Machin-like formulae
M000000522
$$\pi=4\arctan\left(\frac{1}{2}\right)+4\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{13}\right)+4\arctan\left(\frac{1}{21}\right)$$
Compact formula
4[2] + 4[5] + 4[13] + 4[21]
Lehmer's measure
6.40662