Please clarify Battlemage

"Battlemage gives the player character Gain Added Spell Damage equal to the Damage of Your Main Hand Weapon"

What if my weapon has the following modifier:
(Devastating)
"(51–59)% increased Elemental Damage with Attack Skills"

Is this 51-59% damage increase
a) is of my weapon
b) is of something else, for example "is of the skill"

(And there may be other modifiers. "Adds (89–121) to (180–210) Fire Damage", "+2 to Level of Socketed Melee Gems", "(35–38)% increased Critical Strike Chance", "+(456–624) to Accuracy Rating", "(16–20)% increased Global Accuracy Rating. 15% increased Light Radius", "Hits can't be Evaded" etc.)
(One may argue that more critical chance, more accuracy means: more damage [with this weapon].)

Just the flat damage you see on top

If your main weapon does 40-60 fire damage, lets say it adds 50 fire damage for simplicity.

Now if your spell has 130% added damage effectiveness, battlemage will add (1.3*50) or 65 extra fire damage. If your spell has 50% damage effectiveness, battlemage will add (0.5 * 50) or 25 extra fire damage.

Then this gets boosted by spell damage, fire damage, any other applicable categories (aoe, crits, etc.).

Increased melee damage or attack bonuses do not apply, either on the tree or the weapon itself.

If the weapon itself has %increased physical damage, that increases the flat damage of the weapon so does help. Or if it has "Adds 200-300 cold damage" or similar, that also counts.