M000000023

$$\pi=508\arctan\left(\frac{1}{192}\right)+516\arctan\left(\frac{1}{1068}\right)+244\arctan\left(\frac{1}{11379}\right)-400\arctan\left(\frac{2}{81487}\right)+176\arctan\left(\frac{1}{173932}\right)-244\arctan\left(\frac{1}{3819719818}\right)$$
Compact formula508[192] + 516[1068] + 244[11379] - 400[81487/2] + 176[173932] - 244[3819719818]
Lehmer's measure1.52679
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 2007-8.]