Machin-like formulae
M000370
$$\pi=22\arctan\left(\frac{1}{7}\right)+8\arctan\left(\frac{1}{443}\right)+2\arctan\left(\frac{1}{1393}\right)+4\arctan\left(\frac{1}{11018}\right)$$
Compact formula
22[7] + 8[443] + 2[1393] + 4[11018]
Lehmer's measure
2.12663
References
ARNDT (1993)
(full reference coming soon)