Machin-like formulae
M000164
$$\pi=68\arctan\left(\frac{1}{23}\right)+32\arctan\left(\frac{1}{182}\right)+40\arctan\left(\frac{1}{5118}\right)+20\arctan\left(\frac{1}{6072}\right)$$
Compact formula
68[23] + 32[182] + 40[5118] + 20[6072]
Lehmer's measure
1.71074
References
ARNDT (1993)
(full reference coming soon)