M000000082

$$\pi=\frac{5380}{7}\arctan\left(\frac{1}{239}\right)\frac{-3056}{7}\arctan\left(\frac{1}{5827}\right)\frac{-128}{7}\arctan\left(\frac{2}{97059}\right)+\frac{848}{7}\arctan\left(\frac{2}{226043}\right)+\frac{512}{7}\arctan\left(\frac{2}{2513489}\right)+\frac{3056}{7}\arctan\left(\frac{1}{1561886607}\right)+\frac{128}{7}\arctan\left(\frac{1}{14130722757}\right)+\frac{848}{7}\arctan\left(\frac{1}{109027476193}\right)\frac{-848}{7}\arctan\left(\frac{2}{3375905320682366575989}\right)$$
Compact formula5380/7[239] - 3056/7[5827] - 128/7[97059/2] + 848/7[226043/2] + 512/7[2513489/2] + 3056/7[1561886607] + 128/7[14130722757] + 848/7[109027476193] - 848/7[3375905320682366575989/2]
Lehmer's measure1.60627
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 on 24 September 2009.]