Machin-like formulae
M000000528
$$\pi=12\arctan\left(\frac{1}{3}\right)+4\arctan\left(\frac{1}{13}\right)-12\arctan\left(\frac{1}{23}\right)-12\arctan\left(\frac{1}{30}\right)-4\arctan\left(\frac{1}{38}\right)$$
Compact formula
12[3] + 4[13] - 12[23] - 12[30] - 4[38]
Lehmer's measure
5.03796