Machin-like formulae
M000369
$$\pi=48\arctan\left(\frac{1}{18}\right)+32\arctan\left(\frac{1}{99}\right)+12\arctan\left(\frac{1}{239}\right)+32\arctan\left(\frac{1}{307}\right)$$
Compact formula
48[18] + 32[99] + 12[239] + 32[307]
Lehmer's measure
2.12025
References
LEHMER (1938)(*2.24178)
(full reference coming soon)