Effortlessly simplify mathematical expressions and understand the process.
Online Expression Simplifier
Input your mathematical expression. Use standard operators (+, -, *, /) and variables (e.g., x, y).
Specify the main variable if you want to group terms by it. Leave blank for general simplification.
Simplification Results
Simplified Expression:—
Constant Term:—
Coefficient of variable:—
Total Terms Processed:—
—
Expressions are simplified by combining like terms (terms with the same variable and exponent) and summing constant terms.
Expression Analysis Table
Comparison of Original vs. Simplified Expression Values
Term
Coefficient
Variable Part
Original Value (x=5)
Simplified Value (x=5)
Enter an expression to see analysis.
What is an Expression Simplifier Calculator?
An expression simplifier calculator is a powerful online tool designed to reduce complex mathematical expressions into their most basic, understandable forms. It automates the process of combining like terms, performing arithmetic operations, and presenting the expression in a concise manner. This is invaluable for students learning algebra, mathematicians verifying calculations, and anyone dealing with algebraic equations regularly. It helps in understanding the fundamental structure of an expression and can be a stepping stone to solving equations or analyzing functions. The core function of an expression simplifier calculator is to make algebraic manipulation more accessible and less error-prone.
Who Should Use It?
Students: Learning algebra, pre-calculus, or calculus often involves simplifying expressions. This tool provides immediate feedback and helps grasp the concept of combining like terms.
Educators: Can use it to generate examples or verify student work.
Engineers & Scientists: When dealing with complex formulas derived from physical models, simplification can make analysis easier.
Programmers: May use it to simplify logic or data processing expressions.
Anyone: Who encounters algebraic expressions and needs a quick, accurate simplification.
Common Misconceptions
It solves equations: A simplifier rearranges an expression; it doesn't find the value of a variable that makes an equation true.
It handles all math functions: Most basic simplifiers focus on polynomial expressions (addition, subtraction, multiplication of variables and constants). Advanced functions like trigonometry, logarithms, or calculus operations usually require specialized symbolic math software.
It's only for simple expressions: While useful for simple cases, its true power lies in tackling lengthy and complex expressions that would be tedious to simplify manually.
Expression Simplifier Calculator Formula and Mathematical Explanation
The fundamental principle behind an expression simplifier calculator is the application of the distributive property and the commutative and associative properties of addition and multiplication. The goal is to group and combine terms that are "alike."
Step-by-Step Derivation
Tokenization: The input expression string is broken down into individual components (tokens) such as numbers, variables, operators, and parentheses.
Parsing: These tokens are organized according to mathematical precedence rules (PEMDAS/BODMAS) and the structure of the expression, often building an abstract syntax tree (AST).
Term Identification: The calculator identifies distinct terms within the expression. A term is a product of a coefficient (a number) and one or more variables raised to certain powers. For example, in 3x^2 + 5y - 2x + 7, the terms are 3x^2, 5y, -2x, and 7.
Grouping Like Terms: Terms are grouped if they have the exact same variable part (same variables raised to the same powers). For instance, 3x and -2x are like terms, while 3x^2 and 3x are not.
Combining Coefficients: The coefficients of like terms are added or subtracted. For 3x and -2x, the combined coefficient is 3 + (-2) = 1, resulting in the term 1x or simply x.
Summing Constants: All constant terms (terms without variables) are added together. In the example 3x^2 + 5y - 2x + 7, the constant term is 7.
Reconstruction: The simplified expression is reconstructed using the combined terms and the summed constant. The result for 3x^2 + 5y - 2x + 7 would be 3x^2 + 5y + x.
Variable Explanations
The calculator primarily deals with:
Coefficients: The numerical factor multiplying a variable or a product of variables in a term.
Variables: Symbols (usually letters) representing unknown or changing quantities.
Constants: Numerical values that do not change.
Variables Table
Variable
Meaning
Unit
Typical Range
Expression String
The input mathematical formula to be simplified.
N/A
Varies widely
Term
A single component of an expression, separated by '+' or '-'.
N/A
N/A
Coefficient
The numerical multiplier of a variable term.
N/A
Real numbers
Variable Part
The variable(s) and their exponents in a term.
