M000000041

$$\pi=2324\arctan\left(\frac{1}{1023}\right)+732\arctan\left(\frac{1}{1710}\right)+2656\arctan\left(\frac{1}{5832}\right)-1416\arctan\left(\frac{1}{110443}\right)-1464\arctan\left(\frac{2}{2513489}\right)+1416\arctan\left(\frac{1}{4841182}\right)+332\arctan\left(\frac{1}{6826318}\right)$$
Compact formula2324[1023] + 732[1710] + 2656[5832] - 1416[110443] - 1464[2513489/2] + 1416[4841182] + 332[6826318]
Lehmer's measure1.56525
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.]