silver_ratio

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

No annotations are provided, so the description carries the full burden. It implies a read-only operation (fetching a constant) and mentions the constant's appearance in 'octagon constructions,' adding some contextual value. However, it lacks details on error handling, performance, or output format, which are important for a tool with no output schema.

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 highly concise and front-loaded: it immediately states the tool's purpose, provides the constant's value and formula, and adds brief context. Every sentence earns its place, with no wasted words or unnecessary details.

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 the tool's simplicity (zero parameters, no annotations, no output schema), the description is adequate but not complete. It explains what the tool returns (the silver ratio) and adds mathematical context, but it does not specify the return type (e.g., numeric value, string) or any behavioral constraints, which could be helpful for an AI agent.

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?

The tool has zero parameters, and the input schema has 100% description coverage (empty schema). The description does not need to explain parameters, so it meets the baseline. It appropriately focuses on the tool's purpose without redundant parameter information.

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 tool's purpose: 'Get the silver ratio δ ≈ 2.41421.' It specifies the mathematical constant and provides its approximate value and alternative expression (1 + √2). However, it does not explicitly differentiate from sibling tools like 'golden_ratio' or other constant-fetching tools, which prevents a perfect score.

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 includes domain/category tags ('Domain: arithmetic, Category: general'), which imply a general arithmetic context, but it provides no explicit guidance on when to use this tool versus alternatives like 'golden_ratio' or other mathematical constant tools. There are no usage examples, prerequisites, or comparisons to sibling tools.

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