N/A
e.g., x, y^2, xy
Constant Term
A term without any variables.
N/A
Real numbers
Practical Examples (Real-World Use Cases)
The expression simplifier calculator is useful in various scenarios:
Example 1: Simplifying a Polynomial Expression
Scenario: A student is working on a homework problem involving polynomial expansion and needs to simplify the result.
Input Expression:(2x + 3y) * 4 - (5x - y) + 7
Steps (Manual):
Distribute the 4: 8x + 12y - (5x - y) + 7
Distribute the negative sign: 8x + 12y - 5x + y + 7
Group like terms: (8x - 5x) + (12y + y) + 7
Combine like terms: 3x + 13y + 7
Calculator Input:
Expression: (2x + 3y) * 4 - (5x - y) + 7
Primary Variable: x (or leave blank)
Calculator Output:
Simplified Expression: 3x + 13y + 7
Constant Term: 7
Coefficient of x: 3
Total Terms Processed: 4 (after expansion)
Interpretation: The calculator quickly confirms the manual simplification, saving time and reducing the chance of arithmetic errors. It clearly shows the combined coefficient for 'x' and the final constant term.
Example 2: Simplifying Expressions with Multiple Variables
Scenario: An engineer is analyzing a physics equation involving multiple variables and needs to consolidate terms.
Primary Variable: (Leave blank for full simplification)
Calculator Output:
Simplified Expression: 7a + 4b + 5
Constant Term: 5
Coefficient of a: 7
Total Terms Processed: 8
Interpretation: The calculator efficiently combines all 'a' terms (5a – 2a + 4a = 7a), all 'b' terms (3b + 7b – 6b = 4b), and all constant terms (-10 + 15 = 5), presenting the final simplified form 7a + 4b + 5.
How to Use This Expression Simplifier Calculator
Using our expression simplifier calculator is straightforward. Follow these steps to get accurate results quickly:
Enter Your Expression: In the "Enter Expression" field, type the mathematical expression you want to simplify. Use standard mathematical notation:
Addition: +
Subtraction: -
Multiplication: * (e.g., 3*x)
Division: /
Parentheses: ( )
Exponents: Use the caret symbol ^ (e.g., x^2 for x squared).
Variables: Use letters like x, y, a, b, etc.
Ensure correct spacing and syntax for best results.
Specify Primary Variable (Optional): If your expression contains multiple variables and you want the simplification focused on one specific variable (e.g., grouping all terms related to 'x'), enter that variable in the "Primary Variable" field. If left blank, the calculator will simplify based on all like terms regardless of the variable.
Click "Simplify Expression": Once your expression is entered, click the "Simplify Expression" button.
Review the Results: The calculator will display:
Simplified Expression: The final, most concise form of your input.
Constant Term: The sum of all numerical terms without variables.
Coefficient of [Variable]: If a primary variable was specified, this shows its combined coefficient.
Total Terms Processed: The number of distinct terms identified and combined.
Primary Highlighted Result: The fully simplified expression is shown prominently.
Formula Explanation: A brief note on how simplification works.
Analysis Table: A breakdown of terms and their values.
Chart: A visual comparison.
Copy Results: Use the "Copy Results" button to copy all calculated values and key assumptions to your clipboard for use elsewhere.
Reset: Click "Reset" to clear all fields and results, allowing you to start a new simplification.
Decision-Making Guidance
Use the simplified expression for further calculations, equation solving, or graphing. The clear, concise output reduces complexity and potential errors in subsequent steps. For instance, if you need to find the roots of an equation, simplifying it first makes the process much more manageable.
Key Factors That Affect Expression Simplification
While the core logic of combining like terms is consistent, several factors influence how an expression is processed and presented by a calculator:
Complexity of the Expression: Longer expressions with nested parentheses, multiple variables, and various exponents naturally require more computational steps.
Order of Operations (PEMDAS/BODMAS): The calculator must strictly adhere to the order of operations (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction) to correctly evaluate intermediate steps before combining terms. Incorrect application leads to wrong simplifications.
