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

With no annotations, the description carries the full behavioral burden, and it does disclose two useful facts: negative x returns 0, and access is metered ('5 free trial calls per signed wallet'). It still omits behavior for invalid lambda, numeric parsing of string inputs, and the shape of the returned value.

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 core computation and edge case are front-loaded in a single efficient sentence. The trailing free-trial promo with emoji is noise, but it does carry the payment/metering fact, so it is not purely 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?

For a simple two-parameter math utility with no output schema and no annotations, the description is minimally viable: it explains the formula's inputs and one edge case. It should say more about accepted numeric formats for the string-typed params and what a successful response contains.

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 schema alone documents nothing. The description compensates partially by defining x as the evaluation point and lambda as the rate, but leaves the odd string typing of both numeric parameters and any range/validation constraints unaddressed.

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 a specific verb and resource: 'Computes the exponential distribution PDF at x for rate lambda'. The distribution name is enough to tell it apart from sibling PDF tools such as x402-normal-pdf and x402-uniform-pdf, though no sibling is named 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 when-to-use guidance, no mention of when this PDF is preferable to the other distribution PDFs in the family, and no prerequisites. The only contextual line is a promotional note about free trial calls, which is not usage guidance.

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