Machin-like formulae
M000000589
$$\pi=8\arctan\left(\frac{1}{2}\right)-4\arctan\left(\frac{1}{6}\right)+4\arctan\left(\frac{1}{18}\right)-4\arctan\left(\frac{1}{31}\right)$$
Compact formula
8[2] - 4[6] + 4[18] - 4[31]
Lehmer's measure
6.07419