Machin-like formulae
M000000507
$$\pi=8\arctan\left(\frac{1}{4}\right)+12\arctan\left(\frac{1}{8}\right)-8\arctan\left(\frac{1}{21}\right)+4\arctan\left(\frac{1}{57}\right)$$
Compact formula
8[4] + 12[8] - 8[21] + 4[57]
Lehmer's measure
4.09409