prime_counting_function

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

No annotations are provided, so the description carries full burden. It states the tool approximates π(x), implying a computational or mathematical operation, but does not disclose behavioral traits like accuracy, performance characteristics, or error handling. This is a significant gap for a tool with no structured 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 description is concise and front-loaded, stating the purpose directly. The domain and category tags are efficiently appended, though they might be redundant if already implied by the tool's context. No unnecessary sentences are present.

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 lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not explain what the approximation entails, how results are returned, or any limitations, making it inadequate for a tool with mathematical 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?

Schema description coverage is 0%, and the description does not add any parameter semantics. It mentions 'x' in the function notation but provides no details on its meaning, valid range, or units. With one undocumented parameter, the description fails to compensate for the lack of schema documentation.

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 approximates the prime counting function π(x), which is a clear purpose. However, it does not differentiate from sibling tools like 'prime_count' or 'prime_counting_sieve', which might serve similar or overlapping purposes in prime number analysis. The domain and category tags add context but don't enhance specificity.

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?

No guidance is provided on when to use this tool versus alternatives. The description lacks any mention of prerequisites, constraints, or comparisons to sibling tools such as 'prime_count' or 'prime_counting_sieve', leaving the agent without usage context.

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