In CSS we can use several different methods to define a color:
red
#FF0000
Typically, css optimization is all about minimizing the number of bytes going over the wire. The hexadecimal colors tend to be the shortest (in your example, #f00 could be used instead of #ff0000).
I realize this isn't exactly answering the question you've asked but I haven't seen any browser tests which attempt to measure how different color representations affect rendering speed.
I too was curious about this (it's a Friday afternoon). Here's a JSPerf for the various CSS colour methods:
http://jsperf.com/css-color-names-vs-hex-codes/18
Here are the results including color names, short hex, hex, rgb, rgba, hsl, and hsla. You can run the test yourself here.
If we assume a modern browser making full use of the GPU then the internal color representation will be RGB floats. Ignoring the color name - which is probably just a map to hex anyway - I think that hex and channels will be the fastest. HSB will undoubtedly be the slowest, as the conversion from HSB to RGB does require some work - about 50 lines of C code.
However, I think that for the purpose of CSS, this is a completely irrelevant question. Even for HSB to RGB the amount of work on one color will be totally trivial. By way of support for this, I have several programs - including those running on mobiles - which do color manipulation at a per-pixel level on largish images where I am doing RGB->HSB->(some manipulation)->RGB. Even performing this operation 100,000 times on an ipad only results in a delay of a couple of seconds - so on this relatively slow platform, I think your typical worst case conversion can be safely assumed to take less then 0.0001 seconds. And that's being pessimistic.
So just use whatever is easiest to code.
ADDED: to support the don't worry about this option. Internally a GPU will manipulate colors as an array of floats, so in C terms
float color[4];
or something similar. So the only conversion being done for the numeric options is a simple divide by 255.
On the other hand conversion of HSB to RGB takes considerably longer - I'd estimate, from having written code to do it, about 10 to 20 operations. So in crude terms HSB is considerably slower, BUT 20 (or even 20,000) operations on a modern GPU isn't worth worrying about - it's imperceptible.
Edit: Each process has to get down to a binary value for r, g, and b. Hex and rgb bytes are already set up for that, so I guess they might actually be roughly the same speed. The rest have to go through a process to reach a hex/rgb value
#FF0000 = memory values of: 1111 1111 0000 0000 0000 0000
rgb(255,0,0) = memory values of: 1111 1111 0000 0000 0000 0000
Both cases are most likely stored in 3 int variables. So the real question is, which is faster to process into binary values for these integers? HEX or DEC? I think HEX, but I can't back that up. Anyhow, the code just takes the binary values of these variables.
I used the same tool from jsperf.com that the others did, and created my own test for different color formats. I then ran the test on IE11, Edge17, FF64 and Chrome71 and gathered all results in a compact excel spreadsheet.
Top three are green, bottom three are red, best and worst are bold.
I don't know why Chrome is so prone to named colors format, but it made me repeat the test many times with the same and different parameters. Results remain constant.
You cannot get conclusive results of any one format being the absolute best, but my conclusion is as follows.
I will keep using hex over named, lowercase over uppercase and start using short over long hex when possible.
Feel free to update results if they change with new versions of browsers.