Machin-like formulae
M000314
$$\pi=48\arctan\left(\frac{1}{26}\right)+80\arctan\left(\frac{1}{57}\right)-20\arctan\left(\frac{1}{239}\right)-48\arctan\left(\frac{1}{2057}\right)$$
Compact formula
48[26] + 80[57] - 20[239] - 48[2057]
Lehmer's measure
1.99851
References
HCL (26Jan95)(*2.05885)
(full reference coming soon)