Machin-like formulae
M000376
$$\pi=40\arctan\left(\frac{1}{22}\right)+28\arctan\left(\frac{1}{41}\right)+48\arctan\left(\frac{1}{75}\right)+8\arctan\left(\frac{1}{4193}\right)$$
Compact formula
40[22] + 28[41] + 48[75] + 8[4193]
Lehmer's measure
2.17433
References
STØRMER (1896)
(full reference coming soon)