M000000107

$$\pi=3056\arctan\left(\frac{1}{1068}\right)+508\arctan\left(\frac{1}{3323}\right)+1768\arctan\left(\frac{1}{20457}\right)+860\arctan\left(\frac{2}{81487}\right)+752\arctan\left(\frac{1}{83247}\right)+684\arctan\left(\frac{1}{173932}\right)+2784\arctan\left(\frac{1}{409557}\right)$$
Compact formula3056[1068] + 508[3323] + 1768[20457] + 860[81487/2] + 752[83247] + 684[173932] + 2784[409557]
Lehmer's measure1.63528
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 15 August 2006.]