Machin-like formulae
M000000534
$$\pi=4\arctan\left(\frac{1}{2}\right)+4\arctan\left(\frac{1}{3}\right)+4\arctan\left(\frac{1}{13}\right)-4\arctan\left(\frac{1}{23}\right)-4\arctan\left(\frac{1}{30}\right)$$
Compact formula
4[2] + 4[3] + 4[13] - 4[23] - 4[30]
Lehmer's measure
7.72689