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

Annotations already establish this is a safe, read-only, idempotent computation, so the description isn't burdened with the safety profile. It adds genuine behavioral semantics beyond that: measurements are treated as independent, and repeated uses of the same variable share its uncertainty — a non-obvious mathematical assumption worth disclosing.

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?

Five short sentences, front-loaded with the core action and immediately followed by the syntax needed to call it. Nearly every sentence earns its place; the one on raw/rounded/human-readable/LaTeX results is mildly redundant given an output schema exists.

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?

Output schema exists, so return values needn't be enumerated. For a two-parameter tool with a nested object and strict additionalProperties:false, the description covers naming rules, value format, the empty-variables case, and uncertainty propagation semantics — enough to call it correctly.

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 burden, and it largely does: variable names are single ASCII letters, lowercase e is reserved for Euler's number, the value format is a string like "3±0.1", and an empty object is valid. The expression parameter's accepted operator set is still only implied by the example.

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 opens with a specific verb and resource: 'Evaluate a mathematical expression and propagate measurement uncertainty.' That is precise enough that an agent knows exactly what computation this performs, and there are no sibling tools to confuse it with.

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?

It gives concrete usage context — use ± for measurements, with the worked example 2*x with variables {"x":"3±0.1"} — plus the edge case of passing variables: {} when no variables are needed. Since no sibling tools exist, there are no alternatives to route against, so this is clear context without exclusions.

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