feat: improve SSA type-awareness in EQ and MUL instructions (#4691)

# Description

## Problem\*

Resolves <!-- Link to GitHub Issue -->

## Summary\*

This PR adds some improvements for SSA generation for programs such as
in #4688 where we now make more use of information on casted values.

## 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: jfecher <[email protected]>

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

@@ -130,6 +130,12 @@ impl Binary {
                     let zero = dfg.make_constant(FieldElement::zero(), operand_type);
                     return SimplifyResult::SimplifiedTo(zero);
                 }
+                if dfg.resolve(self.lhs) == dfg.resolve(self.rhs)
+                    && dfg.get_value_max_num_bits(self.lhs) == 1
+                {
+                    // Squaring a boolean value is a noop.
+                    return SimplifyResult::SimplifiedTo(self.lhs);
+                }
             }
             BinaryOp::Div => {
                 if rhs_is_one {
@@ -164,6 +170,22 @@ impl Binary {
                     let one = dfg.make_constant(FieldElement::one(), Type::bool());
                     return SimplifyResult::SimplifiedTo(one);
                 }
+
+                if operand_type.is_unsigned() {
+                    // If we're comparing a variable against a constant value which lies outside of the range of
+                    // values which the variable's type can take, we can assume that the equality will be false.
+                    let constant = lhs.or(rhs);
+                    let non_constant = if lhs.is_some() { self.rhs } else { self.lhs };
+                    if let Some(constant) = constant {
+                        let max_possible_value =
+                            2u128.pow(dfg.get_value_max_num_bits(non_constant)) - 1;
+                        if constant > max_possible_value.into() {
+                            let zero = dfg.make_constant(FieldElement::zero(), Type::bool());
+                            return SimplifyResult::SimplifiedTo(zero);
+                        }
+                    }
+                }
+
                 if operand_type == Type::bool() {
                     // Simplify forms of `(boolean == true)` into `boolean`
                     if lhs_is_one {