Run a mathematical operation

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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint, so the safety profile is covered. The description adds meaningful behavioral details beyond the annotations: unknown fields are rejected before execution, exact and approximate results are kept separate, and a single ordinary call is sufficient, which helps the agent avoid unnecessary retries or fallback behavior.

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 dense but well organized: use cases first, exclusions second, mandatory calling convention third, and high-value examples last. Every sentence earns its place, and the most important structural instruction is front-loaded rather than buried.

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?

For a tool with 44 operations, nested argument objects, and an output schema, the description is strong: it covers selection criteria, invocation shape, when to call describe, and exact/approximate result behavior. It could say slightly more about how math.run relates to math.batch and math.search, and 'one successful ordinary call is sufficient' is a bit ambiguous, but overall it is complete enough for reliable agent 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 coverage is 67%, so the description needs to add some value, and it does. It explains the critical arguments-object contract ('{operation, arguments}; never flatten'), warns that unknown fields are rejected, and gives concrete argument shapes for integer.machine_arithmetic and combinatorics.count. It does not enumerate every operation's parameters, but it appropriately defers to math.describe for unfamiliar shapes.

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 specific verb and resource: run a mathematical operation, with a clearly scoped purpose ('exact or reliability-sensitive mathematics'). It names the domains it covers, explicitly excludes trivial low-risk arithmetic, and distinguishes itself from math.describe by noting which operations need no describe call.

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?

It gives explicit when-to-use guidance ('Use for exact or reliability-sensitive mathematics...'), when-not-to-use guidance ('Do not use for trivial low-risk arithmetic'), and directs the agent to math.describe when operation arguments are unfamiliar. It also gives a concrete structural rule for passing arguments that prevents a common invocation error.

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