prime_number_theorem_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. The description mentions 'analyze' but doesn't specify what kind of analysis is performed, what the output format might be, whether this is a computational or theoretical analysis, or any behavioral constraints. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding how the tool behaves.

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 very concise - a single sentence plus domain/category tags. It's front-loaded with the core purpose. However, the domain/category tags might be redundant if the server already categorizes tools. The description could be more informative without sacrificing conciseness.

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 mathematical nature of the tool, 1 undocumented parameter, no annotations, and no output schema, the description is incomplete. It doesn't explain what the tool actually returns, how the error analysis is performed, or what mathematical context is assumed. For a tool about the Prime Number Theorem (a sophisticated mathematical concept), more context would be helpful for proper usage.

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 1 parameter (x) with 0% schema description coverage, meaning the parameter is completely undocumented in the schema. The description doesn't mention the parameter at all, providing no semantic information about what 'x' represents (e.g., upper bound, input value, precision parameter). With 0% schema coverage, the description fails to compensate for the missing parameter documentation.

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 the tool's purpose as 'Analyze the error in Prime Number Theorem approximation' which specifies the verb (analyze) and resource (error in Prime Number Theorem approximation). However, it doesn't distinguish this tool from sibling tools like 'approximation_error' or 'convergence_comparison' that might also analyze errors in mathematical approximations. The domain/category tags provide some context but don't clarify uniqueness.

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. There are many sibling tools related to approximation errors, prime numbers, and mathematical analysis, but the description doesn't indicate when this specific tool is appropriate versus tools like 'approximation_error', 'prime_counting_function', or 'convergence_comparison'. No usage context, prerequisites, or exclusions are mentioned.

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