Machin-like formulae
M000009121
$$\pi=16\arctan\left(\frac{1}{4}\right)-8\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{7}\right)+8\arctan\left(\frac{1}{13}\right)-8\arctan\left(\frac{1}{21}\right)$$
Compact formula
16[4] - 8[5] + 4[7] + 8[13] - 8[21]
Lehmer's measure
5.92895