Machin-like formulae
M000000521
$$\pi=8\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{7}\right)+8\arctan\left(\frac{1}{13}\right)+8\arctan\left(\frac{1}{21}\right)$$
Compact formula
8[5] + 4[7] + 8[13] + 8[21]
Lehmer's measure
4.26798