M000117

$$\pi=176\arctan\left(\frac{1}{109}\right)+380\arctan\left(\frac{1}{239}\right)-48\arctan\left(\frac{1}{682}\right)+96\arctan\left(\frac{1}{12943}\right)-176\arctan\left(\frac{1}{6826318}\right)$$
Compact formula176[109] + 380[239] - 48[682] + 96[12943] - 176[6826318]
Lehmer's measure1.65366
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81, 120–121, 1997. [DOI: 10.2307/3618793]

ARNDT (1993) (full reference coming soon)