taylor_series

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

With no annotations, the description carries the full burden, but for a pure mathematical computation this is minor. It does disclose one useful behavioral trait – the O-term is dropped from the result – which tells the agent the exact output form. It does not state defaults, precision, or failure behavior (e.g., non-analytic points).

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?

A single front-loaded sentence that names the operation and its three operative inputs, with the parenthetical output note appended compactly. No filler sentences.

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?

An output schema exists, so the description need not explain return values, and the (O-term dropped) note covers format. However, with 0% parameter descriptions and no usage guidance, an agent lacks format details for point/variable and any when-to-use context.

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 coverage is 0%, so the description must compensate, and it only partially does. It references expression, point, and order in prose, but says nothing about the variable parameter (default 'x') or the expected format of point (string, default '0'). Key semantics for 4 undocumented parameters are left to inference.

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 operation (Taylor series expansion) on a named resource (expression) with clear scope (about a point, to a given order). It is readily distinguishable from siblings like expand_expression or differentiate. It stops short of explicitly naming alternatives, but the operation itself is unambiguous.

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 guidance on when to use this tool versus related siblings such as expand_expression or differentiate, nor any stated prerequisites or context. The usage is only implied by the operation name itself.

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