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

Annotations already establish read-only, idempotent, non-destructive behavior, so the description's added context is what matters here: it discloses the numeric-to-string output switch past 15 digits, the pricing model ($0.001 USDC per successful call via x402 on Solana), and an equivalent HTTPS endpoint. That is meaningful behavioral detail beyond the annotations.

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 definition and examples, followed by range, output-format rule, and payment details — each sentence serves a purpose. The pricing and endpoint sentences are somewhat operational rather than mathematical, but they are necessary for an x402-gated tool.

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?

With a single required parameter and no output schema, the description supplies the definition, sample values, domain, and output-format caveat. The only minor gap is not stating the type of the value for small n (presumably an integer) versus the decimal string past 15 digits, but the contrast strongly implies it.

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 carry parameter meaning; it explains that n is 1-based, bounded to 1–20, and backs this with worked examples (T1..T4) that concretely define what n selects. It largely compensates for the empty schema, though the bounds duplicate the schema's min/max rather than adding new constraint detail.

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 resource ('the nth tangent number') and anchors it with concrete output values (T1=1, T2=2, T3=16, T4=272) so the agent knows exactly what is computed. It also notes the derivation from Bernoulli B(2n), which hints at its relation to the sibling bernoulli tool, though it does not explicitly contrast with alternatives.

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 the valid domain (n runs from 1 to 20) and the output-format threshold (past 15 digits becomes a decimal string), which is useful usage context. However, it never says when to prefer this over sibling sequence tools like bernoulli or euler_secant, so guidance is implied rather than explicit.

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