Machin-like formulae
M000000502
$$\pi=8\arctan\left(\frac{1}{4}\right)+4\arctan\left(\frac{1}{7}\right)+8\arctan\left(\frac{1}{8}\right)-8\arctan\left(\frac{1}{21}\right)$$
Compact formula
8[4] + 4[7] + 8[8] - 8[21]
Lehmer's measure
4.70787