Machin-like formulae
M000000516
$$\pi=20\arctan\left(\frac{1}{4}\right)-12\arctan\left(\frac{1}{18}\right)-20\arctan\left(\frac{1}{21}\right)-8\arctan\left(\frac{1}{57}\right)$$
Compact formula
20[4] - 12[18] - 20[21] - 8[57]
Lehmer's measure
3.78342