Depression is “invisible”, says Matt Haig at the start of his best-selling book Reasons to Stay Alive. The theatre, however, deals in the visible and this production – jointly presented by the Crucible and English Touring Theatre – rises to the challenge of capturing the book’s essence by engaging choreographer Jonathan Watkins to stage April De Angelis’s text. The result is theatrically inventive without making me feel, as I did with the book, that I was living inside Haig’s head.

One of De Angelis’s key ideas is to seize on the book’s spasmodic conversations across time between the younger Matt, who at 24 was almost driven to kill himself while living in Ibiza, and his older self. Two actors embody his contrasting personae but, while it’s a neat solution to a problem, it robs the story of some of its tension. In the book we follow Haig’s hard-won journey from darkness into light. On stage, the older Matt says early on that “you will cry euphoric tears at the Beach Boys”, which provides reassurance that feels premature.

Watkins relies as much on physical theatre as on the text to convey Matt’s depression. Simon Daw’s design consists of three portable screens, which look like a fractured cerebellum and revolve to reveal climbing frames. Matt’s perilous ascent of them evokes his struggle to escape his condition. At other times, movement is used to enhance meaning. A key theme is the unwavering support of Matt’s girlfriend, and later wife, Andrea. But the idea of support is ingeniously explored by showing Andrea herself being saved from potential collapse by a succession of protective bodies.

Everything is done, in the course of 75 minutes, to give the subject of depression theatrical life. Matt’s list of famous fellow sufferers, ranging from Buzz Aldrin to Tennessee Williams, is chanted by the cast as they vigorously run – one of the book’s most eagerly advocated forms of therapy. When Matt, driving to Nottingham to see Swan Lake, feels a demon at his side, we see a masked figure lasciviously licking his face. What you get on stage is an objective representation of everything that is in the book. The thing that is hard to reproduce is the sense of Matt Haig talking to you personally in a way that allows you to identify with his anxieties and see the world through his eyes.

But if this production helps remove the stigma from depression, it will have done its work. It is also well performed. Mike Noble captures the desperation of the younger Matt, for whom a solo walk to a local shop seems a Herculean task, and Phil Cheadle as the older Matt suggests that even a belief that life is supremely worth living can never banish residual fears. Janet Etuk as Andrea, Chris Donnelly and Connie Walker as Matt’s parents and Dilek Rose in multiple roles all make expressive use of their bodies as well as their voices. It is a striking piece of theatre. It remains, however, an illustrative complement to the book rather than a substitute for reading it.

• At the Crucible, Sheffield, until 28 September. Then touring until 16 November.