Machin-like formulae
M000000509
$$\pi=8\arctan\left(\frac{1}{2}\right)-4\arctan\left(\frac{1}{4}\right)+4\arctan\left(\frac{1}{18}\right)+4\arctan\left(\frac{1}{21}\right)$$
Compact formula
8[2] - 4[4] + 4[18] + 4[21]
Lehmer's measure
6.53583