Machin-like formulae
M000006615
$$\pi=8\arctan\left(\frac{1}{3}\right)-8\arctan\left(\frac{1}{4}\right)+8\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{7}\right)+8\arctan\left(\frac{1}{21}\right)$$
Compact formula
8[3] - 8[4] + 8[5] + 4[7] + 8[21]
Lehmer's measure
7.12714