This project demonstrates how the tame fusible number function evaluates. s is the input times 64. The tame fusible number function f(n) returns -n if n<0, and f(n-f(n-1))/2 otherwise. Each evaluation of f is represented by a horizontal line, and its height corresponds to the input. The recursive subcalls for a particular call to f correspond to the lines completely under the line for the call to f. Dark(er) orange lines are multiples of 1, light orange lines are multiples of 0.25. The bottommost line is -1.
The function is M from page 13 of https://arxiv.org/pdf/2003.14342 . r is the output of the function, but it's only correct if you can see the end of the computation (or if you're past it).