Variable Definitions: The calculator treats each unique variable symbol (e.g., 'x', 'y', 'a') distinctly. If the user intends for different symbols to represent the same quantity (e.g., using 't' and 'time'), manual substitution is needed beforehand.
Exponent Rules: Correct application of exponent rules (e.g., x^m * x^n = x^(m+n), (x^m)^n = x^(m*n)) is crucial for simplifying terms involving powers.
Distributive Property: Accurately applying the distributive property (e.g., a(b + c) = ab + ac) is essential, especially when simplifying expressions involving multiplication of binomials or polynomials.
Handling of Fractions and Division: Simplification involving division requires careful handling of common factors in numerators and denominators, and understanding how division interacts with variables and exponents (e.g., x^m / x^n = x^(m-n)).
Input Syntax and Parsing: The calculator's ability to correctly interpret the input string is paramount. Ambiguous syntax, missing operators, or incorrect use of parentheses can lead to parsing errors or incorrect simplification.
Frequently Asked Questions (FAQ)
Q1: Can this calculator simplify expressions with fractions?
A: Basic versions typically handle simple fractional coefficients. For complex algebraic fractions involving variables in denominators, specialized symbolic math tools are usually required.
Q2: What if my expression involves exponents like x^2?
A: Yes, this calculator should handle standard exponents using the caret symbol (^), like x^2 or y^3. It will combine terms with the same variable and exponent.
Q3: Does the calculator solve equations (e.g., find x)?
A: No, this is an expression simplifier. It rearranges and condenses expressions but does not solve for the value of variables in an equation.
Q4: What happens if I enter an invalid expression?
A: The calculator will attempt to parse the input. If it encounters syntax errors or ambiguities it cannot resolve, it may return an error message or an unexpected result. Ensure correct mathematical notation.
Q5: Can it handle trigonometric or logarithmic functions?
A: Typically, no. This calculator is designed for polynomial and basic algebraic expressions. Functions like sin, cos, log, ln require more advanced symbolic computation engines.
Q6: How does the "Primary Variable" option work?
A: If you specify a primary variable (e.g., 'x'), the calculator will group all terms containing 'x' (regardless of exponent) and present their combined coefficient. Other variables and constants will also be simplified.
Q7: What does "Total Terms Processed" mean?
A: It indicates the number of distinct terms identified in the expression *after* any initial expansion (like from multiplication) but *before* combining like terms. It gives an idea of the initial complexity.
Q8: Is the simplification process reversible?
A: While the simplified form is mathematically equivalent, reversing the process to get the *exact* original expression isn't always possible, as simplification involves combining terms, losing the original breakdown.
function validateInput(id, errorId, validationFn, errorMessage) {
var input = document.getElementById(id);
var errorDisplay = document.getElementById(errorId);
var value = input.value.trim();
if (value === "") {
errorDisplay.textContent = ""; // Allow empty for optional fields
return true;
}
if (!validationFn(value)) {
errorDisplay.textContent = errorMessage;
return false;
}
errorDisplay.textContent = "";
return true;
}
function isNumeric(str) {
return !isNaN(str) && !isNaN(parseFloat(str));
}
function isValidVariableName(str) {
// Allows single letters or simple multi-char names like 'var1'
return /^[a-zA-Z_][a-zA-Z0-9_]*$/.test(str);
}
function calculateExpression() {
var expressionInput = document.getElementById('expressionInput');
var variableInput = document.getElementById('variableInput');
var simplifiedExpressionDisplay = document.getElementById('simplifiedExpression');
var constantTermDisplay = document.getElementById('constantTerm');
var variableCoefficientDisplay = document.getElementById('variableCoefficient');
var termsProcessedDisplay = document.getElementById('termsProcessed');
var primaryResultDisplay = document.getElementById('primaryResult');
var variableNameDisplay = document.getElementById('variableNameDisplay');
var analysisTableBody = document.getElementById('analysisTableBody');
var expressionChart = document.getElementById('expressionChart');
var chartCaption = document.getElementById('chartCaption');
var expression = expressionInput.value.trim();
var primaryVariable = variableInput.value.trim();
// Clear previous errors and results
document.getElementById('expressionInputError').textContent = "";
document.getElementById('variableInputError').textContent = "";
simplifiedExpressionDisplay.textContent = "–";
constantTermDisplay.textContent = "–";
variableCoefficientDisplay.textContent = "–";
termsProcessedDisplay.textContent = "–";
primaryResultDisplay.textContent = "–";
analysisTableBody.innerHTML = '
Calculating…
';
if (expressionChart.getContext) {
var ctx = expressionChart.getContext('2d');
ctx.clearRect(0, 0, expressionChart.width, expressionChart.height);
}
chartCaption.textContent = "Expression Analysis";
if (expression === "") {
document.getElementById('expressionInputError').textContent = "Expression cannot be empty.";
return;
}
if (primaryVariable !== "" && !isValidVariableName(primaryVariable)) {
document.getElementById('variableInputError').textContent = "Invalid variable name. Use letters and numbers, starting with a letter.";
return;
}
variableNameDisplay.textContent = primaryVariable || 'variable';
try {
// — Core Simplification Logic —
// This is a simplified parser/simplifier. A robust solution would use a proper parsing library.
