M000240

$$\pi=68\arctan\left(\frac{1}{22}\right)+12\arctan\left(\frac{1}{172}\right)-8\arctan\left(\frac{1}{682}\right)-28\arctan\left(\frac{1}{5357}\right)$$
Compact formula68[22] + 12[172] - 8[682] - 28[5357]
Lehmer's measure1.81330
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81, 120–121, 1997. [DOI: 10.2307/3618793]

MRW (1980) (full reference coming soon)