Machin-like formulae
M000000634
$$\pi=4\arctan\left(\frac{1}{2}\right)+12\arctan\left(\frac{1}{3}\right)-8\arctan\left(\frac{1}{4}\right)-8\arctan\left(\frac{1}{13}\right)$$
Compact formula
4[2] + 12[3] - 8[4] - 8[13]
Lehmer's measure
7.97650