thanks a lot for your comments and suggestions.

I did not expect such micro-optimizations to bring such a significant performance improvement, that's interesting. Especially replacing the division by 2 by a bit shift is the type of thing that I had stopped doing decades ago, when I figured that the C compiler I was using at the time was doing this type of optimization at least as well and often better than I was able to do. Good to be reminded that the optimizations you suggested can also be quite useful. Thank you.

Following this very interesting thread and your new thread on MCE::Flow + Caching via File::Map, I made a new blog post on the Collatz sequence, trying to summarize some of the findings: http://blogs.perl.org/users/laurent_r/2020/04/revisiting-the-collatz-sequence-pwc-54.html. I did not try to explain your demonstration using File::Map for caching with parallel processing (your other thread) because I'm not sure to fully understand everything and was afraid of mis-representing your work. People can follow the link and read your own words.

Thank you very much for your challenging ideas.