Run a mathematical operation

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

Annotations already mark destructiveHint=true, and the description does not contradict that. It adds valuable behavioral context: read the mathematical value in `output` before execution status, and failed or incomplete runs are not mathematical conclusions. This goes beyond annotations and helps the agent interpret results safely.

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 well-structured and tightly written. The opening sentence states the core purpose, subsequent sentences add usage guidance and result interpretation, and two examples illustrate the format without excessive length. Every sentence contributes to correct invocation.

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 that this is a generic runner for arbitrary math tools, the description is remarkably complete: it explains how to invoke, how to read the output, when to use math.find, and how to treat failures. The output schema exists, so return values do not need to be spelled out, and the examples cover both a simple numeric computation and a more complex verification tool.

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?

Despite 0% schema description coverage, the description explains that capability_id identifies the installed math tool and payload is the typed input, and it provides two concrete JSON examples that demonstrate exact shape and nesting. It also directs users to math.find with view CONTRACT when the payload shape is unknown, effectively documenting parameter discovery.

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 clearly states the action: 'Run one installed math tool by ID with its typed `payload`.' It specifies the resource (installed math tool) and the verb (run), and distinguishes itself from the sibling tool math.find by explicitly pointing to math.find for unknown payload shapes.

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 provides explicit guidance on when to use math.run vs math.find: 'If the payload shape is unknown, use math.find with view CONTRACT.' It also warns against using the producer as a switch for independent checking and instead directs to dedicated checker tool IDs, which is clear when-not advice.

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