How does the reduced mana reservation formula works?

So Im debating if i should buy an alpha howl or not but Im not sure how the formula works,currently i have 20% reduced mana reservation from my nodes and lvl 20 reduced mana gem, i can run 2 auras each costing 35% of my mana and have still 250 mana spare from my 836 pool.

Now if i buy alpha howl, will I be able to run a third aura?

The total amount of % auras * reduced mana gem * reduced mana reserve passives

For example

Purity (40) + Hatred (60) + Determination (60) = 160%
Level 20 reduced mana = 71%
Sovereignty nodes = 16% reduced reserved = 84% multiplier

160 * .71 * .84 = 95.4% mana reserved

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haplessG00N wrote:

The total amount of % auras * reduced mana gem * reduced mana reserve passives

For example

Purity (40) + Hatred (60) + Determination (60) = 160%
Level 20 reduced mana = 71%
Sovereignty nodes = 16% reduced reserved = 84% multiplier

160 * .71 * .84 = 95.4% mana reserved

I'm pretty sure the costs are calculated for every aura seperately, rounded and then added.
It wouldn't make a difference for the above example, but if you look at the effect of a reduced mana gem alone the difference would be:
(40+60+60) * .71 = 113,6 = 114
(40 * .71) + (60 * .71) + (60 * .71) = 28.4 + 42.6 + 42.6 = 29 + 43 + 43 = 115