bayes_theorem

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

With no annotations provided, the description carries full burden. It explicitly gives the mathematical calculation, so an agent knows the exact transformation performed. No hidden behaviors are relevant for a deterministic mathematical tool.

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 consists of a single, front-loaded sentence that states the exact formula. Every word is necessary and there is no wasted content.

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 simplicity of the tool (3 numeric parameters, no output schema), the description is largely sufficient. The formula implies the return value. However, it could explicitly state that the output is the posterior probability 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 description coverage is 100% (each parameter has a clear description like 'P(hypothesis)'). The description adds the formula but no extra semantic value beyond what the schema already provides, so 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?

The description states the specific formula 'P(hypothesis|evidence) = P(evidence|hypothesis) * P(hypothesis) / P(evidence)', which clearly identifies the tool's purpose as calculating a conditional probability via Bayes' theorem. It differentiates from sibling tools like 'bayes_update_hypotheses' which likely handles multiple hypotheses.

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?

No guidance is provided on when to use this tool versus alternatives such as 'bayes_update_hypotheses'. The description only gives the formula without context for appropriate use cases or exclusions.

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