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

Annotations already declare readOnly/idempotent/non-destructive, so the bar is lower, yet the description adds real behavioral detail: binade spacing for powers of two, subnormal handling for zero, infinity mapping, and NaN payload preservation. It also discloses cost ($0.001 USDC x402) and an HTTPS access path, which is useful operational context. Return structure is not described, keeping it below 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?

The core definition is front-loaded in the first sentence, followed by tightly packed edge-case rules and then pricing/access metadata. Each sentence is functional, though the price/URL tail is operational boilerplate rather than semantics.

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 no output schema and 0% parameter coverage, the description carries the edge-case semantics well but leaves the input contract and return format unexplained. For a 3-parameter math tool this is adequate but with clear gaps an agent would need to resolve by inspecting the schema.

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% for the three parameters (bits, value, width). The description only implicitly maps 'binary32 or binary64' to the width parameter and the NaN-payload mention hints at the bit-pattern input, but it never explains what 'bits' vs 'value' expect or their formats. Compensation is minimal against a full coverage gap.

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 a precise computational resource: the ULP of a binary32 or binary64 value. The concept (unit in the last place) is specific and distinct from siblings like float_next, float_order, or float_bits. It stops short of naming an alternative sibling for differentiation, but the operation is unambiguous.

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 explicit guidance on when to use this versus float_bits, float_next, float_order, or float_round. The edge-case rules (power of two, zero, NaN) describe behavior, not selection context, so an agent gets no when/when-not routing.

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