isArithmeticExpression() in Javascript

Following from some work that I blogged about two days ago (Calculator in Python for dummies) I've now extended the functionality thinking into the AJAX scripts that sit on top of this Python server-side functionality. How this was implemented is boring but the following function helped me a lot. Here's the code with a very basic unit test after:

function isArithmeticExpression(s) {
  return /[\d]\s*\+\s*[\d]|[\d]\s*\-\s*[\d]|[\d]\s*\/\s*[\d]|[\d]\s*\*\s*[\d]|[\d]\s*\^\s*[\d]/.test(s) &&
        s.split(/\)/).length == s.split(/\(/).length &&
        !/[A-Za-z_]/.test(s);
}

function assert(fact) {
  if (!fact) alert("Assert failure!");
}
assert(isArithmeticExpression('') == false);
assert(isArithmeticExpression('++123') == false);
assert(isArithmeticExpression('+123') == false);
assert(isArithmeticExpression('2+123') == true);
assert(isArithmeticExpression('2 + 123') == true);
assert(isArithmeticExpression('2 + - 123') == false);
assert(isArithmeticExpression('2 + 123') == true);
assert(isArithmeticExpression('(2 + 123)') == true);
assert(isArithmeticExpression('2^6') == true);
assert(isArithmeticExpression('(2+1))^6') == false);
assert(isArithmeticExpression('a+123') == false);
assert(isArithmeticExpression('1a1+2x3') == false);

Basically, it returns true if the string appears to contain only numbers and one of the expected operators +, -, *, / or ^ in between two numbers.

It's far from perfect. I can think of cases where it will actually fail. But those cases are very rare and are too unlikely to happy and cause a major problem in this application and I'd rather get on with it than to spend any more time on this. After all, this is just a Javascript that tries to help if it can. The server-side code needs to "perfect" and if someone enters a weird expression, the server-side error handling will at least pick it up.