M000000127

$$\pi=\frac{166}{7}\arctan\left(\frac{2}{15}\right)\frac{-22}{7}\arctan\left(\frac{1}{1710}\right)+\frac{48}{7}\arctan\left(\frac{1}{105218}\right)\frac{-4}{7}\arctan\left(\frac{2}{2513489}\right)+\frac{48}{7}\arctan\left(\frac{1}{7167807}\right)$$
Compact formula166/7[15/2] - 22/7[1710] + 48/7[105218] - 4/7[2513489/2] + 48/7[7167807]
Lehmer's measure1.96103
References
Wetherfield, Michael Roby and Chien-Lih, Hwang. Computing pi: Lists of Machin-type (inverse cotangent) identities for pi/4, [Online; accessed 04-February-2024], 2013. [web.archive.org/web/20240204042153/http] [Found by MRW.]