Machin-like formulae
M000000117
$$\pi=176\arctan\left(\frac{1}{109}\right)+380\arctan\left(\frac{1}{239}\right)-48\arctan\left(\frac{1}{682}\right)+96\arctan\left(\frac{1}{12943}\right)-176\arctan\left(\frac{1}{6826318}\right)$$
Compact formula
176[109] + 380[239] - 48[682] + 96[12943] - 176[6826318]
Lehmer's measure
1.65366
References
Arndt, Jörg. Remarks on arithmetical algorithms and the computation of π, 1993. [
www.jjj.de/joerg.html
]
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