Machin-like formulae
M000395
$$\pi=20\arctan\left(\frac{1}{8}\right)+8\arctan\left(\frac{1}{18}\right)+12\arctan\left(\frac{1}{57}\right)$$
Compact formula
20[8] + 8[18] + 12[57]
Lehmer's measure
2.47346
References
SCHELLBACH (1832)
(full reference coming soon)