Machin-like formulae
M000163
$$\pi=64\arctan\left(\frac{1}{21}\right)+28\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{769}\right)-16\arctan\left(\frac{2}{433287}\right)$$
Compact formula
64[21] + 28[239] - 16[769] - 16[433287/2]
Lehmer's measure
1.71067
References
MRW (2Aug09)(*1.82119 - 4-term identity)
(full reference coming soon)