Machin-like formulae
M000000334
$$\pi=80\arctan\left(\frac{1}{57}\right)+96\arctan\left(\frac{1}{68}\right)+48\arctan\left(\frac{1}{117}\right)-20\arctan\left(\frac{1}{239}\right)$$
Compact formula
80[57] + 96[68] + 48[117] - 20[239]
Lehmer's measure
2.01918
References
Arndt, Jörg. Remarks on arithmetical algorithms and the computation of π, 1993. [
www.jjj.de/joerg.html
]
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