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

Annotations already declare readOnlyHint=true and destructiveHint=false, so the tool is safe to call. The description adds substantial behavioral context beyond that: it explains that the response returns text and structured data only, that 'rows' is a validation verdict requiring a retry on failure, and describes the preview/omits behavior (static preview at t=0, 3D as wireframes). It also notes no image is attached, which is non-obvious. This goes well beyond the annotations without contradicting them.

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 long and dense, but the density is justified by the tool's complexity. It is structured logically: purpose first, then row examples, then a pointer to a syntax resource, then response details. However, it could be tightened—some examples (like the list of random variables) feel exhaustive and could be trimmed to a few representative cases. It is not minimal, but it earns its length for a tool that accepts many grammar variants.

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 high complexity (many row types, validation, response semantics, preview behavior) and the presence of an output schema, the description covers all essential aspects. It explains how to construct the input, how to handle validation failures, what fields the response contains (rows, share_url, url, preview, preview_omits), and even links to an external syntax resource. Nothing critical is missing for a correct invocation.

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?

Although schema coverage is 100%, the tool description massively enriches the parameter semantics. It details the allowed row types (equations, inequalities, bare expressions, parametric tuples, definitions, coordinate fields, derivatives, integrals, sums, slope fields, random variables, view/camera rows) and explains the 'draggable' concept for points. It also clarifies the 'equations' array is flat and ordered. This transforms a bare array-of-strings schema into a rich, actionable spec.

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 opens with a precise verb ('Build a link') and a specific resource ('the equation.io grapher'), and immediately states the key behavior (validation through the app's parser). It clearly differentiates from the sibling decode_graph_url by framing the encode direction and even mentions 'when editing an existing graph (see decode_graph_url)'. This gives the agent a distinct mental model without needing to inspect the schema.

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 implies when to use this tool (to create or update a graph link) and explicitly points to decode_graph_url for reading existing graphs, with the instruction to include unchanged rows when editing. It also gives a practical usage hint: before the first non-trivial graph, read the 'syntax' MCP resource. It lacks a formal 'when not to use' statement, but the direction is clear enough to score a 4.

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