exponential_cdf

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

No annotations are provided, so the description carries full burden for behavioral disclosure. It only states what the tool calculates, without mentioning input constraints (e.g., rate > 0), output format, error handling, computational characteristics, or side effects. For a mathematical tool with parameters, this is a significant gap in behavioral context.

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—a single sentence with no wasted words. It's front-loaded with the core purpose and includes supplementary domain/category information efficiently. Every element earns its place, making it easy to parse quickly.

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 the tool's mathematical nature, 2 parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It doesn't explain the exponential distribution's context, parameter meanings, return value format, or usage examples. For a tool that performs a specific probability calculation, more contextual information is needed for effective use.

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%, meaning parameters 'x' and 'rate' are completely undocumented in the schema. The description adds no parameter semantics—it doesn't explain what 'x' represents (e.g., value at which to evaluate CDF) or 'rate' (e.g., rate parameter λ of the distribution). With low coverage, the description fails to compensate, leaving parameters ambiguous.

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 clearly states the tool's purpose: 'Calculate the cumulative distribution function (CDF) of the exponential distribution.' It specifies the verb ('calculate') and resource ('CDF of exponential distribution'), and includes domain/category context. However, it doesn't differentiate from sibling tools like 'exponential_pdf' or 'exponential_sample', which would require a 5.

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 alternatives. It mentions the domain ('probability') and category ('general'), but doesn't specify use cases, prerequisites, or when to choose this over related tools like 'normal_cdf' or 'binomial_cdf' from the sibling list. This leaves the agent with insufficient context for appropriate tool selection.

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