symbolic_partial_derivative

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

No annotations, so description carries burden. It discloses the key behavior of treating other variables as constants, but does not specify output format, error handling, or domain limitations (e.g., symbolic only). Example helps but incomplete.

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?

Extremely concise: one sentence plus an example. No wasted words. Front-loaded with the core definition.

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?

Given three parameters, no output schema, and a list of sibling tools, the description is fairly complete. Could mention return type (symbolic expression) or limitations, but the example covers common usage. Minor gap for completeness.

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 descriptions cover all three parameters with 100% coverage. Description adds an example but no additional semantic meaning beyond what schema provides. Baseline 3 is appropriate.

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 it computes partial derivatives of multivariable expressions with respect to a specified variable, treating other variables as constants. Example makes concrete. Distinct from siblings like symbolic_integrate and symbolic_limit.

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?

Implies use for partial derivatives when other variables are held constant, but does not explicitly state when not to use or provide alternatives among siblings. Lacks guidance on order or complex expressions.

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