Sacrifice an artifact. If you do, search your library for an artifact card. If that card's converted mana cost is less than or equal to the sacrificed artifact's converted mana cost, put it onto the battlefield. If it's greater, you may pay, where X is the difference. If you do, put it onto the battlefield. If you don't, put it into its owner's graveyard. Then shuffle your library.
10/4/2004 Additional mana spent to cover the differences in mana costs is not part of the mana cost of this spell. It is spent during spell resolution.
10/4/2004 The one from the library enters the battlefield when the spell is resolved, and this does not count as the casting of an artifact.
10/4/2004 You can’t sacrifice more than one artifact to this spell.
10/4/2004 If the chosen artifact costs less than or the same as the sacrificed artifact, you simply put it onto the battlefield without paying any additional costs.
10/4/2004 Because the “search” requires you to find a card with certain characteristics, you don’t have to find the card if you don’t want to.
1/1/2011 The sacrifice of an artifact is an effect of the spell, not a cost, which means it happens as the spell resolves. If Transmute Artifact is countered, you do not have to sacrifice an artifact.