Machin-like formulae
M000059
$$\pi=176\arctan\left(\frac{1}{57}\right)+28\arctan\left(\frac{1}{239}\right)-48\arctan\left(\frac{1}{682}\right)+96\arctan\left(\frac{1}{12943}\right)$$
Compact formula
176[57] + 28[239] - 48[682] + 96[12943]
Lehmer's measure
1.58604
References
STØRMER (1896)(¢¢2.30154, ¢¢2.37598, ¢¢2.38268)
(full reference coming soon)