M000185

$$\pi=122\arctan\left(\frac{1}{38}\right)-34\arctan\left(\frac{1}{463}\right)+12\arctan\left(\frac{1}{2682}\right)+6\arctan\left(\frac{1}{8827}\right)+34\arctan\left(\frac{1}{390112}\right)$$
Compact formula122[38] - 34[463] + 12[2682] + 6[8827] + 34[390112]
Lehmer's measure1.73211
References
MATSUMOTO (2000) (full reference coming soon)