Machin-like formulae
M000000253
$$\pi=64\arctan\left(\frac{1}{20}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{515}\right)-32\arctan\left(\frac{1}{4030}\right)$$
Compact formula
64[20] - 4[239] - 16[515] - 32[4030]
Lehmer's measure
1.83519
References
Arndt, Jörg. Remarks on arithmetical algorithms and the computation of π, 1993. [
www.jjj.de/joerg.html
]
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