M000000351

$$\pi=28\arctan\left(\frac{1}{11}\right)+12\arctan\left(\frac{2}{39}\right)-8\arctan\left(\frac{1}{682}\right)$$
Compact formula28[11] + 12[39/2] - 8[682]
Lehmer's measure2.08831
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 16 August 2006.]