Machin-like formulae
M000010569
$$\pi=8\arctan\left(\frac{1}{2}\right)-16\arctan\left(\frac{1}{4}\right)+12\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{18}\right)+16\arctan\left(\frac{1}{21}\right)$$
Compact formula
8[2] - 16[4] + 12[5] + 4[18] + 16[21]
Lehmer's measure
7.96651