Enchanter's Elixir not providing a 25% boost

My Enchanting is at level 100, and I have:

• Enchanter (5/5)
• Fire Enchanter
• Insightful Enchanter
• Corpus Enchanter
• Extra Effect

Here is a chart of the effect:

              (tested) (tested)   (theoretical) (theoretical)      (actual)
Glass Boots:  base     base+grand Elixir(*1.25) +Necromage(*1.31)  Actual
resist fire   +15%     +46%       +58%          +60%               +54%
regen stamina +10%     +31%       +39%          +40%               +36%

Game version is 3.10.0.

The end result is approximately a 17% boost to enchanting; even an Enchanter's Philter (+20%) should be better.

These results are correct, it's just that the potions are affecting your base skill rather than directly affecting enchantment strength. Enchanting's base skill has a particularly weak* effect on things (and it's non-linear, so only a fraction of that +x% manifests in enchantment strength); it's all about the perks.

The formula is

net magnitude = base magnitude * soul multiplier * skill multiplier *
                (1 + Enchanter perk) * (1 + specific perk modifier)

where skill multiplier is "approximately"

skill multiplier = 1 + (skill / 100) * (skill / 100 - 0.14) / 3.4

It is the above skill value that enchantments affect, not the net magnitude. Therefore, your skill multiplier should be

skill multiplier = 1 + 1.25 * (1.25 - 0.14) / 3.4
                 = 1.4081

Plugging that back into the net magnitude formula we get the following for Resist Fire (base magnitude = 15%) and Regen Stamina (base magnitude = 10%)

net magnitude = 15% * 1 * 1.4081 * 2 * 1.25
              = 52.9%
net magnitude = 10% * 1 * 1.4081 * 2 * 1.25
              = 35.2%

Like the UESP page said, the skill multiplier formula was approximate, so I'd say this is close enough. The point is that potions affect your base Enchanting skill, which has a non-linear and weak relationship with enchantment strength. In fact, Enchanting at 100 only grants +25% to enchantment strength over Enchanting at 15 (rather than 100 / 15 = 6.7x), so taking 2 perks and Enchanting 20 is better than no perks and Enchanting 100.

* It actually looks something like this. The above formula doesn't seem to be totally precise, but the gist should be evident:

Notes (as the comments show I should have been clearer here):
+46% = Necromage maximum (5 items of Fortify Alchemy)
+37% = Max with 5 items of Fortify Alchemy (Falmer Helmet + Circlet)
+32% = Max with 4 items of Fortify Alchemy
+25% = Enchanter's Elixir (best non-crafted item)