Server Quality Checklist

Tool Scores

• list_functionsA
  4.7/5.0
  Behavior5/5

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

  Beyond the readOnlyHint annotation, the description reveals important behavioral nuances: every function exists on all 8 engines but is computed via native primitives, so results may diverge at poles, branch cuts, or ties, and that divergence is intended backend behavior. This is rich, honest context that an agent needs before trusting listed functions.

  Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

  Conciseness5/5

  Is the description appropriately sized, front-loaded, and free of redundancy?

  The description is front-loaded with purpose and return fields, then usage guidance, then filter options, then behavioral caveats. Every sentence earns its place; there is no filler or repetition of schema/annotation content.

  Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

  Completeness5/5

  Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

  For a simple read-only list tool with one optional parameter and no output schema, the description provides everything an agent needs: what it lists, what each entry contains, how to filter, how it relates to evaluate, and a warning about cross-engine divergence. No material gap remains.

  Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

  Parameters4/5

  Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

  The schema already covers the single optional 'category' parameter at 100% coverage, so the baseline is 3. The description adds value by enumerating all valid category values (algebraic, trigonometric, hyperbolic, exponential, special, rounding, introspection), which is especially useful since the schema provides no enum constraint.

  Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

  Purpose5/5

  Does the description clearly state what the tool does and how it differs from similar tools?

  The description states a specific verb and resource: 'List all mathematical functions available via the Ultimath API,' and explicitly lists the returned fields (name, arity, category, description). It clearly distinguishes itself from the sibling 'evaluate' tool by framing itself as the discovery step for functions to pass to evaluate.

  Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

  Usage Guidelines4/5

  Does the description explain when to use this tool, when not to, or what alternatives exist?

  It explicitly tells the agent when to use this tool: 'Use this to discover what functions you can pass to the evaluate tool.' It names the sibling evaluate as the downstream consumer, but it does not explicitly state a when-not condition or directly contrast with evaluate in an 'instead' formulation.

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

• evaluateA
  5/5.0
  Behavior5/5

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

  The description explains nontrivial behavior far beyond the readOnlyHint annotation: engine divergence is real behavior, not a bug; comparison semantics differ per engine (e.g., `!=` can be a proof of difference while `==` is not a proof of equality); and trailing `+0i` indicates unproven realness rather than decoration. This is precisely the kind of behavioral nuance an agent needs.

  Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

  Conciseness5/5

  Is the description appropriately sized, front-loaded, and free of redundancy?

  The description is long but every section earns its place: purpose, when-to-use, engine behavior, comparison semantics, realness, syntax, and precedence are all distinct and clearly organized. It is front-loaded with the core purpose and usage guidance before diving into technical details.

  Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

  Completeness5/5

  Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

  Given the tool's complexity, the description is unusually complete. It covers return content (per-engine results and precision diagnostics), engine semantics, exact closed-form output, precision limits, supported operations, syntax constraints, and points to list_functions for the authoritative list. Nothing essential is missing for an agent to invoke it correctly.

  Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

  Parameters5/5

  Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

  Schema coverage is 100%, but the description adds substantial meaning beyond the schema: explicit-multiplication rules, precedence order, complex-number syntax, unsupported constructs like type casts, the precision ceiling tied to the plan, and examples. This makes the expression parameter far more usable than the schema alone.

  Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

  Purpose5/5

  Does the description clearly state what the tool does and how it differs from similar tools?

  The description opens with a specific verb and resource: 'Verify any numeric result that has to be trusted, via the Ultimath API.' It clearly states what the tool does, names its multi-engine evaluation behavior, and differentiates it from computing by hand, running code, and the sibling list_functions tool.

  Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

  Usage Guidelines5/5

  Does the description explain when to use this tool, when not to, or what alternatives exist?

  It gives explicit when-to-use guidance: 'Use this whenever the correctness of a number matters,' and enumerates concrete scenarios such as floating-point-sensitive expressions, cancellation, singularities, branch cuts, and ties. It also says 'Prefer it over computing by hand or running code,' directly routing the agent away from alternatives.

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