probability.normal_pdf

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

Annotations already cover safety (readOnly, idempotent, closed-world), and the description adds real value on top: string-in/string-out contract, scipy float64 computation, 10-significant-digit rounding of the result, and the density-vs-probability caveat. It does not discuss edge cases (sigma=0 rejection, extreme-tail underflow), which keeps it short of a 5.

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?

Three tight sentences, front-loaded with what is computed, then the I/O contract, then the disambiguation from normal_cdf. No filler; every clause carries information an agent needs.

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?

With only three simple scalar params and an output schema present, the description covers computation semantics, input encoding, constraint on sigma, output rounding, and sibling routing. Nothing an agent needs to invoke it correctly is missing.

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 carry the load, and it does: it names all three params, states they are decimal strings, gives mu's meaning and default 0, and criticality notes sigma must be positive with default 1. Minor gap: no hint about accepted formats/precision for x beyond 'decimal string'.

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+resource ('정규분포의 확률밀도 f(x; μ, σ)를 구한다') and immediately distinguishes itself from the sibling normal_cdf by noting it returns a density, not a probability. An agent can tell it apart from normal_cdf/normal_ppf without opening any schema.

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?

Explicitly routes the agent: interval probability should be computed as the difference of normal_cdf, i.e. a when-not-this-tool condition plus a named alternative. That is exactly the guidance needed to choose among normal_pdf/normal_cdf/normal_ppf.

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