On TV: "Robin Williams: Come Inside My Mind"

Directed by Marina Zenovich and produced by the tireless Alex Gibney for HBO, the documentary Robin Williams: Come Inside My Mind is at once a tribute, a celebration and a doomed exercise, attempting to get inside the head of one of the least predictable comic performers of his generation, and thereby puzzle out what led him to take his own life, aged 63 in 2014. It opens with a clip from Inside the Actors Studio, where Williams responds to a question from host James Lipton (himself no longer with us) regarding the workings of his mind with an extended riff on the daily life of the human brain. It's manic, electric, and the studio audience responds as one, with a standing ovation, yet - crucially - Williams is generalising, deflecting; he doesn't speak to the possessive pronoun in the original question. If he didn't know how his mind worked, how can we? What's evident is that he had a gift, and that he was a gift, both to audiences and to filmmakers piecing together an appreciation of the life and work out of the bounteous footage available. Zenovich casts her net enjoyably wide: we get the stand-up alongside clips from Williams' now rarely repeated teatime TV staples (Happy Days, Mork & Mindy), plus outtakes from same (in which Pam Dawber is returned to us as a terrific sport and a lost babe) and excerpts from the many, many hours the subject logged on late-night chatshow sofas. (In American public life, this may be as close as we get to seeing a performer on the psychiatrist's couch.)

Yet the film also digs deep, and here Come Inside My Mind bears Gibney's no-stone-unturned influence: we get messages Williams left on pal Billy Crystal's answerphone, an outtake of him making Philip Seymour Hoffman crack up on the set of Patch Adams, a glorious return to the 2003 Critics' Choice Awards, where Williams lost to Jack Nicholson and Daniel Day-Lewis and still gave the night's funniest acceptance speech, and an offcut from an EPK interview with his World's Greatest Dad director Bobcat Goldthwait that goes swiftly - and unusably - off-topic. Biographically, there are almost as many lows as highs. There was that triple gutpunch, not long after his elevation to the A-list, of seeing Popeye crash-and-burn, John Belushi white out on the same drugs Williams himself was blitzing, and Mork & Mindy being unceremoniously canned. And there was the abiding, apparently unsolveable problem of how to come down from the pure dopamine hit of onstage adulation: the drink and drugs Williams turned to in order to sustain the high offered few lasting physical benefits, though they also generated a smart late-life routine about addiction ("I went to rehab in wine country, just to keep my options open") which made light of heavy personal experience. To quote Steve Martin, Williams' co-star in a 1988 revival of Waiting for Godot you'd pay good money to see repeated in its entirety: "On stage, he was the master: funny and quick and in control. In life, he wasn't on stage any more."

There's enough here to make fans and sceptics alike rethink elements of the career. It's clear that Williams found love and stability with his second wife Marsha - it may be the only time in Hollywood history that running off with the nanny generated more happiness than misery - and that fatherhood gave this only child a ready audience of youngsters with which to goof around. That, I think, explains some of the film choices for which he took such a critical hammering - though the evidence still suggests that Williams was always vastly funnier and more entertaining with the child locks off. He could be subtle, too, lest we forget: Zenovich has the clips from Good Will Hunting, One Hour Photo and Being Human to illustrate that, plus an audio masterclass in the art of doing nothing that reveals an astute actorly intelligence behind the onstage freewheeling and spitballing. Eventually, Come Inside My Mind addresses the underlying health issues and tiredness that was a consequence of giving it all, night after night, take after take. (The devil-may-care Goldthwait, with whom Williams was both personally and professionally close, may be the key to understanding what weighed on these shoulders in their final years.) Yet he'd given a lot to so many, and the film-shrine Zenovich and Gibney have curated in his wake proves at least the equal - in its scope, its detail and its profound love for its flawed, troubled subject - of Judd Apatow's excellent HBO retrospective The Zen Diaries of Garry Shandling. One of the reasons the past few years have been so depressing is that we've lost many of the people who made us laugh, at exactly the moment we needed them most.

Robin Williams: Come Inside My Mind screens on Sky Arts this Wednesday at 12.15am.