Machin-like formulae
M000006414
$$\pi=4\arctan\left(\frac{1}{2}\right)+4\arctan\left(\frac{1}{3}\right)-4\arctan\left(\frac{1}{4}\right)+4\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{21}\right)$$
Compact formula
4[2] + 4[3] - 4[4] + 4[5] + 4[21]
Lehmer's measure
9.26577