M000000019

$$\pi=152\arctan\left(\frac{1}{47}\right)-56\arctan\left(\frac{1}{610}\right)-24\arctan\left(\frac{2}{296489}\right)+56\arctan\left(\frac{1}{15628852}\right)-28\arctan\left(\frac{1}{54608393}\right)-24\arctan\left(\frac{1}{18677233307}\right)$$
Compact formula152[47] - 56[610] - 24[296489/2] + 56[15628852] - 28[54608393] - 24[18677233307]
Lehmer's measure1.51607
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 Amrik Singh Nimbran on 11 September 2009.]