sqrt_cf_expansion

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

No annotations are provided, so the description carries the full burden. It discloses key behavioral traits: it computes continued fraction expansions, specifically for square roots, and notes that results are periodic for non-perfect squares. This adds valuable context beyond the input schema, though it could include more details like output format or error handling.

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, with a single sentence that directly states the tool's function and a key property, followed by domain/category tags. Every word earns its place, with no redundancy or unnecessary elaboration.

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 moderate complexity (mathematical computation), no annotations, no output schema, and low schema coverage, the description is minimally adequate. It covers the core purpose and a behavioral trait, but lacks details on output format, error cases, or performance considerations, which could hinder 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, and the description does not explicitly mention the parameter 'n'. However, it implies that 'n' is the number whose square root is processed, as it refers to '√n'. This adds some semantic meaning, but does not fully compensate for the lack of schema documentation, such as constraints on 'n' (e.g., non-negative integers).

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 continued fraction expansion of √n (periodic for non-perfect squares).' It specifies the verb ('Find'), resource ('continued fraction expansion of √n'), and a key behavioral characteristic (periodicity for non-perfect squares). However, it does not explicitly differentiate from sibling tools like 'continued_fraction_expansion' or 'sqrt', which could cause ambiguity.

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 implies usage context through the domain and category tags ('Domain: arithmetic, Category: continued_fractions'), suggesting it's for mathematical computations involving square roots and continued fractions. However, it lacks explicit guidance on when to use this tool versus alternatives like 'sqrt' or 'continued_fraction_expansion', and does not mention prerequisites or exclusions.

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