So what you're saying is that GotEM removes 0.3s from the 1.5s GCD.
With 0 haste, I fully and wholeheartedly agree with you.
However, the text from GotEM reads:
Reduces the base global cooldown of your Rejuvenation, Lifebloom and Wild Growth spells by 20%.
Gift of the Earthmother - Spell - World of Warcraft
I agree with you completely that:
However, you have also stated:
Originally Posted by uliko
Most casting time reduction talents are before haste (like naturalist, mages imp. fire/frostbolt and starlight wrath), but for some reason GotEM is not
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(rest of quote removed as its the part I have issue with)
It appears I was confused by the logic you where employing. I understood the statement above to indicate that, GotEM is not taking 20% of 1.5s off your cast time, it is taking 20% off the adjusted GCD after haste has lowered the GCD.
The logic of taking off 0.3s because

only applies if the GotEM adjustment is done on the 1.5s base GCD first or ...
From what I can deduce, in order to fit the model you've presented, haste and GotEM interact as such (this was what I needed you to explain for me to get your model):
 + \frac{1.5}{h}))
where
x is the resulting casting time (or GCD) and
h remains our percentage haste.
If this is the model you're presenting to calculate the casting speed based on GotEM's interactions with haste, then I can accept that on the basis that I haven't done accurate empirical testing yet as i haven't been able to get a high enough haste value on my gear to validate or negate either model.
Model A (yours):
Model B (my assumed model from my reading):
I was not trying to be contentious or claim a higher knowledge, I simply did not interpret your statements across the various posts to indicate that the GotEM bonus was fixed. I beleived from all you had indicated, that the 20% reduction was applied to the
effective GCD after haste had been applied. Your model, if I have it correct now, does not matter whether haste is applied before or after, as they are applied independently to the 1.5s GCD.
Also my confusion may have come from the fact that in Beta, GotEM began as a fixed value, was nerfed to a smaller fixed value, then buffed to a percentage, then a further percentage. Therefore it didn't make sense that it would be a percentage of a fixed value as this is no different to a fixed value anyway.
EDIT: Corrected an error with the presentation of the latex equations