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I'm putting images related to my recent work examining weapon damage types here. This first graph shows the differences between measured damage values (that is, the bonuses and penalties due to damage type vs. monster type) of various 5* weapons at depth 28, and compares those to estimates based on the following formulas:
Penalty = (Base - 20) * 0.85
Bonus = 0.94 * 100 - (MIN(Base, 160) - 125)^2/100

This graph contains both values from pure special damage weapons and split normal/special weapons, including both basic and charge attacks. In the case of split damage weapons, the "base special damage" is assumed to be 1/2 the weapon's base damage. The measured bonus/penalty are the full values, and the estimated bonus/penalty is calculated using the base special damage. (This is equivalent to assuming that the normal and special contributions to the base damage are equal, and bonuses/penalties are calculated independently).

The next graph contains similar measured values from 5* weapons at depth 27. Note that the shape of the curves is the same, although the actual values are obviously different.

And this third graph shows estimated damages for 5* weapons of various damage types and base damage values against different targets, based on the formulas listed above.

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