You can simplify the 2x sqrts as sqrt(a*b), overall less operations so perhaps more accurate. It would also let you get rid of the funky lane swivels.
As this would only use 1 lane, perhaps if you have multiple of these to normalize, you could vectorize it.
my thoughts exactly - crazy to know all these arcane SIMD opcodes but not know basic maths!!
I did a version of this with my form for requesting an account on my fediverse server. The problem I was having is that there exist these very unsophisticated bots that crawl the web and submit their very unsophisticated spam into every form they see that looks like it might publish it somewhere.
First I added a simple captcha with distorted characters. This did stop many of the bots, but not all of them. Then, after reading the server log, I noticed that they only make three requests in a rapid succession: the page that contains the form, the captcha image, and then the POST request with the form data. They don't load neither the CSS nor the JS.
So I added several more fields to the form and hid them with CSS. Submitting anything in these fields will fail the request and ban your session. I also modified the captcha, I made the image itself a CSS background, and made the src point to a transparent image instead.
And just like that, spam has completely stopped, while real users noticed nothing.