Machin-like formulae
M000000519
$$\pi=4\arctan\left(\frac{1}{3}\right)+8\arctan\left(\frac{1}{5}\right)+8\arctan\left(\frac{1}{21}\right)-4\arctan\left(\frac{1}{38}\right)$$
Compact formula
4[3] + 8[5] + 8[21] - 4[38]
Lehmer's measure
4.91588