{
  "title": "Symbolic expression simplifier",
  "human_url": "https://happytails.ai/en/calculators/symbolic-expression-simplifier/",
  "agent_url": "https://happytails.ai/agents/en/calculators/symbolic-expression-simplifier/",
  "language": "en",
  "markdown_url": "https://happytails.ai/en/calculators/symbolic-expression-simplifier.md",
  "content": "Symbolic expression simplifier\nSimplify 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.\nHow to use Symbolic expression simplifier\nType the expression, such as sqrt(x^2)*x^3/x + 3x^3 - x^3.\nAdd assumptions such as x > 0 if you want them used.\nRun the simplifier and read the simplified form, the steps and any gated rewrites.\nCheck the spot checks, then download the JSON report or the CSV of steps.\nHow can we improve this tool?\nReport a problem or share an idea.\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\nUseful next steps\nGraphing calculator\nScientific calculator\nFractions\nExpressions 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.\nHow it simplifies\nThe 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).\nAssumptions and gated rewrites\nCancelling 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.\nSpot checks are evidence, not proof\nThe original and simplified expressions are evaluated at five sample points. Agreement supports the result; the rewrites themselves are the proof.",
  "content_format": "text/plain",
  "visibility": "public",
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      "name": "Graphing calculator",
      "url": "https://happytails.ai/en/calculators/graphing-calculator/"
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    {
      "name": "Scientific calculator",
      "url": "https://happytails.ai/en/calculators/scientific-calculator/"
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      "name": "Fractions",
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  "tool": {
    "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"
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  "markdown": "# Symbolic expression simplifier\n\n- Human page: https://happytails.ai/en/calculators/symbolic-expression-simplifier/\n- Markdown: https://happytails.ai/en/calculators/symbolic-expression-simplifier.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/symbolic-expression-simplifier/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `symbolic-expression-simplifier` |\n| Category | calculators |\n| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |\n| Browser execution | Use the visible action or interactive controls. |\n| Browser processing | Browser; see tool notes for network behavior. |\n| HTTP API | Not callable through HTTP. |\n| Browser-agent interface | run_current_tool |\n\n### Implementation notes\n\nSimplifies exactly on your device and checks the result at five sample points. Expressions are limited to 1,000 characters and 24 nesting levels.\n\n### Inputs and settings\n\nText input: Expression.\n\nExample or placeholder shown in the interface (not a validated fixture):\n\n```text\nsqrt(x^2)*x^3/x + 3x^3 - x^3\n```\n\nUse ^ 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.\n\n| Setting | Meaning | Control type | Default | Constraints |\n| --- | --- | --- | --- | --- |\n| `assumptions` | Assumptions (optional) | text | \"\" |  |\n\n### Browser-agent workflow\n\n1. Open the human page in a browser that supports WebMCP.\n2. Discover the interface exposed by that page; use its actual schema.\n3. Select files on the page first when the tool requires files.\n4. Call `run_current_tool` with valid input and settings.\n5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.\n\nCalls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.\n\n### Planning specification\n\nExpressions 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.\n\nThis describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.\n\n### Complete machine-readable capability record\n\n```json\n{\n  \"id\": \"symbolic-expression-simplifier\",\n  \"category\": \"calculators\",\n  \"built\": true,\n  \"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.\",\n  \"implementation\": {\n    \"fields\": [\n      {\n        \"key\": \"assumptions\",\n        \"label\": \"Assumptions (optional)\",\n        \"value\": \"\",\n        \"type\": \"text\",\n        \"maxLength\": 200,\n        \"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.\"\n      }\n    ],\n    \"presentation\": \"metrics\",\n    \"inputCodeDirection\": \"ltr\",\n    \"registrationFamily\": \"exact-math-functions\",\n    \"inputMaxLength\": 1000,\n    \"inputErrorCode\": \"EXACT_MATH_FUNCTIONS_EXPRESSION_TOO_LONG\",\n    \"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.\",\n    \"experience\": {\n      \"automatic\": false,\n      \"single\": true,\n      \"inputMaxLength\": 1000,\n      \"inputMode\": \"text\",\n      \"label\": \"Expression\",\n      \"placeholder\": \"sqrt(x^2)*x^3/x + 3x^3 - x^3\",\n      \"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.\",\n      \"helpParts\": [\n        \"Use ^ for powers, * or nothing for products, and functions such as sqrt(x) or ln(x).\",\n        \"Up to 1,000 characters.\",\n        \"Review the settings before running.\"\n      ],\n      \"action\": null\n    },\n    \"mode\": \"explicit\",\n    \"interactive\": false\n  },\n  \"execution\": \"Browser interface\",\n  \"api\": null,\n  \"browser_agent\": {\n    \"supported\": true,\n    \"name\": \"run_current_tool\",\n    \"discovery\": \"WebMCP on the human page in a supporting browser\",\n    \"verification\": \"See audit/API-AUDIT.md; availability is not verification\"\n  }\n}\n```\n\n## Page guide\n\nSimplify 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.\n\n### How to use Symbolic expression simplifier\n\n1. Type the expression, such as sqrt(x^2)\\*x^3/x + 3x^3 - x^3.\n2. Add assumptions such as x > 0 if you want them used.\n3. Run the simplifier and read the simplified form, the steps and any gated rewrites.\n4. Check the spot checks, then download the JSON report or the CSV of steps.\n\nHow can we improve this tool?\n\nReport a problem or share an idea.\n\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\n\n## Useful next steps\n\n- [Graphing calculator](https://happytails.ai/en/calculators/graphing-calculator/) ([Markdown](https://happytails.ai/en/calculators/graphing-calculator.md))\n\n- [Scientific calculator](https://happytails.ai/en/calculators/scientific-calculator/) ([Markdown](https://happytails.ai/en/calculators/scientific-calculator.md))\n\n- [Fractions](https://happytails.ai/en/calculators/fractions/) ([Markdown](https://happytails.ai/en/calculators/fractions.md))\n\nExpressions 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.\n\n## How it simplifies\n\nThe 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).\n\n### Assumptions and gated rewrites\n\nCancelling 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.\n\n### Spot checks are evidence, not proof\n\nThe original and simplified expressions are evaluated at five sample points. Agreement supports the result; the rewrites themselves are the proof.\n"
}