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Symbolic expression simplifier

Open Symbolic expression simplifier on Happytails.ai. This view has the same page content and links, with explicit tool capabilities. Read the processing notes before using a tool.

Tool capabilities

{
  "id": "symbolic-expression-simplifier",
  "category": "calculators",
  "built": true,
  "requirements": "Expressions are limited to 1,000 characters, 512 symbols, 24 nesting levels and 100 digits per number, with at most 12 assumed variables. Supported functions are sin, cos, tan, asin, acos, atan, exp, ln, log, sqrt and abs. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report and a CSV of steps.",
  "implementation": {
    "fields": [
      {
        "key": "assumptions",
        "label": "Assumptions (optional)",
        "value": "",
        "type": "text",
        "maxLength": 200,
        "help": "Optional, such as x > 0, y >= 0 or t != 0, separated by commas. Rewrites like x/x to 1 are applied only when an assumption allows them."
      }
    ],
    "presentation": "metrics",
    "inputCodeDirection": "ltr",
    "registrationFamily": "exact-math-functions",
    "inputMaxLength": 1000,
    "inputErrorCode": "EXACT_MATH_FUNCTIONS_EXPRESSION_TOO_LONG",
    "note": "Simplifies exactly on your device and checks the result at five sample points. Expressions are limited to 1,000 characters and 24 nesting levels.",
    "experience": {
      "automatic": false,
      "single": true,
      "inputMaxLength": 1000,
      "inputMode": "text",
      "label": "Expression",
      "placeholder": "sqrt(x^2)*x^3/x + 3x^3 - x^3",
      "help": "Use ^ for powers, * or nothing for products, and functions such as sqrt(x) or ln(x). Up to 1,000 characters. Review the settings before running.",
      "helpParts": [
        "Use ^ for powers, * or nothing for products, and functions such as sqrt(x) or ln(x).",
        "Up to 1,000 characters.",
        "Review the settings before running."
      ],
      "action": null
    },
    "mode": "explicit",
    "interactive": false
  },
  "execution": "Browser interface",
  "api": null,
  "browser_agent": {
    "supported": true,
    "name": "run_current_tool",
    "discovery": "WebMCP on the human page in a supporting browser",
    "verification": "See audit/API-AUDIT.md; availability is not verification"
  }
}

Page guide

Simplify an algebraic expression exactly, with every rewrite listed. Rewrites that would change where the expression is defined are only applied when your assumptions allow them.

How to use Symbolic expression simplifier
  1. Type the expression, such as sqrt(x^2)*x^3/x + 3x^3 - x^3.
  2. Add assumptions such as x > 0 if you want them used.
  3. Run the simplifier and read the simplified form, the steps and any gated rewrites.
  4. Check the spot checks, then download the JSON report or the CSV of steps.

Useful next steps

Graphing calculatorScientific calculatorFractions

Expressions are limited to 1,000 characters, 512 symbols, 24 nesting levels and 100 digits per number, with at most 12 assumed variables. Supported functions are sin, cos, tan, asin, acos, atan, exp, ln, log, sqrt and abs. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report and a CSV of steps.

How it simplifies

The simplifier folds exact numbers, collects like terms, expands polynomial parts and applies identities that hold everywhere, such as sqrt(u^2) = abs(u). Fractions stay exact, so 1/3 stays 1/3. Method: OpenStax, College Algebra 2e, chapter 1 Prerequisites (2021).

Assumptions and gated rewrites

Cancelling x/x, turning abs(x) into x or exp(ln(x)) into x is only valid for some values. Those rewrites are applied when an assumption such as x > 0 or x != 0 proves them, and are otherwise listed as gated rewrites with the condition they need.

Spot checks are evidence, not proof

The original and simplified expressions are evaluated at five sample points. Agreement supports the result; the rewrites themselves are the proof.