M000000029

$$\pi=2324\arctan\left(\frac{1}{580}\right)-1592\arctan\left(\frac{1}{1710}\right)+332\arctan\left(\frac{1}{5827}\right)+908\arctan\left(\frac{2}{226043}\right)+860\arctan\left(\frac{2}{2513489}\right)-332\arctan\left(\frac{1}{1561886607}\right)+908\arctan\left(\frac{1}{109027476193}\right)-908\arctan\left(\frac{2}{3375905320682366575989}\right)$$
Compact formula2324[580] - 1592[1710] + 332[5827] + 908[226043/2] + 860[2513489/2] - 332[1561886607] + 908[109027476193] - 908[3375905320682366575989/2]
Lehmer's measure1.54508
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 in September 2009.]