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

Goes well beyond the annotations (which only cover read-only/idempotent safety) by disclosing per-call cost ($0.001 USDC via x402 on Solana), the HTTPS equivalent endpoint, and the important output nuance that results past 15 digits are returned as decimal strings rather than integers. Missing only failure/payment-failure behavior, but for a pure read-only computation this is strong added context.

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, then examples, then domain, then output representation, then pricing/transport. Four compact sentences with no filler; the only minor redundancy is restating the 0..20 range already in the schema.

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 deterministic math function with no output schema, the description covers everything an agent needs: what is computed, the valid input domain, sampled values for verification, how output is represented at large magnitudes, and the cost/transport. Nothing material is left open.

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 the parameter meaning, and it does: it defines n as the index into E(2n) and bounds it to 0..20, plus worked examples mapping n to values. The range duplicates the schema's minimum/maximum, so the added value is the index-to-sequence mapping rather than the bounds.

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 mathematical resource and pins it down with both a closed formula (E(2n) = (-1)^n * a(2n)) and concrete values for n=0,2,4,6, so an agent can identify the sequence unambiguously. It does not, however, distinguish itself from nearby siblings such as euler_zigzag, tangent_number, or bernoulli, which a reader must disambiguate on their own.

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 description never says when to reach for this tool versus the many sibling sequence tools, nor does it state any prerequisite or exclusion. Usage is only inferable from the math definition itself, which is the bare minimum.

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