M000000045

$$\pi=\frac{5380}{7}\arctan\left(\frac{1}{239}\right)\frac{-3056}{7}\arctan\left(\frac{1}{5827}\right)\frac{-128}{7}\arctan\left(\frac{2}{97059}\right)+\frac{848}{7}\arctan\left(\frac{1}{103697}\right)-48\arctan\left(\frac{2}{2513489}\right)+\frac{3056}{7}\arctan\left(\frac{1}{1561886607}\right)+\frac{848}{7}\arctan\left(\frac{2}{18280007883}\right)+\frac{128}{7}\arctan\left(\frac{1}{14130722757}\right)$$
Compact formula5380/7[239] - 3056/7[5827] - 128/7[97059/2] + 848/7[103697] - 48[2513489/2] + 3056/7[1561886607] + 848/7[18280007883/2] + 128/7[14130722757]
Lehmer's measure1.57043
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 9 August 2010.]