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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint and destructiveHint=false, so safety is covered. The description adds genuinely new behavioral context beyond the annotations: the $0.001 USDC per successful call cost, the x402/Solana payment mechanism, and an alternative HTTPS endpoint. It does not specify error behavior for out-of-range input, but the priced-call disclosure is the important addition.

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?

Roughly three short sentences, all front-loaded: definition first, examples second, domain and price last. No padding or repeated restatement of the title, though the endpoint URL is somewhat boilerplate metadata rather than task-relevant instruction.

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 pure math function with no output schema, the description supplies the operation, the domain, sample return values, cost and transport. An agent can call it correctly after reading it. The only gap is the absence of any routing signal against the closely named ruler_* siblings.

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 0%, so the description must carry the burden, and it partly does: it explains that n is the integer being valued and gives three concrete input/output examples. However, it adds nothing about the minimum of 1 other than the loose range sentence, and the examples leave the exact return shape implicit. Two of the three examples are the only thing preventing this from being a 2.

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 states precisely what is computed: 'The ruler value of n, the exponent of 2 in n', backed by three worked examples (v2(1)=0, v2(8)=3, v2(12)=2). It is unambiguous on its own, though it does not distinguish itself from the sibling family ruler_max / ruler_prefix / ruler_sum / ruler_odd.

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?

The domain constraint 'n runs from 1 to 1000000000000' tells the agent when the call is valid, and the price line signals the paid x402 path. But there is no guidance on when to pick this over ruler_prefix or ruler_sum, and no statement of exclusions or preconditions.

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