Machin-like formulae
M000010437
$$\pi=6\arctan\left(\frac{1}{2}\right)-12\arctan\left(\frac{1}{4}\right)+12\arctan\left(\frac{1}{5}\right)+2\arctan\left(\frac{1}{8}\right)+2\arctan\left(\frac{1}{18}\right)+12\arctan\left(\frac{1}{21}\right)$$
Compact formula
6[2] - 12[4] + 12[5] + 2[8] + 2[18] + 12[21]
Lehmer's measure
9.07382