M000255

$$\pi=96\arctan\left(\frac{1}{53}\right)+80\arctan\left(\frac{1}{57}\right)-20\arctan\left(\frac{1}{239}\right)+48\arctan\left(\frac{1}{4443}\right)$$
Compact formula96[53] + 80[57] - 20[239] + 48[4443]
Lehmer's measure1.84406
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)