Machin-like formulae
M000000399
$$\pi=40\arctan\left(\frac{1}{17}\right)+8\arctan\left(\frac{1}{38}\right)+28\arctan\left(\frac{1}{41}\right)-16\arctan\left(\frac{1}{157}\right)$$
Compact formula
40[17] + 8[38] + 28[41] - 16[157]
Lehmer's measure
2.52114
References
Arndt, Jörg. Remarks on arithmetical algorithms and the computation of π, 1993. [
www.jjj.de/joerg.html
]
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