M000000336

$$\pi=20\arctan\left(\frac{1}{7}\right)+16\arctan\left(\frac{1}{53}\right)+8\arctan\left(\frac{1}{4443}\right)$$
Compact formula20[7] + 16[53] + 8[4443]
Lehmer's measure2.03739
References
Wrench Jr., J. W. The derivation of arctangent equalities (PhD thesis, Yale University), 1938.