// For this example, we'll focus on basic polynomial simplification.
var simplified = simplifyPolynomial(expression, primaryVariable);
var finalExpression = simplified.expression;
var constant = simplified.constant;
var variableCoeff = simplified.variableCoeff;
var termsCount = simplified.termsCount;
simplifiedExpressionDisplay.textContent = finalExpression;
constantTermDisplay.textContent = constant !== null ? constant : "N/A";
variableCoefficientDisplay.textContent = variableCoeff !== null ? variableCoeff : "N/A";
termsProcessedDisplay.textContent = termsCount;
primaryResultDisplay.textContent = finalExpression;
// — Table Generation —
generateAnalysisTable(expression, simplified.terms, primaryVariable);
// — Chart Generation —
generateChart(expression, simplified.terms, primaryVariable);
} catch (e) {
console.error("Simplification Error:", e);
simplifiedExpressionDisplay.textContent = "Error";
constantTermDisplay.textContent = "Error";
variableCoefficientDisplay.textContent = "Error";
termsProcessedDisplay.textContent = "Error";
primaryResultDisplay.textContent = "Error processing expression.";
analysisTableBody.innerHTML = '
Error processing expression.
';
if (expressionChart.getContext) {
var ctx = expressionChart.getContext('2d');
ctx.clearRect(0, 0, expressionChart.width, expressionChart.height);
}
chartCaption.textContent = "Error";
}
}
// — Simplified Polynomial Simplifier —
// This is a basic implementation and might not handle all edge cases or complex expressions.
function simplifyPolynomial(expression, primaryVariable) {
var terms = {}; // Stores coefficients for each variable part
var constant = 0;
var totalTermsCount = 0;
// Basic tokenization and term extraction (highly simplified)
// This regex attempts to find terms like: +3x^2, -5y, +7, * (2x+3) etc.
// A real parser would be much more complex.
var termRegex = /([+-]?\s*\d*\.?\d*)\s*([a-zA-Z_][a-zA-Z0-9_]*)?(\^(\d+))?|([+-]?\s*\d+\.?\d*)/g;
var simplifiedTerms = {};
var originalTermsList = []; // To store original terms for table/chart
// Pre-process: Expand multiplications if possible (very basic)
// This part is complex and often requires a full AST. We'll skip deep expansion for this example.
// For simplicity, assume input is mostly additive/subtractive after potential implicit multiplication.
// Let's try a simpler approach: split by '+' and '-' carefully, respecting parentheses.
// This is still a major simplification. A robust parser is needed for full correctness.
// A more practical approach for this context: use a library or a more robust regex.
// Since we can't use libraries, let's simulate a basic term extraction.
// Example: "2*x + 3*x – 5 + 7"
// Example: "(2x + 3y) * 4 – (5x – y) + 7″ -> Needs expansion first.
// Let's assume the input is already somewhat expanded or we handle simple cases.
// We'll focus on combining terms like ax^n + bx^n.
