Machin-like formulae
M000000409
$$\pi=10\arctan\left(\frac{1}{3}\right)-4\arctan\left(\frac{1}{53}\right)-2\arctan\left(\frac{1}{4443}\right)$$
Compact formula
10[3] - 4[53] - 2[4443]
Lehmer's measure
2.95000
References
Wrench Jr., J. W. The derivation of arctangent equalities (PhD thesis, Yale University), 1938.
Download references as BibTeΧ