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

Annotations already declare readOnlyHint, idempotentHint, non-destructive and closed-world, so the safety profile is fully covered. The description adds a genuine edge-case disclosure ('including vertical lines') and a precondition ('two distinct points'), but does not say how vertical lines are reported or what the response shape is. Useful but modest added context over the annotations.

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?

A single front-loaded sentence led by the verb 'Compute', with each enumerated output earning its place. It is dense rather than padded, though the long capability list is slightly list-like rather than prioritized.

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 an output schema present, the description need not explain return values, and the input schema fully documents all five parameters. Combined with annotations covering safety, an agent has everything needed to invoke this tool correctly; only alternative-routing guidance is absent, which is scored elsewhere.

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%, with every coordinate and the 'unit' enum documented in the schema including range limits and default. The description adds no parameter-level meaning beyond that, so the baseline 3 applies.

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 ('Compute') and enumerates the exact resource outputs: slope, y-intercept, both equation forms, distance, midpoint and inclination. It is unambiguous what the tool produces. It does not, however, differentiate itself from the nearest sibling (pythagorean_theorem_calculator also computes distance between two points), so it falls short of 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 implies usage ('from two distinct points') and flags the vertical-line case, which tells the agent this is the right tool when given a coordinate pair. It offers no explicit when-to-use vs. alternatives comparison and no exclusions, so guidance is only implied.

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