Machin-like formulae
M000000629
$$\pi=4\arctan\left(\frac{1}{2}\right)+4\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{13}\right)+4\arctan\left(\frac{1}{34}\right)+4\arctan\left(\frac{1}{55}\right)$$
Compact formula
4[2] + 4[5] + 4[13] + 4[34] + 4[55]
Lehmer's measure
6.87787