Machin-like formulae
M000377
$$\pi=16\arctan\left(\frac{1}{5}\right)-4\arctan\left(\frac{1}{408}\right)-4\arctan\left(\frac{1}{577}\right)$$
Compact formula
16[5] - 4[408] - 4[577]
Lehmer's measure
2.17588
References
STØRMER (1896)
(full reference coming soon)