Machin-like formulae
M000000259
$$\pi=96\arctan\left(\frac{1}{29}\right)-16\arctan\left(\frac{1}{57}\right)+28\arctan\left(\frac{1}{239}\right)-48\arctan\left(\frac{1}{12238}\right)$$
Compact formula
96[29] - 16[57] + 28[239] - 48[12238]
Lehmer's measure
1.91841
References
Arndt, Jörg. Remarks on arithmetical algorithms and the computation of π, 1993. [
www.jjj.de/joerg.html
]
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