M000213

$$\pi=48\arctan\left(\frac{1}{49}\right)+128\arctan\left(\frac{1}{57}\right)-20\arctan\left(\frac{1}{239}\right)+48\arctan\left(\frac{1}{110443}\right)$$
Compact formula48[49] + 128[57] - 20[239] + 48[110443]
Lehmer's measure1.77990
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81, 120–121, 1997. [DOI: 10.2307/3618793]

TAKANO (1982)(ΒΆΒΆ2.37598) (full reference coming soon)