Machin-like formulae
M000001212
$$\pi=4\arctan\left(\frac{1}{2}\right)+12\arctan\left(\frac{1}{3}\right)-8\arctan\left(\frac{1}{5}\right)-8\arctan\left(\frac{1}{13}\right)-8\arctan\left(\frac{1}{21}\right)$$
Compact formula
4[2] + 12[3] - 8[5] - 8[13] - 8[21]
Lehmer's measure
8.50252