Machin-like formulae
M000000255
$$\pi=96\arctan\left(\frac{1}{53}\right)+80\arctan\left(\frac{1}{57}\right)-20\arctan\left(\frac{1}{239}\right)+48\arctan\left(\frac{1}{4443}\right)$$
Compact formula
96[53] + 80[57] - 20[239] + 48[4443]
Lehmer's measure
1.84406
References
Arndt, Jörg. Remarks on arithmetical algorithms and the computation of π, 1993. [
www.jjj.de/joerg.html
]
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