M000235

$$\pi=48\arctan\left(\frac{1}{15}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{433}\right)+16\arctan\left(\frac{1}{1875333}\right)$$
Compact formula48[15] - 4[239] - 16[433] + 16[1875333]
Lehmer's measure1.80942
References
Chien-Lih, Hwang. More Machin-type identities, The Mathematical Gazette 81, 120–121, 1997. [DOI: 10.2307/3618793]

CASTELLANOS (1988) (*1.94191) (full reference coming soon)