is_optimal_egyptian_fraction

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 checks for optimality but does not explain what 'optimal' entails beyond 'shortest possible,' nor does it describe the return value (e.g., boolean or detailed analysis), error conditions, or computational constraints. This is inadequate for a tool with three parameters and no output schema.

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, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage, and the additional domain/category information is efficiently appended. Every word earns its place, making it easy for an agent to parse quickly.

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 (checking optimality of Egyptian fractions), the lack of annotations, 0% schema description coverage, and no output schema, the description is insufficient. It does not compensate for these gaps by explaining parameters, return values, or behavioral details. The agent would struggle to use this tool correctly without additional context.

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 0% description coverage, and the tool description does not explain the parameters at all. It mentions 'Egyptian fraction representation' but does not clarify what 'numerator', 'denominator', and 'representation' mean or how they relate. With low schema coverage and no parameter details in the description, the agent lacks essential 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: 'Check if Egyptian fraction representation is optimal (shortest possible).' It specifies the verb ('Check'), resource ('Egyptian fraction representation'), and criterion ('optimal (shortest possible)'). However, it does not explicitly differentiate from sibling tools like 'shortest_egyptian_fraction' or 'egyptian_fraction_properties', which is why it doesn't achieve 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 ('egyptian_fractions'), but offers no explicit when-to-use, when-not-to-use, or alternative tool recommendations. This leaves the agent without context for selecting this tool among related siblings.

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