chore: simplify boolean in a mul of a mul

[guipublic]

Description

Problem*

Resolves #6879

Summary*

When multiplying a boolean with the result of another multiplication involving the same boolean, we can discard one multiplication.

Additional Context

The regression is a bit subtle, the optimisation introduced by PR #6875 was simplifying an ifesle instruction if one of its operand is also an ifelse with the same condition.
When the operands are an array and the array with one element modified, the merge of values only happens on the modified element, which induces only one multiplication.
However, when the array is a result of of an ifelse, the optimisation from #6875 replace it with another array (the operand of the inner ifselse). So we are no longer merging two almost identical arrays, and we get one multiplication per array element instead.
So basically, the optimisation is preventing another optimisation.
I could not find a way to get the two optimisation to be effective at the same time. The value merge is done when we eliminate IfElse, so the #6875 must be done before. But then the link between the arrays is not obvious.
Fortunately, since this happens when we have inner If statements with the same condition, that means we are multiplying several times with the condition, and this can be optimised from the instruction simplification pass.

Documentation*

Check one:

• No documentation needed.
• Documentation included in this PR.
• [For Experimental Features] Documentation to be submitted in a separate PR.

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[github-actions]

Changes to circuit sizes

Generated at commit: a5d40d2691c12857f077dab3bfdcb7d76b0f2cb0, compared to commit: ab8807d27b0442bd7e9ff73050f44bacea3add16

🧾 Summary (10% most significant diffs)

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
sha256_var_size_regression	-138 ✅	-0.63%	-217 ✅	-0.27%
fold_call_witness_condition	-1 ✅	-16.67%	-1 ✅	-5.00%

---

Full diff report 👇

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
hashmap	53,816 (-2)	-0.00%	119,079 (-2)	-0.00%
sha256_regression	42,363 (-6)	-0.01%	207,800 (-7)	-0.00%
nested_array_dynamic	3,358 (0)	0.00%	12,754 (-1)	-0.01%
sha256	2,064 (-3)	-0.15%	25,338 (-5)	-0.02%
sha256_var_witness_const_regression	1,702 (-3)	-0.18%	17,231 (-4)	-0.02%
slices	796 (-2)	-0.25%	3,960 (-2)	-0.05%
conditional_regression_661	35 (-3)	-7.89%	2,804 (-3)	-0.11%
slice_dynamic_index	1,068 (-7)	-0.65%	6,498 (-7)	-0.11%
conditional_1	9,039 (-24)	-0.26%	18,367 (-30)	-0.16%
sha256_var_size_regression	21,617 (-138)	-0.63%	79,344 (-217)	-0.27%
fold_call_witness_condition	5 (-1)	-16.67%	19 (-1)	-5.00%

[github-actions]

Compilation Report

Program	Compilation Time	%
sha256_regression	1.332s	-1%
regression_4709	0.776s	-1%
ram_blowup_regression	15.000s	-1%
rollup-root	3.530s	-17%
rollup-block-merge	3.630s	-5%
rollup-base-public	31.600s	-16%
rollup-base-private	12.700s	-36%
private-kernel-tail	1.008s	-4%
private-kernel-reset	6.844s	-3%
private-kernel-inner	2.086s	-6%
noir-contracts	84.700s	-1%

[github-actions]

Execution Report

Program	Execution Time	%
sha256_regression	0.100s	0%
regression_4709	0.001s	0%
ram_blowup_regression	0.581s	0%
rollup-root	0.106s	-16%
rollup-block-merge	0.105s	-19%
rollup-base-public	1.440s	-42%
rollup-base-private	0.644s	-63%
private-kernel-tail	0.024s	4%
private-kernel-reset	0.388s	-1%
private-kernel-inner	0.116s	-1%

[github-actions]

Compilation Memory Report

Program	Peak Memory
keccak256	78.50M
workspace	123.62M
regression_4709	422.91M
ram_blowup_regression	1.58G
rollup-base-public	2.55G
rollup-base-private	1.25G
private-kernel-tail	201.95M
private-kernel-reset	716.58M
private-kernel-inner	292.22M

[github-actions]

Execution Memory Report

Program	Peak Memory	%
keccak256	74.61M	0%
workspace	123.31M	0%
regression_4709	315.93M	0%
ram_blowup_regression	512.47M	0%
rollup-base-public	773.36M	100%
rollup-base-private	424.91M	-49%
private-kernel-tail	181.99M	0%
private-kernel-reset	255.57M	0%
private-kernel-inner	215.17M	0%

[TomAFrench]

This PR drops the number of opcodes in rollup-base-private from 617798 (ab8807d) to 215613. Not bad!

[TomAFrench]

LGTM!