Machin-like formulae
M000000579
$$\pi=6\arctan\left(\frac{1}{2}\right)+2\arctan\left(\frac{1}{6}\right)+2\arctan\left(\frac{1}{31}\right)-2\arctan\left(\frac{1}{57}\right)$$
Compact formula
6[2] + 2[6] + 2[31] - 2[57]
Lehmer's measure
5.84707