I did some math to find out which AP items were the best if you wanted as much damage as possible. I only did the math for Void staff, Horizon Focus, Shadowflame and Rabadon (considering you already have Luden and sorcerer boots).
In the end Horizon Focus is always higher if you can proc its effect. So I’m wondering why every Lux player for example aren’t buying it second item.
Remember that HF triggers on slow/root. So champions like Lux or even champ buying Rylai will always triggers hypershot.