Machin-like formulae
M000253
$$\pi=64\arctan\left(\frac{1}{20}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{515}\right)-32\arctan\left(\frac{1}{4030}\right)$$
Compact formula
64[20] - 4[239] - 16[515] - 32[4030]
Lehmer's measure
1.83519
References
ARNDT (1993)
(full reference coming soon)