Walking a fine line

Calculus Level 4

Suppose two real numbers \(x\) and \(y\) are chosen randomly and uniformly from the interval \([-1, 1]\). The probability that \(xy \gt (x + y)\) is \(\dfrac{a - \ln{b}}{b}\), where \(a\) and \(b\) are positive coprime integers. Find \(a + b\).