M000000086

$$\pi=176\arctan\left(\frac{1}{57}\right)-20\arctan\left(\frac{1}{239}\right)+96\arctan\left(\frac{2}{1511}\right)+48\arctan\left(\frac{1}{4443}\right)$$
Compact formula176[57] - 20[239] + 96[1511/2] + 48[4443]
Lehmer's measure1.61155
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 HCL on 21 January 1995.]