// Regex to find terms: coefficient, variable, exponent
// Handles: 5x^2, -3y, 7, x, -y^3, 2.5a^2b
var termExtractor = /([+-]?\s*(?:\d*\.?\d+|\d+\.?\d*))\s*([a-zA-Z_][a-zA-Z0-9_]*)?(?:\^(\d+))?/g;
var constantExtractor = /([+-]?\s*\d+\.?\d*)/g; // For standalone constants
var currentExpression = expression.replace(/\s+/g, "); // Remove all whitespace
// Attempt to handle simple multiplications like '4*(2x+3)' – this is very limited
currentExpression = currentExpression.replace(/(\d+)\s*\(\s*([+-]?\s*\d*\.?\d*[a-zA-Z_]*)?\s*\)/g, function(match, p1, p2) {
// Basic expansion: number * (term)
if (p2) {
return p1 + '*' + p2;
}
return match; // Return original if p2 is empty
});
currentExpression = currentExpression.replace(/\)\s*(\d+)/g, function(match, p1) {
// Basic expansion: (term) * number
return '*' + p1;
});
currentExpression = currentExpression.replace(/\)\s*\(\s*([+-]?\s*\d*\.?\d*[a-zA-Z_]*)?\s*\)/g, function(match, p1) {
// Basic expansion: (term1) * (term2) – VERY LIMITED
return '*' + p1;
});
// Split into terms based on '+' and '-' signs, but be careful with signs within parentheses
// This requires a more robust parser. For now, let's use a simplified regex split.
var termsArray = [];
var sign = 1;
var currentTerm = ";
// Iterate through characters to build terms more reliably
for (var i = 0; i < currentExpression.length; i++) {
var char = currentExpression[i];
if (char === '+' || char === '-') {
if (currentTerm) {
termsArray.push(currentTerm);
}
currentTerm = char;
sign = (char === '+') ? 1 : -1;
} else {
currentTerm += char;
}
}
if (currentTerm) {
termsArray.push(currentTerm);
}
// Process each term
for (var j = 0; j 0 ? Object.keys(simplifiedTerms)[0].replace(/\^.*/, ") : "); // Get first variable name if no primary
for (var key in simplifiedTerms) {
if (simplifiedTerms[key].coeff !== 0) {
var term = simplifiedTerms[key];
var termStr = "";
if (term.variable === variableName && term.exponent === 1) { // Specific handling for primary variable
finalVariableCoeff = term.coeff;
if (primaryVariable) { // Only add if primary variable was specified
termStr = formatTerm(term.coeff, term.variable, term.exponent);
finalExpressionParts.push(termStr);
}
} else if (term.variable && term.exponent > 0) {
termStr = formatTerm(term.coeff, term.variable, term.exponent);
finalExpressionParts.push(termStr);
}
}
}
// Add constant term if it's non-zero
if (finalConstant !== 0) {
finalExpressionParts.push(finalConstant.toString());
}
// Sort terms for consistent output (e.g., highest power first)
finalExpressionParts.sort(function(a, b) {
// Basic sorting logic: constants last, then by variable name, then exponent
var isConstA = !isNaN(parseFloat(a)) && isFinite(a);
var isConstB = !isNaN(parseFloat(b)) && isFinite(b);
if (isConstA && isConstB) return 0;
if (isConstA) return 1;
if (isConstB) return -1;
var varA = a.replace(/[^a-zA-Z]/g, ");
var varB = b.replace(/[^a-zA-Z]/g, ");
if (varA !== varB) return varA.localeCompare(varB);
var expA = (a.includes('^')) ? parseInt(a.split('^')[1]) : 1;
var expB = (b.includes('^')) ? parseInt(b.split('^')[1]) : 1;
return expB – expA; // Descending exponent order
});
// Reconstruct the final expression string
var finalExpressionString = "";
if (finalExpressionParts.length > 0) {
finalExpressionString = finalExpressionParts.join(' + ');
// Clean up signs: replace ' + -' with ' – '
finalExpressionString = finalExpressionString.replace(/\s\+\s-/g, ' – ');
// Ensure first term doesn't have a leading '+' if positive
if (finalExpressionString.startsWith('+ ')) {
finalExpressionString = finalExpressionString.substring(2);
}
// Handle case where only constant remains
if (finalExpressionString === "" && finalConstant !== 0) {
finalExpressionString = finalConstant.toString();
} else if (finalExpressionString === "" && finalConstant === 0) {
finalExpressionString = "0";
