Identify constant (closed form)

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

Annotations already indicate readOnly and idempotent. Description adds valuable behavioral details: PSLQ algorithm, 50+ digit reevaluation, honest UNIDENTIFIED output. No contradictions.

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?

Single paragraph, front-loaded with purpose, then method, usage, and parameter hints. Every sentence adds value with no redundancy.

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 2 params, 100% schema coverage, and detailed annotation, the description fully covers inputs, process, and output behavior (closed form or UNIDENTIFIED).

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% (baseline 3). Description adds extra guidance: 'give many digits, >16' for value, and example constant names for basis, enhancing usability beyond 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?

Explicitly states 'Identify a real number's closed form', with method details (PSLQ, closed-form search) and honesty condition. Clearly distinguishes from sibling 'identify_sequence' and other tools.

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?

Provides explicit when-to-use: 'Use when you have a numeric constant and want to know what it IS.' Does not explicitly state when not to use or mention alternatives, but context is clear enough.

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