Simplify the Expression Calculator

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Expression Evaluator

Use this calculator to evaluate mathematical expressions by plugging in specific numerical values for variables. While it doesn't perform symbolic simplification (like combining 2x + 3x into 5x), it simplifies an expression by reducing it to a single numerical value based on your input.

Use standard operators (+, -, *, /, ** for power). For functions, use Math.sin(), Math.cos(), Math.tan(), Math.sqrt(), Math.log() (natural log), etc.
function calculateExpression() { var expressionInput = document.getElementById("expressionInput").value; var xVal = parseFloat(document.getElementById("xValue").value); var yVal = parseFloat(document.getElementById("yValue").value); var zVal = parseFloat(document.getElementById("zValue").value); var resultDiv = document.getElementById("result"); // Basic validation for variable inputs, default to 0 if not a valid number if (isNaN(xVal)) xVal = 0; if (isNaN(yVal)) yVal = 0; if (isNaN(zVal)) zVal = 0; // Prepare the expression for evaluation // Replace common math functions with Math. prefix if not already present // Also replace ^ with ** for exponentiation var processedExpression = expressionInput .replace(/(\b)(sin|cos|tan|sqrt|log|pow)(\()/g, 'Math.$2$3') // Add Math. prefix to common functions .replace(/\^/g, '**'); // Replace ^ with ** for exponentiation try { // Create a function to evaluate the expression in a controlled scope // This is a safer alternative to direct eval() for user-provided expressions var evaluateFunc = new Function('x', 'y', 'z', 'return ' + processedExpression); var finalResult = evaluateFunc(xVal, yVal, zVal); if (isNaN(finalResult) || !isFinite(finalResult)) { resultDiv.innerHTML = "Error: Invalid expression or calculation resulted in an undefined/infinite value. Please check your input."; } else { resultDiv.innerHTML = "Simplified Value: " + finalResult.toFixed(6); // Format to 6 decimal places } } catch (e) { resultDiv.innerHTML = "Error: " + e.message + ". Please ensure your expression is mathematically valid and uses correct syntax."; } } .calculator-container { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background-color: #f9f9f9; padding: 25px; border-radius: 10px; box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1); max-width: 600px; margin: 30px auto; border: 1px solid #e0e0e0; } .calculator-container h2 { text-align: center; color: #333; margin-bottom: 20px; font-size: 1.8em; } .calculator-container p { color: #555; margin-bottom: 20px; line-height: 1.6; } .form-group { margin-bottom: 18px; } .form-group label { display: block; margin-bottom: 8px; color: #444; font-weight: bold; } .form-group input[type="number"], .form-group textarea { width: calc(100% – 22px); padding: 12px; border: 1px solid #ccc; border-radius: 6px; font-size: 1em; box-sizing: border-box; transition: border-color 0.3s ease; } .form-group input[type="number"]:focus, .form-group textarea:focus { border-color: #007bff; outline: none; box-shadow: 0 0 5px rgba(0, 123, 255, 0.2); } .form-group textarea { resize: vertical; min-height: 80px; } .form-group small { display: block; margin-top: 5px; color: #777; font-size: 0.85em; } .calculate-button { display: block; width: 100%; padding: 14px; background-color: #007bff; color: white; border: none; border-radius: 6px; font-size: 1.1em; font-weight: bold; cursor: pointer; transition: background-color 0.3s ease, transform 0.2s ease; margin-top: 25px; } .calculate-button:hover { background-color: #0056b3; transform: translateY(-2px); } .calculate-button:active { background-color: #004085; transform: translateY(0); } .result-container { margin-top: 30px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 6px; font-size: 1.1em; color: #155724; text-align: center; word-wrap: break-word; } .result-container strong { color: #0f3d1a; } /* Error styling */ .result-container.error { background-color: #f8d7da; border-color: #f5c6cb; color: #721c24; }

Understanding Mathematical Expressions and Their Evaluation

A mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. These symbols can include numbers, variables (like x, y, z), and operators (like +, -, *, /). Expressions are fundamental to algebra, calculus, physics, engineering, and many other fields.

What Does "Simplify an Expression" Mean?

The term "simplify an expression" can have a few meanings:

  1. Symbolic Simplification: This involves rewriting an expression in a simpler, equivalent form without changing its value. For example, simplifying 2x + 3x - 5 to 5x - 5, or (a+b)(a-b) to a^2 - b^2. This type of simplification often requires advanced symbolic computation tools.
  2. Numerical Evaluation: This involves substituting specific numerical values for the variables within an expression and then performing all the arithmetic operations to arrive at a single numerical result. This is the form of "simplification" that our calculator provides. It reduces a complex expression to a concrete number.

How This Calculator Works

Our Expression Evaluator focuses on the second type of simplification: numerical evaluation. You provide a mathematical expression as a string, and then you input specific numerical values for any variables (x, y, z) present in that expression. The calculator then substitutes these values into the expression and computes the final numerical outcome.

This tool is incredibly useful for:

  • Quickly checking the value of a formula for different inputs.
  • Verifying homework problems in algebra or calculus.
  • Performing "what-if" scenarios in scientific or engineering calculations.
  • Understanding how changes in variable values affect the overall result of an expression.

Supported Operations and Functions

The calculator supports standard arithmetic operations:

  • Addition: +
  • Subtraction: -
  • Multiplication: *
  • Division: /
  • Exponentiation: ** (e.g., x**2 for x squared)

It also supports common mathematical functions by using the Math. prefix (e.g., Math.sin(), Math.cos(), Math.sqrt(), Math.log() for natural logarithm, etc.). For example, to calculate the sine of x, you would write Math.sin(x).

Examples:

Let's look at some examples of how to use the calculator:

Example 1: Basic Arithmetic

  • Expression: (x + y) * z
  • Value for x: 5
  • Value for y: 3
  • Value for z: 2
  • Calculation: (5 + 3) * 2 = 8 * 2 = 16
  • Result: 16.000000

Example 2: Using Exponents and Functions

  • Expression: x**2 + Math.sin(y) - z
  • Value for x: 4
  • Value for y: Math.PI / 2 (approximately 1.570796)
  • Value for z: 10
  • Calculation: 4^2 + Math.sin(Math.PI / 2) - 10 = 16 + 1 - 10 = 7
  • Result: 7.000000

Example 3: Complex Expression

  • Expression: (x + 2*y) / Math.sqrt(z) + Math.log(x)
  • Value for x: 10
  • Value for y: 5
  • Value for z: 4
  • Calculation: (10 + 2*5) / Math.sqrt(4) + Math.log(10) = (10 + 10) / 2 + 2.302585 = 20 / 2 + 2.302585 = 10 + 2.302585 = 12.302585
  • Result: 12.302585

Limitations

It's important to remember that this calculator is an expression evaluator, not a symbolic algebra system. It cannot:

  • Combine like terms (e.g., simplify 2x + 3x to 5x).
  • Factor expressions (e.g., simplify x^2 - 1 to (x-1)(x+1)).
  • Solve equations for unknown variables.

For those advanced tasks, you would need a dedicated computer algebra system (CAS).

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