Muller order (root of p^3 = p^2 + p + 1): 1.8393
secant order (golden ratio):              1.6180
function      three-point: last orders                two-point: last orders
cos x - x     1.841 1.840 1.840                       1.619 1.619 1.618
exp(x) - 2    1.840 1.840 1.840                       1.618 1.618 1.618
x^3 - x - 2   1.841 1.840 1.840                       1.618 1.618 1.618
sin x - 1/2   1.841 1.840 1.839                       1.619 1.618 1.618
x^2 - 2       2.001 2.001 2.000                       1.619 1.618 1.618
order high precision done