Machin-like formulae
M000371
$$\pi=16\arctan\left(\frac{1}{5}\right)-8\arctan\left(\frac{1}{408}\right)+4\arctan\left(\frac{1}{1393}\right)$$
Compact formula
16[5] - 8[408] + 4[1393]
Lehmer's measure
2.13179
References
STØRMER (1896)
(full reference coming soon)