M000000022

$$\pi=332\arctan\left(\frac{1}{107}\right)+68\arctan\left(\frac{1}{4443}\right)+272\arctan\left(\frac{1}{11343}\right)-20\arctan\left(\frac{2}{226043}\right)-136\arctan\left(\frac{1}{595667}\right)-20\arctan\left(\frac{1}{109027476193}\right)+20\arctan\left(\frac{2}{3375905320682366575989}\right)$$
Compact formula332[107] + 68[4443] + 272[11343] - 20[226043/2] - 136[595667] - 20[109027476193] + 20[3375905320682366575989/2]
Lehmer's measure1.52229
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 23 September 2009.]