Machin-like formulae
M000310
$$\pi=64\arctan\left(\frac{1}{20}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{515}\right)-64\arctan\left(\frac{1}{8040}\right)+32\arctan\left(\frac{1}{1620050}\right)$$
Compact formula
64[20] - 4[239] - 16[515] - 64[8040] + 32[1620050]
Lehmer's measure
1.97493
References
ESCOTT (1903)
(full reference coming soon)