Find a rational approximation for a positive number using the Stern-Brocot tree and continued fractions, with an optional maximum denominator.
Find best rational approximation using the Stern-Brocot tree and continued fractions.
| Name | Required | Description | Default |
|---|---|---|---|
| target | Yes | Positive number to approximate | |
| max_denominator | No | Maximum denominator allowed (default 1000) |
Changes observed during successful MCP inspections.
v0.1.11Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions the underlying algorithm but does not describe the return format (e.g., fraction as numerator/denominator or decimal), accuracy guarantees, or any other behavioral trait beyond the method.
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 a single, front-loaded sentence with no wasted words. It is appropriately sized for a simple computational tool.
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?
With no output schema, the description should explain what the approximation returns, but it does not. An agent lacks information about the result format and any usage context beyond the algorithm name.
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?
Schema description coverage is 100%, so the schema already fully documents both parameters. The description adds no extra meaning beyond what is in the schema, making the baseline score of 3 appropriate.
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 a specific verb 'Find' and a precise resource 'best rational approximation', plus the method (Stern-Brocot tree, continued fractions). It is clear what the tool does, but it does not differentiate itself from siblings like continued_fraction or ratio_simplify.
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?
There is no explicit guidance on when to use this tool versus alternatives, nor any when-not conditions or prerequisites. Usage is only implied by the purpose statement.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.