Machin-like formulae
M000000335
$$\pi=48\arctan\left(\frac{1}{38}\right)+80\arctan\left(\frac{1}{57}\right)+28\arctan\left(\frac{1}{239}\right)+96\arctan\left(\frac{1}{268}\right)$$
Compact formula
48[38] + 80[57] + 28[239] + 96[268]
Lehmer's measure
2.03480
References
Gauss, Carl Friedrich. Werke volume 2, 1863.
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