Machin-like formulae
M000000311
$$\pi=\frac{176}{5}\arctan\left(\frac{1}{11}\right)\frac{-36}{5}\arctan\left(\frac{1}{239}\right)\frac{-64}{5}\arctan\left(\frac{1}{682}\right)\frac{-48}{5}\arctan\left(\frac{1}{12943}\right)$$
Compact formula
176/5[11] - 36/5[239] - 64/5[682] - 48/5[12943]
Lehmer's measure
1.97677
References
Arndt, Jörg. Remarks on arithmetical algorithms and the computation of π, 1993. [
www.jjj.de/joerg.html
]
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