M000000106

$$\pi=176\arctan\left(\frac{1}{57}\right)-20\arctan\left(\frac{1}{239}\right)+48\arctan\left(\frac{1}{348}\right)-48\arctan\left(\frac{1}{812852}\right)+48\arctan\left(\frac{1}{1453603235443}\right)$$
Compact formula176[57] - 20[239] + 48[348] - 48[812852] + 48[1453603235443]
Lehmer's measure1.63484
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81(490), 120–121, 1997. [DOI: 10.2307/3618793]

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 26 May 1995.]