Archmage vs. Expanded Mind

Howdy, I was doing some theory crafting to optimize my Xerath's power potential.

I almost always get Seraph's Embrace so I was curious whether the 5% ability power increase from Archmage was better than getting Expanded Mind + Seraph's.

Now from my items I get 559 base AP.

I also get 2000ish mana at level 18 with Seraph's

Archmage gives me 5% = 27.95 extra AP

Expanded mind + Seraph's = 2100 mana

With Seraph's = 63 extra AP

Now obviously having both is nice but I was considering trying to go for Intelligence to get a total of 10% base cooldown at the start.

I made this thread to double check my math with you fine folks and also ask whether or not Archmage us really that good because it doesn't seem to be.

But I'm not mathematician.

One of the items included is Rabadon's. Do we know if that stacks with Archmage or are they separate? I calculated it separately.