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

Annotations already cover safety (readOnlyHint, idempotentHint, destructiveHint=false), so the bar is lower. The description adds genuinely non-structured context: it is a paid endpoint at $0.001 USDC per successful call via x402 on Solana, with an equivalent HTTPS POST URL. That payment/auth detail is exactly the kind of behavior an agent needs and cannot get from annotations or schema.

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?

Front-loaded with the core operation, followed by examples, domain, then pricing/endpoint in a logical order. Every sentence carries information, though the clause about valuation is ambiguous and slightly muddies the otherwise crisp definition.

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 one-parameter, no-output-schema math utility, the description covers semantics, domain, cost, and transport. The only real gap is that with no output schema the description should state what is actually returned (odd part alone, or odd part plus 2-adic valuation, as the example implies).

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, and it does: it states the domain explicitly ('n runs from 1 to 1000000000000', matching the schema's min/max) and conveys what n means through worked examples. Minor gap: the phrasing 'the valuation is 2' hints at a returned quantity that is never clarified as input or output.

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 opening sentence gives a precise verb+resource: 'Remove every factor of 2 from n', which unambiguously defines the operation. Worked examples (12 -> 3, 7 -> 7) confirm the semantics. However, it never distinguishes itself from the sibling family (ruler, ruler_max, ruler_prefix, ruler_sum), so an agent must infer the difference from names alone.

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?

There is no statement of when to use this tool versus ruler, ruler_prefix, ruler_sum or the many other number-theory siblings. The domain constraint (n from 1 to 1e12) and the paid/HTTPS access routes are present, but that is operational guidance, not selection guidance.

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