Machin-like formulae
M000000496
$$\pi=8\arctan\left(\frac{1}{4}\right)+12\arctan\left(\frac{1}{7}\right)-8\arctan\left(\frac{1}{21}\right)-8\arctan\left(\frac{1}{57}\right)$$
Compact formula
8[4] + 12[7] - 8[21] - 8[57]
Lehmer's measure
4.17007