Machin-like formulae
M000000499
$$\pi=6\arctan\left(\frac{1}{2}\right)+2\arctan\left(\frac{1}{4}\right)-2\arctan\left(\frac{1}{21}\right)-2\arctan\left(\frac{1}{57}\right)$$
Compact formula
6[2] + 2[4] - 2[21] - 2[57]
Lehmer's measure
6.30871