). It provides some context via the domain/category but lacks explicit guidance on trade-offs or specific scenarios.

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