I didn’t find any way to solve it with a BFS or some smart DFS, BUT: for those who balk at implementing a equations solver (like me, I was not in the mood today), it is solvable with a genetic programming / iterative reparation approach, the hard part being to get enough guaranties that the solution is the actual minimum.
It is pretty random, and maybe not very elegant, but at least it did the job with my input (and took a lot more time to run than an equation solver would 
).
