khinchin

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It implies this is a read-only operation that returns a constant value, which is straightforward. However, it doesn't mention potential limitations like precision, computational behavior, or error handling. The description adds basic context about the constant's mathematical definition but lacks operational details an agent might need.

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: the first phrase states the core purpose, followed by mathematical context and categorization. Every sentence earns its place - the constant value, its mathematical definition, and domain/category context are all relevant. No wasted words or redundant information.

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?

For a zero-parameter tool with no annotations and no output schema, the description provides adequate but minimal information. It tells what constant is returned and its approximate value, which is the essential information. However, it doesn't specify the return format (e.g., numeric precision, data type) or any behavioral constraints. Given the tool's simplicity, the description is complete enough to be functional but lacks some operational details.

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 tool has zero parameters (schema description coverage 100%), so there are no parameters to document. The description appropriately doesn't waste space discussing nonexistent parameters. The baseline for zero parameters is 4, as the description correctly focuses on what the tool does rather than parameter 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 clearly states the tool's purpose: 'Get Khinchin's constant K ≈ 2.68545.' It specifies the exact mathematical constant being retrieved and provides its approximate value. The additional context 'Geometric mean of continued fraction coefficients' helps distinguish it from other constant-retrieval tools like 'e', 'pi', or 'golden_ratio' among the siblings.

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. While it mentions the domain ('arithmetic') and category ('general'), it doesn't specify scenarios where Khinchin's constant is needed over other constants or mathematical tools. There's no mention of prerequisites, typical use cases, or comparisons with sibling tools that might provide similar functionality.

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