Machin-like formulae
M000334
$$\pi=80\arctan\left(\frac{1}{57}\right)+96\arctan\left(\frac{1}{68}\right)+48\arctan\left(\frac{1}{117}\right)-20\arctan\left(\frac{1}{239}\right)$$
Compact formula
80[57] + 96[68] + 48[117] - 20[239]
Lehmer's measure
2.01918
References
ARNDT (1993)
(full reference coming soon)