Machin-like formulae
M000000515
$$\pi=12\arctan\left(\frac{1}{4}\right)+8\arctan\left(\frac{1}{8}\right)-4\arctan\left(\frac{1}{18}\right)-12\arctan\left(\frac{1}{21}\right)$$
Compact formula
12[4] + 8[8] - 4[18] - 12[21]
Lehmer's measure
4.32121