compute_pi_machin

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

No annotations are provided, so the description carries full burden. It states the formula but doesn't disclose behavioral traits like computational complexity, precision limits, error handling, or output format. For a mathematical computation tool, this leaves significant gaps in understanding its operation.

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 concise and front-loaded with the core purpose and formula. The domain/category note is slightly redundant but not wasteful. It efficiently communicates the essential information in a single sentence.

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 no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain the parameter's role, the tool's behavior, or what the output looks like (e.g., numeric value, precision). For a computational tool, this leaves too much undefined.

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 0%, so the description must compensate. It mentions 'terms' indirectly via the formula but doesn't explain what the 'terms' parameter means (e.g., number of iterations, precision level). The description adds minimal semantic value beyond the bare schema.

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 computes pi using Machin's formula, providing the specific mathematical formula and categorizing it as arithmetic/mathematical_constants. It distinguishes itself from sibling tools like compute_pi_chudnovsky, compute_pi_leibniz, and compute_pi_nilakantha by specifying the algorithm, though it doesn't explicitly contrast them.

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 is provided on when to use this tool versus alternatives like other pi-computation tools (e.g., compute_pi_chudnovsky). The description mentions the domain and category but offers no explicit when/when-not instructions or prerequisites for usage.

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