string_expressions_parser.txt

var StringExpressionParser = function () {
	this.operators = [
    	'+', '-', '*', '/', '^'
    ];
    
    this.priorities = [
        ['*', '/'],
        ['+', '-']
    ];
};

StringExpressionParser.prototype.parse = function (expression) {
	return this.toInfixNotation(expression);
}

StringExpressionParser.prototype.toInfixNotation = function (expression) {
    var output = [], 
        stack = [];
    
    expression = expression
        .trim()
        .replace(/\,/g, '.')
        .replace(/x/g, '*')
        .replace(/([[0-9]*(?:\.?[0-9]+)*|[\(|\)])/g, ' $1 ')
        .split(' ')
        .filter(Boolean);
        
    for (var i = 0; i < expression.length; i++) {    
        if (/[0-9]/.test(expression[i])) {
        	output.push(expression[i]);
            
            continue;
        }
        
        if (this.operators.indexOf(expression[i]) !== -1) {
            while (stack.length > 0 && this.checkPreorities(expression[i], stack[stack.length-1])) {   
                output.push(stack.pop());
            }
            	
            stack.push(expression[i]);
            
            continue;
        }
        
        if (expression[i] === '(') {
            stack.push(expression[i]);
            
            continue;
        }
                
        if (expression[i] === ')') {
        	while (stack[stack.length - 1] !== '(') {
            	output.push(stack.pop());
            }
            
            stack.pop();
            
            continue;
        }
    }

    while (stack.length > 0) {
        output.push(stack.pop());
    }
            
    return this.toPostfix(output).join('');
};

StringExpressionParser.prototype.toPostfix = function (expression) {
    var output = [];
        
    for (var i = 0; i < expression.length; i++) {
        if (/[0-9]/.test(expression[i])) {
        	output.push(parseFloat(expression[i]));
            
            continue;
        }
        
        if (this.operators.indexOf(expression[i]) !== -1) {
            var result = this.calculate(output[output.length - 2], output[output.length - 1], expression[i]);
            
            output = output.slice(0, -2);
            output.push(result)
            
            continue;
        }
    }
    
    return output;
}

StringExpressionParser.prototype.checkPreorities = function (operator1, operator2) {
    for (var i = 0; i < this.priorities.length; i++) {        
    	if (
            (
                this.priorities[i].indexOf(operator1) !== -1 && 
            	this.priorities[i].indexOf(operator2) !== -1
            ) ||
            (
            	this.priorities[i].indexOf(operator2) !== -1 && 
                this.priorities[i + 1] !== undefined && 
                this.priorities[i + 1].indexOf(operator1) !== -1
            )
        ) {
        	return true;
        }
    }
    
    return false;
}

StringExpressionParser.prototype.calculate = function (a, b, operator) {
    switch (operator) {
        case '+':
            return a + b; 
        case '-':
            return a - b;
        case '*':
            return a * b;
        case '/':
            return a / b;
        case '^':
            return Math.pow(a, b);  
    }
}

var stringParser = new StringExpressionParser();

console.log(stringParser.parse('3+4*2/(1-5)^2'));
console.log(stringParser.parse('5+((1+2)*4)-3'));
console.log(stringParser.parse('(100/20+5)-(10/2)*5+((20*2)-(20/4))'));
console.log(stringParser.parse('1.5*2+4'));
console.log(stringParser.parse('5,5 + 2'));
console.log(stringParser.parse('.5 + 2'));
console.log(stringParser.parse('5x2'));