M000000166

$$\pi=\frac{5380}{7}\arctan\left(\frac{1}{239}\right)\frac{-3056}{7}\arctan\left(\frac{1}{5832}\right)\frac{-256}{7}\arctan\left(\frac{1}{103862}\right)+\frac{848}{7}\arctan\left(\frac{1}{110443}\right)\frac{-128}{7}\arctan\left(\frac{1}{740943}\right)+\frac{512}{7}\arctan\left(\frac{2}{2513489}\right)\frac{-848}{7}\arctan\left(\frac{1}{4841182}\right)\frac{-3056}{7}\arctan\left(\frac{1}{6826318}\right)$$
Compact formula5380/7[239] - 3056/7[5832] - 256/7[103862] + 848/7[110443] - 128/7[740943] + 512/7[2513489/2] - 848/7[4841182] - 3056/7[6826318]
Lehmer's measure1.71386
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.]