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

Annotations already declare readOnlyHint=true and idempotentHint=true, so the safety profile is covered. The description adds useful context that the computation is symbolic and returns a string representation of a vector, but it does not disclose potential failure modes, input restrictions beyond 'scalar function,' or behavior on invalid expressions. No contradiction with annotations.

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 description is appropriately short and front-loaded with the main purpose. The Args and Returns sections are standard and add structure without excessive detail. It loses a point for repeating schema information that didn't need restating.

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 one-parameter symbolic math tool, the description is mostly complete: it names the operation, the expected input form, and the output form. Since an output schema is present, the return type does not need further explanation. Minor gaps include lack of mention of variable names beyond the schema and no guidance on error handling, but these are not critical.

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 the schema already documents f_str as a scalar function of x, y, z with an example. The description repeats this information in the Args section without adding meaning beyond the schema. It gives an example, but the schema already provides the same one.

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 states a specific verb and resource: 'Computes the symbolic gradient of a scalar function.' The return type is also clear. It does not explicitly distinguish itself from related siblings like curl, divergence, or directional_deriv, but the mathematical meaning of gradient is well established and the scalar-function input helps disambiguate.

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 provides no guidance on when to use this tool versus siblings such as curl, divergence, or directional_deriv. There is no mention of alternatives, exclusions, or context that would help an agent decide that gradient is the right choice among the many vector calculus tools.

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