M000000110

$$\pi=76\arctan\left(\frac{1}{24}\right)-16\arctan\left(\frac{1}{882}\right)-36\arctan\left(\frac{1}{6948}\right)+4\arctan\left(\frac{1}{50909}\right)-4\arctan\left(\frac{2}{14254596369}\right)$$
Compact formula76[24] - 16[882] - 36[6948] + 4[50909] - 4[14254596369/2]
Lehmer's measure1.63827
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 24 August 2009.]