approximation_error

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but lacks critical details: it doesn't specify what 'approximation error' means (e.g., absolute vs. relative error), how the error is calculated, what the output format is, or any limitations (e.g., supported algorithms, term limits). For a tool with two parameters and no output schema, this is a significant gap in transparency.

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 concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The domain and category tags are appended efficiently. There's no wasted text, though it could benefit from additional context without sacrificing brevity.

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 complexity (two parameters, no annotations, no output schema), the description is incomplete. It doesn't explain how to interpret the results, what algorithms are available, or any error-handling behavior. For a tool that likely outputs numerical error values, the lack of output schema means the description should at least hint at the return type, which it doesn't.

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 input schema has 0% description coverage, so the description must compensate. It mentions 'various pi algorithms' and 'approximation error', which hints at the 'method' parameter (algorithm type) and 'terms' parameter (possibly number of terms in a series). However, it doesn't explain what values 'method' accepts, what 'terms' represents (e.g., iterations, precision), or their relationships. This leaves parameters largely undocumented.

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: 'Calculate approximation error for various pi algorithms.' It specifies the verb ('calculate'), resource ('approximation error'), and domain context ('pi algorithms'). However, it doesn't explicitly distinguish this tool from sibling tools that might also involve pi calculations or error analysis, such as 'compute_pi_chudnovsky' or 'compute_pi_leibniz', which could be used for similar purposes.

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 no guidance on when to use this tool versus alternatives. It mentions 'various pi algorithms' but doesn't specify which algorithms are supported, when this tool is appropriate compared to direct pi computation tools, or any prerequisites. The domain and category tags ('arithmetic', 'mathematical_constants') are too generic to offer meaningful usage context.

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