Ok, instead of making another post or something I'll just edit this post instead. I haven't tested EVERYTHING or anything crazy, but as far as I can tell this seems to be the new formula. I might be inaccurate however with some certain modifiers or conditional flat damage.
(((Base damage + Flat damage) * X% damage with attacks + (Base damage* Base multiplier - Base damage)) +Simple Damage)* X% Damage type buff * X% Vulnerability debuff + Conditional Flat damage * X% More damage debuff
So here are the things that have changed since the first post I made.
X% damage with attacks
This now includes anything that increases the damage of your skills by a %. Including what used to be "Conditional multipliers". This also includes Ferocity Juice for some weird reason. Some things (Like the aforementioned Ferocity Juice) in this category will cause your thumbnails to inaccurately predict damage, so keep that in mind.
Simple Damage
This is from the new version of the "Dangerous Enchantment" blacksmithing recipe. Unlike advertised, it is in fact affected by some multipliers.
X% Damage buff
Any buffs to damage types now seem to stack as one single multiplier, rather than as multiple multipliers. I am not sure if this applies to non-damage type bonuses yet (Ex. Pain Bubble's ranged attack buff).
So as an example, here is the old hammer formula I used earlier before the last two patches(With Ferocity Juice included)
((433 + 578) * 1.98 + (433* 1.85 - 433)) *1.15*1.07*1.10 *1.18 *1.18 *1.63 *1.63 *1.18 *1.25 = 17503
And here is the new hammer formula as of this patch:
((433 + 578) * 3.70+ (433* 1.85 - 433)) *1.22 *1.18 *1.25 =7393
And here is an example of the new hammer formula with a +300 weapon as an example:
(((433 + 578) * 3.70+ (433* 1.85 - 433))+300) *1.22 *1.18 *1.25 =7933
Pretty rough, I lost 10k damage from my main nuke! That's what happens when I use my own build as an example, maybe I should have used Werewolf instead.