What is the cast time of a metamagic’d swift action spell for a spontaneous caster? [duplicate]

I have a sorcerer that wishes to Cold Ice Strike in a game. I don’t mind this, but the issue is they want to apply Empower spell via a metamagic rod to it. Normally with a standard action spell this becomes a full-round action, but Cold Ice Strike is a swift action spell, and I can’t find anything for that.

If the sorcerer casts Empowered Cold Ice Strike, what’s the casting time of it?