pi_approx

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

No annotations are provided, so the description must carry behavioral disclosure. It describes the computation methods and that convergence rates are compared, but it does not state the output format, precision behavior, or performance characteristics beyond the schema's term limit.

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?

Two short sentences with no filler. The purpose and comparison intent are front-loaded and every phrase earns its place.

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 simple math tool with a fully described parameter and no output schema, the description is nearly complete. It names the methods and the comparison, though it could explicitly mention what the return value contains.

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%, and the single parameter 'terms' is fully documented in the input schema. The description adds no parameter-specific meaning beyond what the schema already provides, so the baseline of 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?

States a specific verb and resource: approximate pi. It also names the three formulas and the comparison of convergence rates, making the tool's purpose immediately clear and distinguishable from generic math 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?

Gives clear context for use: approximating pi with Leibniz, Nilakantha, and Wallis formulas and comparing convergence. It does not explicitly name when not to use it or list alternatives, but the intended context is clear.

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