Quick question:

This is a rather complex question you're asking. I'll try to break it down in pieces.

First: AM has recharge of 422s and a duration of 120s. So it requires 422/120 = 3.52 total recharge to be perma. That part is easy (technically, as previously mentioned, you need to factor in activation, but I won't because this is going to get pretty complicated as it is).

If you slot it to the ED soft cap (+0.95), then the combination of slotting plus AM's buff (+0.2) gives a total recharge of 1 + 0.95 + 0.2 = 2.15. You'd need 3.52 - 2.15 = 1.37 more recharge, or +137% recharge.

You say you have Hasten which helps: it offers +0.7 (+70%) recharge. In that case you'd only need +67% recharge more.

But Hasten isn't perma either. In this case, you have a problem. Specifically an algebra problem. I will refer you to my Guide to Recharge, specifically the section on "Multiple Recharge Boosting Powers."

But in summary, working backward we assume that AM goes perma before Hasten, and thus assume that you are always under a +0.2 recharge buff but might not be under the Hasten buff all the time. We then have to solve this equation pair:

1.37 = h + b (average hasten buff plus outside buff equals the buff necessary to make AM perma)
h = 0.7 * 120 * (1.95 + 0.2 + h + b) / 450 (average hasten buff equals hasten's buff times its uptime percentage)

h = 0.7 * 120 * (1.95 + 0.2 + 1.37) / 450
h = 0.657
b = 0.713

In other words, slot both AM and Hasten with +95% recharge, and somehow get +71.3% recharge in invention bonuses (or some other source), and AM will be basically perma. Hasten will, incidentally, be close to perma:

120 * (1.95 + 0.7 + 0.2 + 0.713) = 427.56
450 - 427.56 = 22.44
22.44 / (1.95 + 0.2 + 0.713) = 7.8

Hasten will be up 120s and down about 8s, plus activation time. Just as a double check, hasten's average buff will be about 0.657, so AM's recharge will be:

120 * (1.95 + 0.657 + 0.2 + 0.713) = 422.4
422 < 422.4

So AM is perma under these circumstances. Although technically speaking, this is only on average. The *worst* case Hasten cycling would be the case where Hasten aligns such that all of its downtime occurs in a single AM cycle. In that case, Hasten's average benefit during that one cycle would be 0.7 * (112/120) = 0.653. That is so close to the average (0.657) that its basically a roundoff error. To be safe, and to include activation times, I would say that +75% recharge would make AM perma (and Hasten just about perma) when you are cycling both continuously.

I wish there was an easier way to compute this, but there it is. I hope I got the math right: I'm a bit rushed at the moment, which is why I performed the doublecheck calculation. If I made a boo-boo, the doublecheck says it wasn't a big one.

If I read this right, I need 71.3% recharge without anything on(Hasten or AM in this case) to get AM perma, right?

To be honest, I'm not striving to make it perma, I just wanted to see how close I should try to get. Right now I only have 33.75%, so I have a ways to go I guess.

No what Arcanaville is saying is you need those two powers cycling(make sure thay get clicked as soon as they are up) with 95% recharge slotting in them(ED capped) plus 75% recharge bonus globally to make AM perma.

With that level of recharge assuming you cycle Hasten as fast as it recharges AM will be up "most of the time."

AM gives +30% recharge, not 20%...

Oops, you're right (actually, my guide got it right: I should have probably read that). Ah well, I did say I was rushed. Fortunately, it only changes the computed required recharge by about two percentage points (from 71.3% to 69.4%) and given the wiggle room required by cast times I'd still recommend aiming for about 75% recharge bonus just to be sure.