feat(perf): Follow array sets backwards in array set from get optimiz…

…ation (noir-lang#6208)

# Description

## Problem\*

Part of general effort reduce Brillig bytecode sizes

## Summary\*

Follow-up to noir-lang#6207

From comments inside the PR:
```
/// If we have an array set whose value is from an array get on the same array at the same index,
/// we can simplify that array set to the array we were looking to perform an array set upon.
///
/// Simple case:
/// v3 = array_get v1, index v2
/// v5 = array_set v1, index v2, value v3
///
/// If we could not immediately simplify the array set from its value, we can try to follow
/// the array set backwards in the case we have constant indices:
///
/// v3 = array_get v1, index 1
/// v5 = array_set v1, index 2, value [Field 100, Field 101, Field 102]
/// v7 = array_set mut v5, index 1, value v3
///
/// We want to optimize `v7` to `v5`. We see that `v3` comes from an array get to `v1`. We follow `v5` backwards and see an array set
/// to `v1` and see that the previous array set occurs to a different constant index.
///
/// For each array set:
/// - If the index is non-constant we fail the optimization since any index may be changed.
/// - If the index is constant and is our target index, we conservatively fail the optimization.
/// - Otherwise, we check the array value of the `array_set``. We will refer to this array as array'.
///   In the case above, array' is `v1` from `v5 = array set ...`
///   - If the original `array_set` value comes from an `array_get`, check the array in that `array_get` against array'. 
///   - If the two values are equal we can simplify.
///     - Continuing the example above, as we have `v3 = array_get v1, index 1`, `v1` is
///       what we want to check against array'. We now know we can simplify `v7` to `v5` as it is unchanged.
///   - If they are not equal, recur marking the current `array_set` array as the new array id to use in the checks
```


## Additional Context


## Documentation\*

Check one:
- [X] No documentation needed.
- [ ] Documentation included in this PR.
- [ ] **[For Experimental Features]** Documentation to be submitted in a
separate PR.

# PR Checklist\*

- [X] I have tested the changes locally.
- [X] I have formatted the changes with [Prettier](https://prettier.io/)
and/or `cargo fmt` on default settings.

---------

Co-authored-by: Tom French <[email protected]>

compiler/noirc_evaluator/src/ssa/ir/instruction.rs

@@ -818,25 +818,96 @@ fn try_optimize_array_get_from_previous_set(
     SimplifyResult::None
 }
 
+/// If we have an array set whose value is from an array get on the same array at the same index,
+/// we can simplify that array set to the array we were looking to perform an array set upon.
+///
+/// Simple case:
+/// v3 = array_get v1, index v2
+/// v5 = array_set v1, index v2, value v3
+///
+/// If we could not immediately simplify the array set from its value, we can try to follow
+/// the array set backwards in the case we have constant indices:
+///
+/// v3 = array_get v1, index 1
+/// v5 = array_set v1, index 2, value [Field 100, Field 101, Field 102]
+/// v7 = array_set mut v5, index 1, value v3
+///
+/// We want to optimize `v7` to `v5`. We see that `v3` comes from an array get to `v1`. We follow `v5` backwards and see an array set
+/// to `v1` and see that the previous array set occurs to a different constant index.
+///
+/// For each array_set:
+/// - If the index is non-constant we fail the optimization since any index may be changed.
+/// - If the index is constant and is our target index, we conservatively fail the optimization.
+/// - Otherwise, we check the array value of the `array_set`. We will refer to this array as array'.
+///   In the case above, array' is `v1` from `v5 = array set ...`
+///   - If the original `array_set` value comes from an `array_get`, check the array in that `array_get` against array'.
+///   - If the two values are equal we can simplify.
+///     - Continuing the example above, as we have `v3 = array_get v1, index 1`, `v1` is
+///       what we want to check against array'. We now know we can simplify `v7` to `v5` as it is unchanged.
+///   - If they are not equal, recur marking the current `array_set` array as the new array id to use in the checks
 fn try_optimize_array_set_from_previous_get(
     dfg: &DataFlowGraph,
-    array_id: ValueId,
+    mut array_id: ValueId,
     target_index: ValueId,
     target_value: ValueId,
 ) -> SimplifyResult {
-    match &dfg[target_value] {
+    let array_from_get = match &dfg[target_value] {
         Value::Instruction { instruction, .. } => match &dfg[*instruction] {
             Instruction::ArrayGet { array, index } => {
                 if *array == array_id && *index == target_index {
-                    SimplifyResult::SimplifiedTo(array_id)
+                    // If array and index match from the value, we can immediately simplify
+                    return SimplifyResult::SimplifiedTo(array_id);
+                } else if *index == target_index {
+                    *array
                 } else {
-                    SimplifyResult::None
+                    return SimplifyResult::None;
                 }
             }
-            _ => SimplifyResult::None,
+            _ => return SimplifyResult::None,
         },
-        _ => SimplifyResult::None,
+        _ => return SimplifyResult::None,
+    };
+
+    // At this point we have determined that the value we are writing in the `array_set` instruction
+    // comes from an `array_get` from the same index at which we want to write it at.
+    // It's possible that we're acting on the same array where other indices have been mutated in between
+    // the `array_get` and `array_set` (resulting in the `array_id` not matching).
+    //
+    // We then inspect the set of `array_set`s which which led to the current array the `array_set` is acting on.
+    // If we can work back to the array on which the `array_get` was reading from without having another `array_set`
+    // act on the same index then we can be sure that the new `array_set` can be removed without affecting the final result.
+    let Some(target_index) = dfg.get_numeric_constant(target_index) else {
+        return SimplifyResult::None;
+    };
+
+    let original_array_id = array_id;
+    // Arbitrary number of maximum tries just to prevent this optimization from taking too long.
+    let max_tries = 5;
+    for _ in 0..max_tries {
+        match &dfg[array_id] {
+            Value::Instruction { instruction, .. } => match &dfg[*instruction] {
+                Instruction::ArraySet { array, index, .. } => {
+                    let Some(index) = dfg.get_numeric_constant(*index) else {
+                        return SimplifyResult::None;
+                    };
+
+                    if index == target_index {
+                        return SimplifyResult::None;
+                    }
+
+                    if *array == array_from_get {
+                        return SimplifyResult::SimplifiedTo(original_array_id);
+                    }
+
+                    array_id = *array; // recur
+                }
+                _ => return SimplifyResult::None,
+            },
+            _ => return SimplifyResult::None,
+        }
     }
+
+    SimplifyResult::None
 }
 
 pub(crate) type ErrorType = HirType;