Approximate exp, sin, cos, ln(1+x), and atan(x) at a specified point using a Taylor series with configurable term count.
Taylor series approximation for exp, sin, cos, ln(1+x), and atan(x).
| Name | Required | Description | Default |
|---|---|---|---|
| x | Yes | Point to evaluate at. | |
| terms | No | Number of terms (default 10, max 50). | |
| function | Yes | Function: exp, sin, cos, ln1p, or atan. |
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 states the method is an approximation but omits accuracy, convergence, domain restrictions such as ln(1+x) requiring x > -1, and how the number of terms affects results.
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?
It is a single front-loaded sentence with no filler. Every word supports the purpose, and the function list is immediately visible.
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?
For a simple numerical tool with a fully described input schema, the description is minimally adequate. However, with no output schema and no annotations, it could still clarify the return value, domain limits, and the effect of the terms parameter.
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 documents x, terms, and function. The description adds the useful mapping from ln1p to ln(1+x), but otherwise does not add parameter-level meaning beyond the schema.
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 method, Taylor series approximation, and enumerates the exact functions supported: exp, sin, cos, ln(1+x), and atan(x). This is enough to distinguish it from generic math or approximation siblings.
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?
It says what functions can be approximated but gives no guidance on when to choose this tool versus direct evaluation, numerical methods, or other math siblings. There are no conditions, exclusions, or alternatives named.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.