Machin-like formulae
M000173
$$\pi=76\arctan\left(\frac{1}{24}\right)-16\arctan\left(\frac{1}{882}\right)-36\arctan\left(\frac{1}{6948}\right)+4\arctan\left(\frac{1}{43691}\right)-4\arctan\left(\frac{1}{308142}\right)$$
Compact formula
76[24] - 16[882] - 36[6948] + 4[43691] - 4[308142]
Lehmer's measure
1.72201
References
MATSUMOTO (2000)
(full reference coming soon)