For comparison:

$ time perl min_supply.pl 1 4 3
Required supply: 3
6 steps:
   S->X
   X->Z
   S->X
   X->Z
   S->X
   X->Z

real    0m0.011s
user    0m0.016s
sys     0m0.000s

$ time perl min_steps.pl 1 4 3
3 steps:
   S->Y
   Y->Z
   Z->X

real    0m0.011s
user    0m0.008s
sys     0m0.004s

$ time perl -e1

real    0m0.002s
user    0m0.000s
sys     0m0.000s
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Note that I got a different solution that yours for min steps, but it's has the same number of steps.

Update: I seemed to have imagined that you said yours was slow. Ignore this post.