M000000154

$$\pi=176\arctan\left(\frac{1}{57}\right)+28\arctan\left(\frac{1}{239}\right)-96\arctan\left(\frac{1}{1435}\right)+48\arctan\left(\frac{1}{12238}\right)+96\arctan\left(\frac{2}{15130261}\right)$$
Compact formula176[57] + 28[239] - 96[1435] + 48[12238] + 96[15130261/2]
Lehmer's measure1.69674
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 2 August 2009.]