Create interactive 2D and 3D graphs with validated equations, shareable links, and PNG previews.
Scored across 3 tools
decode_graph_url and encode_graph_url are clearly opposite operations, and show_graph is distinguished as the interactive-rendering path. However, encode_graph_url and show_graph both accept a complete 'equations' array, both validate rows, and both return share links, so the boundary is only clarified by prose rather than by shape, creating mild misselection risk.
All three names use snake_case with a consistent verb_noun structure (decode_graph_url, encode_graph_url, show_graph), and the encode/decode pair forms a clean, predictable symmetric pattern.
Three tools is on the lean side but well matched to the narrow domain of decoding, encoding, and displaying graph links; nothing is redundant and each earns its place, though the surface is thin enough that a couple more operations could plausibly fit.
The decode-to-edit-to-encode-to-display lifecycle is fully covered, with syntax details offloaded to an MCP resource, so no core workflow dead-ends. Minor gaps exist (no standalone validation-only or preview-fetch tool beyond encode_graph_url's overloaded role), but agents can work around them.
Decode an equation.io link (either the #-fragment form or the /g/ share form) into its list of equation rows, so you can edit them and build a new link with encode_graph_url. The rows use the equation.io syntax documented in the "syntax" MCP resource (also at https://equation.io/llms.txt).
| Name | Required | Description | Default |
|---|---|---|---|
| url | Yes | An equation.io graph URL. |
| Name | Required | Description |
|---|---|---|
| equations | Yes |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already establish read-only, idempotent, non-destructive, non-open-world behavior, so the bar is lower. The description adds real value beyond them: it discloses that two URL formats are accepted (#-fragment and /g/ share) and points to the authoritative row-syntax resource, which the agent needs to interpret the result.
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 gives purpose, output shape, the sibling to chain with, and both accepted URL forms; a short second sentence supplies the syntax reference. No filler or redundancy.
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 an output schema present, return values need not be detailed, yet the description still characterizes the result as a list of equation rows and links the syntax documentation required to read them. Minor gaps remain around malformed-URL/error behavior, but nothing essential for correct invocation is missing.
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 100% and there is only one parameter, so baseline is 3. The description goes further by enumerating the two accepted URL forms, adding meaning the terse schema text ('An equation.io graph URL') does not convey.
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?
States a specific verb (decode) and resource (equation.io link) and names the exact output (its list of equation rows). It also names the sibling encode_graph_url as the inverse operation and distinguishes the two accepted URL forms, so an agent can tell it apart from encode_graph_url and show_graph without opening a 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?
Gives a clear workflow context: decode so you can edit the rows and rebuild a link with encode_graph_url, which implicitly routes the agent to the sibling for the reverse direction. It stops short of explicit when-not-to-use guidance and never mentions show_graph, so the sibling set is only partially addressed.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Build an equation.io graph link, validating every row with the app's parser. Pass the COMPLETE graph in "equations": a flat array of strings, one equation or definition per string, in display order — when editing an existing graph (see decode_graph_url), include unchanged rows too.
Rows can be: equations and inequalities in x,y (curves, regions; z makes it 3D), bare expressions in x, y (scalar fields — a curve is written y = f(x); complex plots via w), points (rows report "draggable"), parametric tuples in u,v — and definitions: "a = 2" (a draggable slider), "f(x) = x^3 - a x", coordinate fields like "r = sqrt(x^2+y^2)" for polar. t animates. Also derivatives d/dx, integrals int[a..b] f dx, sums sum[n=1..N], domain()/conformal()/iter() for complex plots, rgb()/hsl()/oklch() color fields, y' = … slope fields, random variables "X ~ Normal(m, s)"/"P(0<X<2)"/"E(X^2)", and "view(x = -5..5, y = -2..2)"/"camera(theta, phi)" framing rows. That is a menu, not the syntax: before your first non-trivial graph, read the "syntax" MCP resource (also at https://equation.io/llms.txt).
The result returns text and structured data only. "rows" gives each equation's validation result: status "ok" with its kind, or "error" with the parser message. The link is usable only once every row is "ok". Give users the share_url (it unfurls to a preview card in chat apps); url is the equivalent #-fragment form. "preview" and "preview_omits" describe the share link's simplified static preview (t = 0, 3D as wireframes), which draws less than the interactive app. No image is attached to the tool response.
| Name | Required | Description | Default |
|---|---|---|---|
| equations | Yes | Every equation in the graph, in display order. One equation or definition per string — do not join rows with ";" (inside quoted text a ";" is data, and kept). |
| Name | Required | Description |
|---|---|---|
| url | Yes | Graph URL using a #-fragment. |
| rows | Yes | |
| valid | Yes | |
| preview | Yes | Static preview availability and limitations. |
| share_url | Yes | Shareable /g/ graph URL. |
| preview_omits | No |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations establish read-only, idempotent, non-destructive behavior, and the description adds substantial operational detail: every row is parser-validated, the link requires all rows to be 'ok', and the response contains text plus structured row results. It also discloses preview behavior and that no image is attached, which goes well beyond the annotations.
