Machin-like formulae
M000381
$$\pi=48\arctan\left(\frac{1}{18}\right)+12\arctan\left(\frac{1}{70}\right)+20\arctan\left(\frac{1}{99}\right)+32\arctan\left(\frac{1}{307}\right)$$
Compact formula
48[18] + 12[70] + 20[99] + 32[307]
Lehmer's measure
2.24177
References
BENNETT (1925)
(full reference coming soon)