I'm told that General Number Field Sieve works with computational complexity $e^{\sqrt[3]{\frac{64}{9}+o(1)}\;(\ln n)^{\frac{1}{3}}\;(\ln\ln n)^{\frac{2}{3}}}$. However, without some computation work it should run with computational complexity $e^{\sqrt[3]{3+o(1)}\;(\ln n)^{\frac{1}{3}}\;(\ln\ln n)^{\frac{2}{3}}}$.
This does not seem to be as a big difference but according to the following table it is:
How can be the difference so huge if only a constant changes?