Optimize arithmetic across multiple instructions

[jfecher]

Problem

Currently when simplifying instructions we only look at one instruction at a time for the most part.

For example, the program:

fn main(x: Field) {
    let x2 = x + 1 - 1;
    assert_eq(x, x2);
}

Does not optimize out x2:

After Array Set Optimizations:
acir(inline) fn main f0 {
  b0(v0: Field):
    v9 = add v0, Field 1
    v10 = sub v9, Field 1
    constrain v0 == v10
    return 
}

Happy Case

There are many cases when multiple instructions could constant combine like this so I won't list them all. Another case as mentioned in #5691 is with addition and less than which can show up in length checks of arrays in some cases:

v23 = add v21, u32 1
v28 = lt v23, u32 9

Which could be simplified to:

v23 = lt v21, u32 8

There are a lot of checks we could add but I think this could be a relatively easy optimization win still since I anticipate patterns like this will show up in user code either directly or as the result of previous optimizations as in the lt case above.

Workaround

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Workaround Description

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Additional Context

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Project Impact

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Blocker Context

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