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

Annotations already declare readOnly=true, destructive=false, openWorld=false, so the safety profile is covered. The description adds no behavioral context of its own: it doesn't say what happens when called with no arguments, whether `list` overrides `query`, or what default precision applies.

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?

It is extremely short with zero filler, but that brevity comes from omission rather than efficiency – a single unframed fragment with no leading verb or noun phrase explaining the operation.

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?

The tool has three optional parameters, an output schema, and clear annotations, so the description need not explain return values. It should still clarify the no-argument default behavior and how `list` interacts with `query`, neither of which appears anywhere.

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 100%, so the baseline is 3. The symbol list (τ, φ, √2, ln2) modestly extends the schema's example values for `query`, but the description says nothing about `list` vs `query` precedence or the precision range beyond what the schema already documents.

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 is a bare symbol list with no verb or operation stated – it restates the title's domain rather than saying what the tool does (return a constant's value? list them?). It does enumerate which constants exist, but an agent cannot tell from this text how the tool behaves or how it differs from siblings like calculator_scientific_constants and calculator_unit_constants.

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?

No when-to-use, when-not-to-use, or alternative is mentioned. The agent is left to infer from the tool name alone, despite two close siblings (calculator_scientific_constants, calculator_unit_constants) that would need explicit disambiguation.

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