M000000017

$$\pi=508\arctan\left(\frac{1}{239}\right)+1024\arctan\left(\frac{1}{1068}\right)+752\arctan\left(\frac{1}{11379}\right)-400\arctan\left(\frac{2}{81487}\right)+176\arctan\left(\frac{1}{173932}\right)-752\arctan\left(\frac{1}{3819719818}\right)$$
Compact formula508[239] + 1024[1068] + 752[11379] - 400[81487/2] + 176[173932] - 752[3819719818]
Lehmer's measure1.50928
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.]