M000000030

$$\pi=508\arctan\left(\frac{1}{239}\right)+512\arctan\left(\frac{1}{515}\right)+240\arctan\left(\frac{1}{11379}\right)+112\arctan\left(\frac{2}{81487}\right)-336\arctan\left(\frac{1}{173932}\right)-240\arctan\left(\frac{1}{3819719818}\right)$$
Compact formula508[239] + 512[515] + 240[11379] + 112[81487/2] - 336[173932] - 240[3819719818]
Lehmer's measure1.54785
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.]