Manhattan3

Same as Manhattan but the distance is weighted by 3. This technique is faster but gives a less precise result in number of strokes as:
d(A,B) = 3 * (|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.