numerical_diff
Numerical differentiation of a math expression using five-point stencil (1st-4th order).
This record as markdown: /tools/io-github-malamutemayhem-unclick-mcp-server/numerical-diff.md
What numerical_diff does on UnClick
AI agents call numerical_diff to retrieve information from UnClick without modifying anything. It is typically the context-gathering step in research, monitoring, and reporting workflows, before the agent takes action elsewhere.
| Parameter | Type | Required | Description |
|---|---|---|---|
h | number | — | Step size (default 1e-7). |
x | number | Yes | Point to evaluate at. |
order | number | — | Derivative order: 1, 2, 3, or 4 (default 1). |
expression | string | Yes | Math expression in x (e.g. 'x^2 + 3*x'). |
Parameters from the server's own tool schema.
Why numerical_diff is rated Low
Even though numerical_diff only reads data, uncontrolled read access leaks sensitive information and racks up API costs: an agent caught in a retry loop can make thousands of calls a minute without anyone noticing.
Risk signalsAccepts freeform code/query input (expression)
Attacks that exploit this kind of access
The rule that runs numerical_diff safely
PolicyLayer is an MCP gateway: it sits between your AI agents and UnClick, and checks every tool call against a rule you set before the call runs. Nothing changes on the server itself. For numerical_diff, this is the rule to start with:
numerical_diff is read-only, so it stays allowed. Everything else on the server is denied unless you say otherwise.
The button opens the PolicyLayer dashboard: create your workspace, connect UnClick, apply this rule, and every numerical_diff call is checked against it from then on.
Questions about numerical_diff
Numerical differentiation of a math expression using five-point stencil (1st-4th order). It is categorised as a Read tool in the UnClick MCP Server, which means it retrieves data without modifying state.
numerical_diff accepts 4 parameters: h, x, order, expression. Required: x, expression. The full parameter table on this page comes from the server's own tool schema.
Register the UnClick MCP server in PolicyLayer and add a rule for numerical_diff: allow, deny, rate-limit, or require approval. Point your MCP client at the PolicyLayer proxy URL and the rule is enforced on every call, before it reaches UnClick. Nothing to install.
numerical_diff is a Read tool with low risk. Read-only tools are generally safe to allow by default.
Yes. Add a rate_limit block to the numerical_diff rule in your PolicyLayer policy. For example, setting max: 10 and window: 60 limits the tool to 10 calls per minute. Rate limits are tracked per agent session and reset automatically.
Set action: deny in the PolicyLayer policy for numerical_diff. The AI agent will receive a policy violation error and cannot call the tool. You can also include a reason field to explain why the tool is blocked.
numerical_diff is provided by the UnClick MCP server (@unclick/mcp-server). PolicyLayer sits as a proxy in front of this server to enforce policies before tool calls reach the server.
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