density_analysis

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 states the tool analyzes density as n increases, implying it might compute or compare density metrics, but it does not describe what the analysis entails (e.g., returns a value, a plot, or a table), any computational constraints, or error handling. This leaves significant gaps for a tool with no 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 extremely concise—a single sentence with no wasted words. It is front-loaded with the core purpose, and the domain/category note is brief and relevant. Every part earns its place, making it efficient for quick understanding.

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 analysis tool), lack of annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not explain what the analysis outputs, how density is defined or computed, or any prerequisites. For a tool with these contextual gaps, more detail is needed to be fully helpful.

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 one parameter 'max_n' with 0% description coverage, and the description does not add any parameter-specific information. It mentions 'as n increases', which loosely relates to 'max_n', but does not explain what 'max_n' represents (e.g., upper bound for n, integer limit) or its valid range. Since schema coverage is low, the description fails to compensate, resulting in a baseline score.

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: 'Analyze density of Farey sequences as n increases.' It specifies the verb ('analyze'), resource ('density of Farey sequences'), and scope ('as n increases'), which is specific and actionable. However, it does not explicitly differentiate from sibling tools like 'farey_sequence' or 'farey_sequence_properties', which is why it falls short of a perfect score.

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 domain ('arithmetic') and category ('farey_sequences'), but this is too vague to help an agent choose between this and sibling tools like 'farey_sequence' or 'farey_sequence_length'. There are no explicit when/when-not instructions or named alternatives.

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