The Prospero Challenge

There are 7866 instructions including the constants. There are 1406 constants leaving only 6460 real instructions to be executed (max, min, add, neg, sub, square, sqrt). Those constants can be directly encoded into most (possibly all) of the instructions when mapped to real machine instructions, which a compiler would likely do unless there was a good reason to keep it in a register or memory location.

Something I saw from a cursory scan were some near duplicate instruction (haven't written code to find all instances):

  a = x - c
  ;; some time later
  b = c - x

Recognizing that b is the negation of a, you can convert the calculation of b to:

  b = -a

This may or may not be faster, but it does mean that we can possibly forget about c earlier (helpful for register allocation and can reduce memory accesses).

Negations can sometimes be removed depending on the lifetime of the variable and its uses. Taking the above, suppose we follow it with this use of b:

  d = e + b ;; or b + e

We can rewrite this as:

  d = e - a

Or if it had been:

  d = e - b

It can be rewritten to:

  d = e + a

And if there are no more uses of b we've eliminated both that variable and another instruction from the program. These and other patterns are things a compiler would detect and optimize.

Though looking at the uses of the results from neg, I think most are used in the sequence of max/min instructions following them so it may not be possible to eliminate them as I showed above.