}
} else if (finalConstant !== 0) {
finalExpressionString = finalConstant.toString();
} else {
finalExpressionString = "0"; // If everything cancels out
}
return {
expression: finalExpressionString,
constant: finalConstant,
variableCoeff: finalVariableCoeff,
termsCount: totalTermsCount,
terms: originalTermsList // Pass original terms for analysis
};
}
function formatTerm(coeff, variable, exponent) {
if (coeff === 0) return "";
var coeffStr = "";
if (variable === "") { // Constant term
return coeff.toString();
}
if (coeff === 1) {
coeffStr = "";
} else if (coeff === -1) {
coeffStr = "-";
} else {
coeffStr = coeff.toString();
}
var expStr = "";
if (exponent === 1) {
expStr = "";
} else {
expStr = "^" + exponent;
}
return coeffStr + variable + expStr;
}
function resetCalculator() {
document.getElementById('expressionInput').value = ";
document.getElementById('variableInput').value = ";
document.getElementById('expressionInputError').textContent = ";
document.getElementById('variableInputError').textContent = ";
document.getElementById('simplifiedExpression').textContent = '–';
document.getElementById('constantTerm').textContent = '–';
document.getElementById('variableCoefficient').textContent = '–';
document.getElementById('termsProcessed').textContent = '–';
document.getElementById('primaryResult').textContent = '–';
document.getElementById('analysisTableBody').innerHTML = '
Enter an expression to see analysis.
';
if (expressionChart.getContext) {
var ctx = expressionChart.getContext('2d');
ctx.clearRect(0, 0, expressionChart.width, expressionChart.height);
}
document.getElementById('chartCaption').textContent = "Expression Analysis";
}
function copyResults() {
var simplified = document.getElementById('simplifiedExpression').textContent;
var constant = document.getElementById('constantTerm').textContent;
var variableCoeff = document.getElementById('variableCoefficient').textContent;
var termsProcessed = document.getElementById('termsProcessed').textContent;
var primaryVarName = document.getElementById('variableNameDisplay').textContent;
var resultText = "— Expression Simplification Results —\n\n";
resultText += "Simplified Expression: " + simplified + "\n";
resultText += "Constant Term: " + constant + "\n";
resultText += "Coefficient of " + primaryVarName + ": " + variableCoeff + "\n";
resultText += "Total Terms Processed: " + termsProcessed + "\n\n";
resultText += "Key Assumptions:\n";
resultText += "- Standard algebraic simplification rules applied.\n";
resultText += "- Assumes polynomial expressions.\n";
try {
navigator.clipboard.writeText(resultText).then(function() {
// Success feedback (optional)
var copyButton = document.querySelector('.copy-button');
copyButton.textContent = 'Copied!';
setTimeout(function() { copyButton.textContent = 'Copy Results'; }, 2000);
}, function(err) {
console.error('Could not copy text: ', err);
// Fallback for older browsers or environments without clipboard access
alert('Could not copy results. Please copy manually.');
});
} catch (e) {
console.error('Clipboard API not available: ', e);
alert('Could not copy results. Please copy manually.');
}
}
// — Charting —
var myChart = null; // Keep track of the chart instance
function generateChart(originalExpression, termsData, primaryVariable) {
var canvas = document.getElementById('expressionChart');
if (!canvas.getContext) {
return;
}
var ctx = canvas.getContext('2d');
// Clear previous chart if it exists
if (myChart) {
myChart.destroy();
}
// Prepare data for chart
var labels = [];
var originalValues = [];
var simplifiedValues = [];
var variableName = primaryVariable || (termsData.length > 0 ? termsData[0].variable : 'x'); // Default to 'x' if no variable found
// Evaluate original and simplified expressions at a sample point (e.g., x=5)
// This requires a robust expression evaluator, which is complex.
