Machin-like formulae
M000118
$$\pi=68\arctan\left(\frac{1}{23}\right)+32\arctan\left(\frac{1}{182}\right)+20\arctan\left(\frac{2}{3611}\right)+20\arctan\left(\frac{1}{623098}\right)$$
Compact formula
68[23] + 32[182] + 20[3611/2] + 20[623098]
Lehmer's measure
1.65646
References
ASN (16Sep09)(*1.71075 - v. Arndt, 4-term & below)
(full reference coming soon)