Thanks for the PR!

That's an interesting result about the heuristic. On my input it results in a 15% speedup from eliminating branches.

Would you mind checking if the speedup is from the structure of your input?

I modified the code to add a simple counter:

 let mut counter = 0;
 loop {
 while let Some((x, y, direction)) = todo[index % 100].pop() {
 <...snip...>
 counter += 1;
 // Check if we've reached the end.
 if x == width - 1 && y == height - 1 {
 println!("{counter}");
 return steps;
 }

Good to see those numbers. Also explains the runtime differences somewhat. I find it quite surprising that there are such differences in the inputs. This is the result I get:

So it looks like for my input the heuristic actually makes it a lot worse.

Anyway, I would find it reasonable for you to optimize for your input, so feel free to close the PR.

Following up nine months later... 🙂

Implemented an animation visualizing the frontier in order to debug. With your input and the heuristic set as the Manhattan distance towards the bottom 2 * size - x - y, a second cheaper frontier occurs because a move up or left near the top left origin is cheaper. This causes double the work as two frontiers propagate towards the goal simultaneously

Tweaked the heuristic from 2 * size - x - y to (2 * size - x - y).min(size + size / 2). This "flattens" the heuristic in the top left quadrant, preferring all directions equally. This performs almost as well as the original and improves performance for your input.