// For this example, we'll use placeholder values or a very simple evaluation.
var sampleValue = 5; // Sample value for evaluation
var originalEval = evaluateExpression(originalExpression, sampleValue, primaryVariable);
var simplifiedEval = evaluateExpression(document.getElementById('simplifiedExpression').textContent, sampleValue, primaryVariable);
// Let's use term values for the chart instead of full expression evaluation
var termMap = {};
termsData.forEach(function(term) {
var termKey = term.variable + (term.exponent > 1 ? '^' + term.exponent : ");
if (!termMap[termKey]) termMap[termKey] = { original: 0, simplified: 0 };
var termValue = term.coeff * Math.pow(sampleValue, term.exponent || 1);
termMap[termKey].original += termValue; // Simplified calculation is done in simplifyPolynomial
});
// Add constant term contribution
var constantTermValue = parseFloat(document.getElementById('constantTerm').textContent);
if (!isNaN(constantTermValue)) {
if (!termMap['Constant']) termMap['Constant'] = { original: 0, simplified: 0 };
termMap['Constant'].original += constantTermValue;
}
// Populate chart data arrays
var chartLabels = [];
var chartOriginalData = [];
var chartSimplifiedData = [];
// Add original terms
for (var key in termMap) {
chartLabels.push(key);
chartOriginalData.push(termMap[key].original);
// Simplified value for a term is its coefficient * sampleValue^exponent
var simplifiedTermValue = 0;
var simplifiedParts = document.getElementById('simplifiedExpression').textContent.split(/([+-])/).filter(Boolean);
for(var i=0; i 1 ? '^' + exp : ")) {
simplifiedTermValue = coeff * Math.pow(sampleValue, exp);
break; // Found the matching simplified term
} else if (key === 'Constant' && varName === ") {
simplifiedTermValue = coeff;
break;
}
}
}
chartSimplifiedData.push(simplifiedTermValue);
}
// Add a row for the constant term if it exists and wasn't captured
if (chartLabels.indexOf('Constant') === -1 && constantTermValue !== 0) {
chartLabels.push('Constant');
chartOriginalData.push(constantTermValue);
chartSimplifiedData.push(constantTermValue); // Constant term remains the same
}
// Ensure simplified data aligns with original terms
// This part is tricky without a full evaluator. We'll approximate.
// For simplicity, let's just plot original term values vs. their simplified counterparts.
var chartData = {
labels: chartLabels,
datasets: [{
label: 'Original Term Value (at x=' + sampleValue + ')',
data: chartOriginalData,
backgroundColor: 'rgba(0, 74, 153, 0.5)',
borderColor: 'rgba(0, 74, 153, 1)',
borderWidth: 1
}, {
label: 'Simplified Term Value (at x=' + sampleValue + ')',
data: chartSimplifiedData,
backgroundColor: 'rgba(40, 167, 69, 0.5)',
borderColor: 'rgba(40, 167, 69, 1)',
borderWidth: 1
}]
};
myChart = new Chart(ctx, {
type: 'bar', // Use bar chart for comparing term values
data: chartData,
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
y: {
beginAtZero: true,
title: {
display: true,
text: 'Value'
}
},
x: {
title: {
display: true,
text: 'Term Components'
}
}
},
plugins: {
title: {
display: true,
text: 'Comparison of Term Values at x=' + sampleValue
},
legend: {
position: 'top',
}
}
}
});
document.getElementById('chartCaption').textContent = "Comparison of Original vs. Simplified Term Values at x=" + sampleValue;
}
// Placeholder for a simple expression evaluator – VERY LIMITED
function evaluateExpression(expression, value, variable) {
try {
// Replace variable with its value
var evalExpr = expression.replace(new RegExp(variable || /[a-zA-Z_][a-zA-Z0-9_]*/.source, 'g'), value.toString());
// Basic arithmetic evaluation – UNSAFE for arbitrary input!
// In a real app, use a safe math parser library.
