I don't know who needs to hear this but...
Akali can get 847 attack range with Hexoptics C44 and Rapid Firecannon.
Akali's passive doubles her attack range using a (buggy) static bonus range increase.
The resulting range and all intermediate range summands are rounded down (floor rounding).
Akali's base attack range: base = 125
Rapid Firecannon range multiplier: rfc = 1.35
Hexoptics C44 additional range: hex = +100
Passive:
base + base = 250
Passive -> RFC:
(base + base) * rfc = 337
RFC -> Passive (Spagetti):
base * rfc + base * rfc * rfc = 395
Hexoptics -> RFC -> Passive (Linguini):
(base + hex) * rfc + (base + hex) * rfc + ((base + hex) * rfc - base - base) * rfc = 678
Hexoptics -> RFC -> Passive (Fettuccine):
((base + hex) + (base + hex) * rfc + hex) * rfc = 847
Linguini happens almost always, Fettuccine is more rare and I think there's also a shiny Tagliatelle (ultra rare) which results in over 900 attack range, but I couldn't reproduce it.
Do with this information what you will.