Machin-like formulae
M000401
$$\pi=16\arctan\left(\frac{1}{5}\right)-4\arctan\left(\frac{1}{41}\right)+8\arctan\left(\frac{1}{99}\right)$$
Compact formula
16[5] - 4[41] + 8[99]
Lehmer's measure
2.55181
References
STØRMER (1896)
(full reference coming soon)