Titillating us with thievery and swordplay, captive women with attitudes, scofflaws on the quest of a lifetime, Disney hit pay dirt with Johnny Depp in “Pirates of the Caribbean: Curse of the Black Pearl.”

So it was only a matter of time before they rattled their coffers and decided to do it again, this time without the water or the eyeliner.

Which isn’t to say that Jake Gyllenhaal in “Prince of Persia: The Sands of Time” is an unabashed rehash of Capt. Jack Sparrow and crew—just that it is an unabashed remake of the modern swashbuckling action thriller.

It’s more chaotic than “Pirates,” more kinetic and fleet of foot, but also less characterdriven and joyfully mischievous. It’s more or less a swashbuckler by the numbers—all the right elements are in all the right places.

But I guess the one thing about formulaic film, it’s formulaic for a reason: to draw in those of us willing to—one more time!—sit through the perils and prospects of yet another daring young man hoping to win the heart of a young lovely and simultaneously save the world or some portion thereof.

Flea-bitten lemming that I am, I sat down and sucked it in and pretty much enjoyed the whole sand-swept shebang.

I mean, hey, I’ve already couch-potatoed my brain through five or six late-night cable viewings of “Pirates of the Caribbean.” So why not switch venues, dry off a spell, turn up the heat?

I’ll admit I like the usually morose (or deeply troubled) Gyllenhaal playing the aloof, angst-free prince Dastan. As an orphan on the WMD-free streets of Nasaf, Dastan was once upon a time adopted by King Sharaman of Persia, who admired the urchin’s spunk.

Royalty agrees with Dastan, and pretty soon he’s riding beside his two princely brothers, ruling an empire. (And one assumes this occurs long after their encounter with Gerard Butler.)

But when the mighty Persian army is misled into attacking the sacred city of Alamut (because political intrigue is always afoot), Dastan and his royal bros suddenly find themselves in dire straits.

Fortunately, there’s a beautiful princess (Arterton) and a magic weapon (although no carpet) on which Dastan must rely to save himself and his family.

As plots go and action-adventures unfold, “Prince of Persia” seems to have all the right ingredients.

If I have a gripe, it’s that the dialogue sometimes suffers (as it’s completely lacking those darling “But why is the rum gone?” lines), while the action is at times a bit too frenetic. The obligatory final scene is so action packed that it almost wanders into the realm of the absurd (and this from a guy who sat through “Transformers” without twitching).

But one must end with a bang, and so director Mike Newell bangs away on cue.

If you’ve reached your fill of this by-the-numbers sort of passion play, I suspect you can easily avoid “Prince of Persia”. But if you own “The Mummy” or even “Aladdin,” and if the sands of the Sahara—not to mention the sands of time—turn you on, then I suspect you may enjoy the ride. (Or if you’ve been addicted to the video game, around since ’89, ditto.)

Besides, Jake even smiles in this one. Cinematic history marches on.