M000000009

$$\pi=5380\arctan\left(\frac{1}{1710}\right)+332\arctan\left(\frac{1}{5827}\right)-2324\arctan\left(\frac{2}{97059}\right)-1416\arctan\left(\frac{1}{103697}\right)-48\arctan\left(\frac{2}{2513489}\right)-332\arctan\left(\frac{1}{1561886607}\right)-1416\arctan\left(\frac{2}{18280007883}\right)+2324\arctan\left(\frac{1}{14130722757}\right)$$
Compact formula5380[1710] + 332[5827] - 2324[97059/2] - 1416[103697] - 48[2513489/2] - 332[1561886607] - 1416[18280007883/2] + 2324[14130722757]
Lehmer's measure1.45929
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 Amrik Singh Nimbran on 3 August 2010.]