Machin-like formulae
M000290
$$\pi=176\arctan\left(\frac{1}{99}\right)+204\arctan\left(\frac{1}{239}\right)+176\arctan\left(\frac{1}{307}\right)-48\arctan\left(\frac{1}{682}\right)+96\arctan\left(\frac{1}{12943}\right)$$
Compact formula
176[99] + 204[239] + 176[307] - 48[682] + 96[12943]
Lehmer's measure
1.91968
References
HCL (27Oct04)(ΒΆΒΆ2.32533)
(full reference coming soon)