Sqrt

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

No annotations are provided, so the description carries the burden, and it does disclose the domain constraint ('non-negative') and the 'principal' root convention. However, it does not state what happens on negative input (error vs. NaN), which is the main behavioral question for this tool.

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?

A single sentence with zero waste, front-loading the operation and the key domain constraint. Perfectly sized for a primitive math function.

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?

An output schema exists, so return values need not be explained, and the domain constraint is present. The only minor gap is undefined error behavior for negative inputs, which for a math primitive is a small omission.

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 description coverage is 100% and the schema already states the value 'Must be >= 0', so the description adds nothing about parameter syntax or format beyond the schema. Baseline 3 is correct when the schema does the heavy lifting.

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?

States a specific verb and resource: 'Return the (principal) square root of a non-negative number.' This clearly distinguishes it from the sibling operations add, subtract, multiply, divide, and power without needing to open any schema.

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?

Usage is only implied by the operation itself; there is no explicit statement of when to prefer this over power (x^0.5) or what to do for edge cases. For a trivial math primitive the intent is obvious, but no routing guidance is given.

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