Rage Extractor
({R/P} can be paid with either {R} or 2 life.) Whenever you cast a spell with {H} in its mana cost, this artifact deals damage equal to that spell's mana value to any target.
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Official rulings (6) · Scryfall
To calculate the mana value of a card with Phyrexian mana symbols in its cost, count each Phyrexian mana symbol as 1.
Phyrexian mana is not a new color. Players can't produce Phyrexian mana.
A card with Phyrexian mana symbols in its mana cost is each color that appears in that mana cost, regardless of how that cost may have been paid.
As you cast a spell or activate an activated ability with one or more Phyrexian mana symbols in its cost, you choose how to pay for each Phyrexian mana symbol at the same time you would choose modes or choose a value for X.
Rage Extractor's ability checks for any spell you cast with any Phyrexian mana symbol in its mana cost, regardless of that symbol's color or how the cost was paid.
If you're at 1 life or less, you can't pay 2 life.