Machin-like formulae
M000000270
$$\pi=64\arctan\left(\frac{1}{21}\right)+12\arctan\left(\frac{1}{239}\right)+16\arctan\left(\frac{1}{421}\right)+16\arctan\left(\frac{1}{1985}\right)$$
Compact formula
64[21] + 12[239] + 16[421] + 16[1985]
Lehmer's measure
1.86104
References
Arndt, Jörg. Remarks on arithmetical algorithms and the computation of π, 1993. [
www.jjj.de/joerg.html
]
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