Machin-like formulae
M000000517
$$\pi=12\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{13}\right)+12\arctan\left(\frac{1}{21}\right)-4\arctan\left(\frac{1}{38}\right)$$
Compact formula
12[5] + 4[13] + 12[21] - 4[38]
Lehmer's measure
3.71769