It's a fairly unremarkable Takashi Miike film. At least it's not one of his manga adaptations, which I approach with trepidation, but it's still an adaption of a novel about Laplace's Demon. In other words, it's nonsense. Laplace's Demon is a 19th century concept that says classical mechanics could calculate the entire future of the universe from a single starting point, if known with sufficient accuracy. This of course contradicts quantum mechanics, chaos theory, thermodynamic irreversibility, cantor diagonalisation and the free will of sentient life.
This film/novel doesn't go into full "Everything Is Deterministic" territory, but it is being po-faced about its fairly silly premise. If you were looking for Mental Miike, try his earlier films. I didn't particularly mind this one, but it's normal. Miike makes lots of normal, ordinary, unremarkable films these days.
We start with a man who died of hydrogen sulphide suffocation, despite being outside in the snow. (Was the body dumped, then? The film doesn't pay much attention to this possibility.) There's a detective who smells foul play and a professor who insists that the death can't possibly have been murder, suicide or natural causes. Uh... right. Then another, identical death takes place. The professor doesn't change his tune.
That professor is the movie's protagonist, incidentally. I didn't hate him, but he's not personally involved in the case, he's dogmatic even when his conclusions are absurd and at one point he agrees to keep quiet about everything and stop getting involved.
There's a girl who can calculate little well-defined snippets of the future and calls herself Laplace's Witch. There are some government bastards. There's a filmmaker whose character could be compared mischievously with Miike himself, although of course all this comes from a novel.
I think it might have helped the film to be a bit clearer about what it was. The original novelist, Keigo Higashino, is an award-winning mystery writer and I think that's what this is too. Unfortunately that doesn't really come across. Our hero doesn't seem like the hero of a mystery story, but just some bloke who's a less interesting lead character than almost anyone else in the film would have been. The film just seems a bit slow. It's based on a ridiculous idea, but it's being all staid and serious about it. You'll probably be hoping that Miike might go apeshit with crazed Laplace nonsense. He doesn't. That never happens.
For a more entertaining but stupider take on Laplace, see the 2015 Ranpo Kitan anime. (I'd been afraid that this film might be an adaptation of that, not because I'd disliked the anime but simply because of Miike.) This film is unremarkable. That said, though, I don't mind it and I liked the dark explanation of the murders.