numerical_diff

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

No annotations are provided, so the description carries the behavioral burden. It discloses the numerical method and supported derivative orders, but not the return format, accuracy caveats, or behavior for invalid expressions.

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?

Single front-loaded sentence with no wasted words, clearly communicating the operation and method.

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 no-annotation, no-output-schema computational tool, the description states method and order range but omits the return value and any usage constraints.

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 all four parameters are documented in the schema. The description only indirectly references order via '1st-4th order' and adds no parameter syntax or defaults beyond the schema.

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 the exact operation (numerical differentiation), the resource (a math expression), and the method (five-point stencil, 1st-4th order), making it easy to distinguish from numerical_integrate or root_find.

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 does not state when to use this tool instead of alternatives such as numerical_integrate or root_find; usage is only implied by the operation name and method.

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