It is so unclear, what you're trying to say, that it may be worth starting again, to try to say it a different way!
The back-end 'instantaneous information system region' - what is that? Even with my background as a consultant in IT - I don't know what that means!
I am guessing that you mean 'the region throughout which we have instantaneous communication' which is still, a bit of a mouthful! Though, it sounds like a great system!
What is "the region achieved by this system" how can a region be 'achieved' by a system? It can't, in my opinion.
Are you perhaps referring to 'the area that the system manages to cover'? In which case it is really the coverage that is being 'achieved' - not 'the region'.
And if 'a fraction' is 0.5 - can we perhaps say '50 percent'? Would that be more intelligible? Or can we simply say 'half'? And as others have stated can we just assume that the audience knows what a fraction is?
By 'algorithm' do you mean the 'guiding principle' or 'underlying systems code' of the system, or something?
I really don't know quite what you are trying to say but here's a guess, how about:
Our rapid system algorithm enables us to reach 50 percent of the entire region, in just a nanosecond. (Sorry I added the time element).
Or: we can cover half of our global network in a only a moment, using our rapid system algorithm.
Although I am left wondering about... the other half! What is that 0.5, actually?
Or, does the 0.5 represent 'time'?
In which case, could it be something like 'we are able to communicate data throughout our entire global network in less than half a second, ensuring up-to-date information almost instantaneously for all our global users'.