def example_unconstrained(x):
    """A unconstrained example. 

    .. math::

        4x^2 - 2.1x^4 + 1/3 * x^6 + xy - 4y^2 + 4y^4

    """
    x1 = x[0]
    x2 = x[1]
    y = (4 * x1 * x1 - 2.1 * x1 ** 4 + 1.0 / 3.0 * x1 ** 6 + x1 * x2 - 4 *
        x2 * x2 + 4 * x2 ** 4)
    return y
