Thumbing through the code made me wonder what the zsh(my normal shell) implementation feels like, and I think it is fair to say your code is easier to wrap your head around than the documentation for floats in zsh.

FWIW - and given that you've only shown Windows timings - on my Linux box hyperfine shows:

    Summary
      './faster_e_demo.sh 15' ran
        1.78 ± 0.16 times faster than './slower_e_demo.sh 15'

¹ https://en.m.wiktionary.org/wiki/contranym - choose one