def METHOD_NAME(self, x, y):
    """
    Calculates the elementwise determinant of the log Jacobian
    """
    x_old, y_old = self._cached_x_y
    if x is not x_old or y is not y_old:
        # This call to the parent class Transform will update the cache
        # as well as calling self._call and recalculating y and log_detJ
        self(x)
    return self._cached_logDetJ