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

Annotations already declare readOnlyHint=true, destructiveHint=false, and openWorldHint=false, so safety behavior is covered. The description adds the useful claim that the result is component-wise partials, but says nothing about ordering of components, symbolic vs numeric output, or computation limits — acceptable but thin given annotations carry the rest.

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?

A single front-loaded sentence with the operation first and the clarifying parenthetical second; nothing is wasted. It is terse to the point of being slightly sparse, but appropriate for a simple math utility.

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?

With an output schema present and full schema coverage, the description needn't explain return values or parameters. For a low-complexity symbolic calculation, the remaining gap — how gradient components map to the variables order — 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 description coverage is 100%, so both parameters are already documented, including that variables defaults to free symbols. The parenthetical 'partials w.r.t. each variable' only loosely reinforces the variables parameter and adds no ordering or format detail beyond the schema, so the baseline 3 applies.

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 names a specific operation (gradient ∇f) on a specific resource (a multivariable expression) and clarifies the output semantics as partials with respect to each variable. It implicitly distinguishes itself from partial_derivative/derivative, though it never names those siblings explicitly.

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?

There is no statement of when to use this rather than calculator_partial_derivative, calculator_derivative, or calculator_critical_points, and no prerequisites or exclusions. The agent must infer the choice from the tool names alone.

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