Machin-like formulae
M000000506
$$\pi=4\arctan\left(\frac{1}{2}\right)+4\arctan\left(\frac{1}{4}\right)+4\arctan\left(\frac{1}{8}\right)-4\arctan\left(\frac{1}{21}\right)$$
Compact formula
4[2] + 4[4] + 4[8] - 4[21]
Lehmer's measure
6.84650