binomial

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

No annotations are provided, so the description must fully disclose behavior. It does not explain what happens for invalid inputs (e.g., k > n), return type, or precision. The description is too minimal 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?

Extremely concise, one sentence with clear subject and verb. No wasted words, perfectly front-loaded.

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 existence of an output schema and the simplicity of the operation, the description captures the core purpose. However, it omits important behavioral details (e.g., limits, error handling) that would be expected for complete understanding.

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 coverage is 100% with descriptions 'Non-negative integer.' The description adds no additional meaning beyond matching the parameter names to the binomial coefficient formula. Baseline 3 is appropriate.

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 states the exact mathematical operation: compute the binomial coefficient C(n,k). It is a specific verb+resource, clearly distinguished from sibling mathematical functions.

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 guidance on when to use this tool vs alternatives like factorial or gamma. No mention of mathematical constraints (e.g., k must be ≤ n) or prerequisites.

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