Machin-like formulae
M000392
$$\pi=20\arctan\left(\frac{1}{6}\right)-4\arctan\left(\frac{1}{43}\right)-8\arctan\left(\frac{1}{117}\right)$$
Compact formula
20[6] - 4[43] - 8[117]
Lehmer's measure
2.38080
References
STØRMER (1896)
(full reference coming soon)