Machin-like formulae
M000000505
$$\pi=12\arctan\left(\frac{1}{3}\right)-4\arctan\left(\frac{1}{4}\right)+4\arctan\left(\frac{1}{21}\right)+4\arctan\left(\frac{1}{57}\right)$$
Compact formula
12[3] - 4[4] + 4[21] + 4[57]
Lehmer's measure
5.08268