differentiate

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

With no annotations provided, the description carries the burden of explaining its behavior. It discloses that the operation is numerical rather than symbolic and that it evaluates at a single point, which is important behavioral context. It could go further by mentioning approximation characteristics or default step-size behavior, but the core semantics are clear.

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 extremely concise, using only two short sentences plus a one-line example. It front-loads the core purpose and packs parameter guidance and an illustrative example into minimal text with no filler.

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 that an output schema exists, return values need not be described. The description covers the essential invocation context: the expression syntax, evaluation point, optional step, and angle mode. It is slightly incomplete regarding angle_mode values and h defaults, but overall sufficient for an agent to select and invoke the tool 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 compensate. It lists all parameters with meaningful hints: 'expression in x', 'at', 'angle_mode', and 'optional h step', and provides a clear example. It does not fully explain accepted angle_mode values or the behavior when h is omitted, but the example and labels provide substantial value beyond the bare 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 states exactly what the tool does: computes the numerical derivative df/dx of an infix expression at a point. It explicitly distinguishes itself from symbolic differentiation, making the purpose unambiguous and differentiating it from any symbolic math sibling.

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 frames itself with 'When:' and clarifies this is a numerical derivative at a point, not symbolic, which tells the agent when to use it. However, it does not name any alternative tools (e.g., symbolic differentiation or integration) or explain when a different tool would be preferable.

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