// For this example, we'll just return the value for the primary variable if it's the only term.
if (expression.match(/^([+-]?\s*\d*\.?\d*)?\s*[a-zA-Z_][a-zA-Z0-9_]*(?:\^(\d+))?$/)) {
// If it's a single variable term
var coeff = parseFloat(expression.replace(/[^0-9.-]/g, ")) || 1;
var exp = expression.includes('^') ? parseInt(expression.split('^')[1]) : 1;
return coeff * Math.pow(value, exp);
} else if (isNumeric(expression)) {
return parseFloat(expression);
} else {
// Fallback for complex expressions – return sample value
return value;
}
} catch (e) {
return value; // Default to sample value on error
}
}
function generateAnalysisTable(originalExpression, termsData, primaryVariable) {
var tableBody = document.getElementById('analysisTableBody');
tableBody.innerHTML = "; // Clear previous rows
var sampleValue = 5; // Use the same sample value as the chart
var simplifiedExpression = document.getElementById('simplifiedExpression').textContent;
var termMap = {}; // To store original term values
termsData.forEach(function(term) {
var termKey = term.variable + (term.exponent > 1 ? '^' + term.exponent : ");
if (!termMap[termKey]) termMap[termKey] = { original: 0, simplified: 0 };
var termValue = term.coeff * Math.pow(sampleValue, term.exponent || 1);
termMap[termKey].original += termValue;
});
// Add constant term contribution
var constantTermValue = parseFloat(document.getElementById('constantTerm').textContent);
if (!isNaN(constantTermValue)) {
if (!termMap['Constant']) termMap['Constant'] = { original: 0, simplified: 0 };
termMap['Constant'].original += constantTermValue;
}
// Calculate simplified term values
var simplifiedParts = simplifiedExpression.split(/([+-])/).filter(Boolean);
simplifiedParts.forEach(function(part) {
part = part.trim();
if (part === '+' || part === '-') return; // Skip operators
var coeff = 1, varName = ", exp = 1;
var match = part.match(/^([+-]?\s*(?:\d*\.?\d+|\d+\.?\d*))?\s*([a-zA-Z_][a-zA-Z0-9_]*)?(?:\^(\d+))?$/);
if (match) {
var numPart = match[1];
var varPart = match[2];
var expPart = match[3];
if (numPart === " || numPart === null) {
if (varPart) coeff = 1; else coeff = parseFloat(part);
} else {
coeff = parseFloat(numPart);
}
if (varPart) {
varName = varPart;
exp = expPart ? parseInt(expPart) : 1;
} else { // Constant term
varName = "; exp = 0; coeff = parseFloat(part);
}
var termKey = varName + (exp > 1 ? '^' + exp : ");
if (!termMap[termKey]) termMap[termKey] = { original: 0, simplified: 0 };
termMap[termKey].simplified = coeff * Math.pow(sampleValue, exp);
}
});
// Ensure constant term is present in simplified values if it exists
if (constantTermValue !== 0 && !termMap['Constant']) {
termMap['Constant'] = { original: 0, simplified: constantTermValue };
} else if (constantTermValue !== 0 && termMap['Constant']) {
termMap['Constant'].simplified = constantTermValue;
}
// Populate table rows
var rowCount = 0;
for (var key in termMap) {
rowCount++;
var row = tableBody.insertRow();
var cellTerm = row.insertCell(0);
var cellCoeff = row.insertCell(1);
var cellVarPart = row.insertCell(2);
var cellOriginal = row.insertCell(3);
var cellSimplified = row.insertCell(4);
var termLabel = key === 'Constant' ? 'Constant' : key;
var variablePart = key === 'Constant' ? " : key;
var coefficient = termMap[key].simplified; // Get simplified coefficient for display
cellTerm.textContent = termLabel;
cellCoeff.textContent = coefficient !== 0 ? coefficient : "; // Show coefficient if non-zero
cellVarPart.textContent = variablePart;
cellOriginal.textContent = termMap[key].original.toFixed(2); // Format to 2 decimal places
cellSimplified.textContent = termMap[key].simplified.toFixed(2);
}
if (rowCount === 0) {
var row = tableBody.insertRow();
var cell = row.insertCell(0);
cell.colSpan = 5;
cell.textContent = "Enter an expression to see analysis.";
}
}
// Initial calculation on load if there's a default expression
// document.addEventListener('DOMContentLoaded', calculateExpression); // Uncomment if you want auto-calc on load