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 front-loaded with the core action and key constraint, then moves logically through row types, syntax guidance, and return behavior. It is long and includes a broad syntax menu that partly duplicates the referenced syntax resource, but the information is dense and relevant for a complex graph language.
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 complex tool with one parameter, validation semantics, and structured output, the description covers input expectations, validation consequences, output fields, preview limitations, and the editing alternative. Since an output schema exists, it does not need to document return structure exhaustively, but it still explains the important return semantics.
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 description adds important meaning to the single equations parameter: it must be the complete graph in display order, unchanged rows must be included when editing, and strings must not be joined with semicolons. It also explains what kinds of strings are valid, which the schema does not cover.
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 specific verb and resource: 'Build an equation.io graph link' and adds that it validates rows with the app's parser. It also distinguishes this from decode_graph_url when editing an existing graph. An agent can identify the tool's job without opening sibling schemas.
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 gives clear usage context: pass the complete graph, include unchanged rows when editing, and consult decode_graph_url for existing graphs. It also directs agents to read the syntax resource before non-trivial use. It does not explicitly compare against show_graph, so it stops short of full alternative routing.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Display an interactive equation.io graph inside the conversation, with editable equations, sliders, pan/zoom, and 3D rotation. Use when the user asks to see or explore a graph. Pass the COMPLETE graph as "equations", one equation or definition per string, preserving unchanged rows when editing. For a slider use "a = 2" then "y = a sin(x)". For advanced syntax read the "syntax" resource (https://equation.io/llms.txt). Returns per-row validation and share links; a row with status "error" is not drawn until its text is corrected and the graph resubmitted. Use encode_graph_url for validation or link-only requests (including share-link preview notes). In clients without UI support, provide share_url.
| Name | Required | Description | Default |
|---|---|---|---|
| equations | Yes | Every equation in the graph, in display order. One equation or definition per string — do not join rows with ";" (inside quoted text a ";" is data, and kept). |
| Name | Required | Description |
|---|---|---|
| url | Yes | Graph URL using a #-fragment. |
| rows | Yes | |
| valid | Yes | |
| share_url | Yes | Shareable /g/ graph URL. |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnly/idempotent/non-destructive, and the description adds genuinely non-obvious behavior: per-row validation results, share links, and that a row with status 'error' is not drawn until corrected and resubmitted. The no-UI fallback (share_url) is also disclosed.
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?
Front-loaded with purpose then usage then mechanics; dense but nearly every sentence carries actionable detail (completeness, slider pattern, error-row behavior, fallback). Slightly long, with the semicolon note partially duplicating the schema.
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 single-required-parameter tool with an output schema, the description covers invocation, editing semantics, error handling, sibling routing, and client-capability fallback. Nothing an agent needs to call it correctly is missing.
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 100%, so baseline is 3, but the description adds real meaning: the graph must be COMPLETE, unchanged rows should be preserved when editing, and it supplies a worked slider example ('a = 2' then 'y = a sin(x)'). That is more than the schema conveys, though the semicolon guidance overlaps with the schema text.
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?
States a concrete verb+resource ('Display an interactive equation.io graph inside the conversation') and enumerates the capability set (editable equations, sliders, pan/zoom, 3D rotation). It also implicitly separates itself from the encode/decode siblings by naming encode_graph_url for validation/link-only work.
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?
Explicit trigger ('Use when the user asks to see or explore a graph') plus an explicit alternative and its condition ('Use encode_graph_url for validation or link-only requests'). It even covers the fallback path for clients without UI support.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Recent tool additions, removals, and schema changes observed during successful MCP inspections.
show_graph3 fields changedOutput schema / properties / previewRemoved value: -{
- "description": "Static preview availability and limitations.",
- "type": "string"
-}Output schema / properties / preview_omitsRemoved value: -{
- "items": {
- "additionalProperties": false,
- "properties": {
- "row": {
- "type": "string"
- },
- "why": {
- "type": "string"
- }
- },
- "required": [
- "row",
- "why"
- ],
- "type": "object"
- },
- "type": "array"
-}Output schema / requiredPrevious value: -[
- "valid",
- "url",
- "share_url",
- "preview",
- "rows"
-]New value: +[
+ "valid",
+ "url",
+ "share_url",
+ "rows"
+]show_graphdecode_graph_urlencode_graph_url
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