M000000119

$$\pi=122\arctan\left(\frac{1}{38}\right)-34\arctan\left(\frac{1}{463}\right)+6\arctan\left(\frac{1}{1164}\right)+34\arctan\left(\frac{1}{390112}\right)-6\arctan\left(\frac{1}{9485443}\right)$$
Compact formula122[38] - 34[463] + 6[1164] + 34[390112] - 6[9485443]
Lehmer's measure1.65649
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 Koepp in 1994.]