Machin-like formulae
M000000563
$$\pi=4\arctan\left(\frac{1}{2}\right)+8\arctan\left(\frac{1}{5}\right)-8\arctan\left(\frac{1}{31}\right)-4\arctan\left(\frac{1}{117}\right)$$
Compact formula
4[2] + 8[5] - 8[31] - 4[117]
Lehmer's measure
5.90664