Manhattan

The Manhattan distance is the distance between 2 points traveled by a taxi when he is in a city ​​arranged in grid as:
d(A,B) = |XA - XB| + |YA - YB|

Depth Graphic

This graphic show the depth of all evaluated branches.
The differents colors represent each moves as:

Right

Left

Up

Down

The Arrival branch is the grey one with red dots. Each dot is a strokes and the length is display at the end of the branch.