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

With no annotations supplied, the description carries the behavioral burden well: it discloses no code execution, the 500-character input limit, per-call cost of €0.0005, and that billing is tied to the Authorization bearer key. It omits error behavior for malformed expressions, which is the main remaining gap for a stateless compute tool.

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 capability and squeezed into three dense sentences where each carries distinct information (capability, limits/cost/auth, parameters). The em-dash parameter dump at the end is slightly run-on but nothing is padding.

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?

An output schema exists so return values need no explanation, and the description covers syntax, size limit, cost, auth, and both parameters — enough to call it correctly. Only error handling and required-ness of expression are unaddressed.

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 partly does by naming both parameters, marking vars optional, and giving a concrete expression example. However, it describes vars as a 'JSON object name→number' while the schema types it as string-or-null, leaving an agent unsure whether to pass an object or a JSON-encoded string, and it never states whether expression is in fact required (the schema lists zero required parameters).

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 verb+resource (evaluate arithmetic) and enumerates the supported grammar: operators, parentheses, named functions, pi/e constants. This distinguishes it cleanly from neighbors like regex_test or unit_convert without opening either schema.

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 'without eval()' framing implies the use case (compute an arithmetic expression safely) and the 500-char cap sets a boundary, but there is no explicit when-to-use-vs-alternative guidance and no statement of what happens for non-arithmetic needs (e.g., unit conversion belongs in unit_convert).

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