“Into the Woods,” the adult fairy-tale by theater giants Stephen Sondheim and James Lapine, is living up to its name, playing amid the forestry at the Delacorte Theater, home of Shakespeare in the Park. Once the sun has set, you’ll have trouble telling the fake foliage from the real thing.

With a cast led by Donna Murphy and Amy Adams, the production takes risks with an enduring musical that was already chaotic; some pay off. You might want binoculars to appreciate the set, a multi-level treehouse that is every adolescent’s dream retreat. The production, directed by Timothy Sheader, is based on a 2010 staging of “Woods” in London’s Regent’s Park.

The Public Theater’s revival of “Into the Woods” begins in modern day, as a boy (Noah Radcliffe, alternating with Jack Broderick), feeling abandoned by his dad after an argument, sulks alongside his knapsack: “Sometimes I wish I had no father,” he says, an appropriate sentiment for a musical that is about parenting, disappointment and growing up.

The family spat sets the tone for a journey to the woods, where the boy transforms into our narrator; that’s a change from the original 1987 "Woods," where the narrator is an older man, and it creates discomfort later on, when the character becomes giant-fodder. But that's an issue for the second act. Once we’ve begun this fairy tale, we’ve got immediate concerns: a witch’s curse has condemned the Baker (Denis O’Hare, typically befuddled) and his wife (Adams, sparkly in her New York stage debut, despite the nest on her head) to a life without children.

The Baker and his wife embark on a search for items that, the witch says, will break the spell: a cow as white as milk, and so on. We know where they can get that stuff. The woods! But there’s trouble out in the woods: tall, terrible giants. And wolves, too, like Ivan Hernandez, whose borderline-pedophiliac seduction of Little Red Ridinghood ("Avenue Q's" Sarah Stiles), another woods-dweller, would land him a decade behind bars if it occurred outside the Delacorte.

Others looking for happiness in this terribly crowded forest include: Cinderella (a serene, bespectacled Jessie Mueller, of "On a Clear Day...") who would love to attend a bash at the king’s palace, if not for the interference of her stepmother and stepsisters; and Jack (Gideon Glick, "Spring Awakening"), who needs to sell his milk-stingy cow, to appease his mom (Kristine Zbornik).

 "Into the Woods” is Sondheim by way of the Brothers Grimm, from whom the tales are borrowed. In the first act, the characters quickly find their version of happiness. But the dark second act, filled with loss after painful loss, asks what happens after happily ever after? To paraphrase the Baker’s Wife, if you want “happy,” you’re in the wrong story. These characters are learning to accept limitations, like Bobby in “Company” or Dot in “Sunday in the Park with George.”

Fans will argue every “Woods” staging has one character who becomes the show’s focal point (Joanna Gleason, anyone?). There’s no question these “Woods” take root around Donna Murphy, the Sondheim veteran (and Tony winner, for “Passion”). From the moment Murphy hobbles onto stage, branches extending from her arms with an aura more “Blair Witch” than fairy-tale villain, she’s a frothing geyser of fury and concentration. 

It was the Baker’s father, in search of food for his pregnant wife, who stole “magic beans” from the Witch’s garden, setting in motion the curse that left the Baker and his wife childless. As Murphy recounts the tale, she thrusts her hips and snarls: “I caught him in the autumn in my garden one night! He was robbing me, raping me, rooting through my rutabaga, raiding my arugula and ripping up my rampion.” We’re just talking about vegetables and I was trembling.

Adams and O’Hare are well-matched as the childless couple on a mission, no moreso than when they try to pawn off their magic beans on Jack so he’ll relinquish his withholding cow, and, later, in their slap-happy homage to partnership, “It Takes Two.” Adams also turns into a savvy comic ragdoll during “Any Moment,” when she’s seduced by Cinderella’s prince (Hernandez, swarthy, again).

Cinderella’s stepmother and stepsisters (Ellen Harvey, Bethany Moore and Jennifer Rias) have gone punk rock, channeling David Bowie or Grace Jones, ca. 1985 and providing some necessary levity.

Sheader has updated other characters with less success. Red Ridinghood, the naive waif whose innocence is taken, seems little more than a bratty, overly confident Manhattan adolescent, wandering around with a red helmet and a whistle. Chip Zien, Broadway’s original Baker, returns to the fairy tale, this time as the Mysterious Man. With his sage demeanor, shabby garb and scraggly beard, he seems more apt to break into “Uncle John’s Band” than to resolve any of these character’s problems.

The treehouse, co-created by U.K. designer Soutra Gilmour and John Lee Beatty, looms 50 feet in the sky, with catwalks and pathways. You can see Belvedere Castle beyond the stage. The actors get a workout climbing around, though sometimes you must really lean forward and squint to absorb a moment. A spiral staircase centerstage proves the ideal way for the woods-folk to pile atop one another and unfurl green umbrellas. Voila! A beanstalk, for quick-and-easy access to the his-and-hers giants who also inform the tale.

And watch out for that “her,” a robotic villain looming high atop the branches. That’s a giant with the recorded voice of Glenn Close, and she’s in a mood. That can’t be a good thing for these lost and lonely souls, all trying to see the forest for the trees.

Tickets to Shakespeare in the Park are free and distributed, two per person, at the Delacorte Theater the day of the show. Visit www.shakespeareinthepark.org for more information.