fermat_numbers

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 states the tool generates numbers but lacks behavioral details: it doesn't specify output format (e.g., list of integers), handling of large indices (potential overflow), performance characteristics, or error conditions (e.g., negative limits). The description is minimal and misses key operational context.

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 and front-loaded: a single sentence directly states the tool's function with the mathematical formula, followed by domain/category tags. There is no wasted text, and every part contributes to understanding the tool's purpose efficiently.

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 complexity (mathematical computation with potential for large numbers), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't address output format, error handling, or practical constraints (e.g., index limits due to computational limits). The domain/category tags add minimal context but don't compensate for these gaps.

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%, but the description adds some semantics: it clarifies that 'limit' refers to an 'index limit' for generating Fermat numbers up to that index. However, it doesn't specify valid ranges (e.g., non-negative integers), default behavior, or examples. With one parameter, the baseline is 4, but the description only partially compensates for the lack of schema details.

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 tool's purpose: 'Generate Fermat numbers F_n = 2^(2^n) + 1 up to index limit.' It specifies the mathematical formula and the action (generate), but does not differentiate from siblings like 'fermat_primality_check' or 'known_fermat_primes', which are related but distinct tools. The domain/category tags add context but aren't part of the core purpose statement.

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 explicit guidance on when to use this tool versus alternatives is provided. The description mentions a 'limit' parameter but doesn't explain when to choose this over other Fermat-related tools (e.g., 'fermat_primality_check' for testing primality). Usage is implied by the tool's name and formula, but no context or exclusions are stated.

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