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

Annotations already declare readOnly/idempotent/non-destructive, so the description adds real value beyond them: it discloses a paid x402 cost per successful call and an equivalent HTTPS endpoint, and gives a worked example (g(0)..g(10)=100) that lets an agent sanity-check output.

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?

The core semantics and the worked example are front-loaded in short, low-waste sentences. The pricing and alternate-endpoint line is slightly tangential but justified for an agent deciding whether it can afford the call.

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 two-integer pure-computation tool with no output schema needed, the definition supplies bounds, ordering constraint, an example, and payment details. Only the inclusivity of the range and the return type remain implicit, which is minor.

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 load. It adds a genuine cross-parameter constraint ('lo must not pass hi') that the schema does not express, but it mostly restates the 0..25 bounds already encoded as minimum/maximum, and never says explicitly that both endpoints are inclusive.

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 operation and resource: the sum of Landau's function over the integer range lo..hi. That is clearly separable from the sibling landau (single value), landau_index and landau_mod, although it never names those siblings explicitly to route the agent.

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 gives range validity ('lo must not pass hi', 'each index runs from 0 to 25') and cost/transport context, but it never says when to choose this over landau or landau_index, nor any conditions under which not to call it. Usage is implied rather than stated.

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