Machin-like formulae
M000386
$$\pi=48\arctan\left(\frac{1}{17}\right)+12\arctan\left(\frac{1}{57}\right)+20\arctan\left(\frac{1}{99}\right)-28\arctan\left(\frac{1}{307}\right)$$
Compact formula
48[17] + 12[57] + 20[99] - 28[307]
Lehmer's measure
2.28539
References
STØRMER (1896)
(full reference coming soon)