The first "better" approximation, while having a better "max distance" (0.019608% vs 0.027253%), has a _worse_ span between min and max (0.039216% vs 0.027253%)

The first "better" approximation, while having a better "max distance" (0.019608% vs 0.027253%), has a _worse_ span between min and max (0.039216% vs 0.027253%), which probably matters for some applications.