perfect_numbers_up_to

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 mentions the method ('Euclid-Euler theorem'), which hints at computational characteristics, but does not describe performance aspects (e.g., time complexity for large limits), output format (e.g., list of integers), or error handling (e.g., behavior for negative limits). For a tool with no annotation coverage, this is a significant gap in transparency.

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, consisting of a single sentence that directly states the tool's purpose and method. The additional domain/category information is minimal and does not detract from clarity. Every word earns its place, with no redundant or verbose phrasing.

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 (mathematical computation with a specific theorem), lack of annotations, and no output schema, the description is incomplete. It does not explain the return values (e.g., list of perfect numbers), performance considerations, or error cases. While concise, it fails to provide sufficient context for safe and effective use by an AI agent.

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 1 parameter with 0% description coverage, so the description must compensate. It adds meaning by specifying that 'limit' defines the upper bound for finding perfect numbers, which clarifies the parameter's role beyond the schema's type information. However, it does not detail constraints (e.g., must be positive integer) or examples, providing only basic semantic context.

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: 'Find all perfect numbers up to limit using Euclid-Euler theorem.' It specifies the verb ('find'), resource ('perfect numbers'), and method ('Euclid-Euler theorem'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'is_perfect_number' or 'pluperfect_numbers,' which is why it doesn't reach a score of 5.

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 method ('Euclid-Euler theorem') but does not specify scenarios where this tool is preferred over other perfect-number-related tools (e.g., 'is_perfect_number' for checking a single number). There are no exclusions or prerequisites stated, leaving usage context implied at best.

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