chore: Avoid creating witness for simple multiplications

[guipublic]

Description

Problem*

Related to #4629

Summary*

Do not create a witness when multiplying a witness (or an affine transformation of a witness) with an expression of degree 1.

Additional Context

This PR does NOT fix the issue #4629, but it should help reducing the overall gates number.
The arithmetic expressions resulting from the multiplication should not explode in width since I only consider multiplication with a witness (or 'affine witness').

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: f9da41612effa881be411a00fda780b7895f4dfe, compared to commit: 86fd0ac4e6dd168227de6b8c97ed08da89e58a89

🧾 Summary (10% most significant diffs)

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
debug_logs	-1 ✅	-2.13%	-1 ✅	-1.33%
hashmap	-5,898 ✅	-2.73%	-5,898 ✅	-1.40%
slice_dynamic_index	-148 ✅	-10.37%	-148 ✅	-2.05%
slices	-79 ✅	-20.26%	-104 ✅	-2.90%
references	-2 ✅	-25.00%	-2 ✅	-8.70%

---

Full diff report 👇

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
regression	350 (+33)	+10.41%	3,360 (+33)	+0.99%
arithmetic_binary_operations	19 (+1)	+5.56%	2,791 (+1)	+0.04%
conditional_1	8,550 (+88)	+1.04%	38,809 (0)	0.00%
conditional_regression_short_circuit	98 (-1)	-1.01%	38,809 (0)	0.00%
merkle_insert	1,779 (-18)	-1.00%	29,042 (0)	0.00%
operator_overloading	563 (-7)	-1.23%	8,224 (0)	0.00%
simple_shield	30 (-9)	-23.08%	29,042 (0)	0.00%
bigint	682 (-1)	-0.15%	8,724 (-1)	-0.01%
regression_3607	43 (-1)	-2.27%	2,804 (-1)	-0.04%
conditional_2	22 (-1)	-4.35%	2,782 (-1)	-0.04%
eddsa	73,144 (-33)	-0.05%	74,517 (-33)	-0.04%
regression_mem_op_predicate	58 (-2)	-3.33%	3,587 (-2)	-0.06%
array_if_cond_simple	116 (-2)	-1.69%	3,146 (-2)	-0.06%
u16_support	263 (-2)	-0.75%	3,076 (-2)	-0.06%
conditional_regression_421	32 (-2)	-5.88%	2,793 (-2)	-0.07%
regression_capacity_tracker	115 (-5)	-4.17%	3,966 (-5)	-0.13%
tuple_inputs	44 (-5)	-10.20%	3,699 (-5)	-0.13%
if_else_chain	47 (-4)	-7.84%	2,809 (-4)	-0.14%
conditional_regression_661	32 (-4)	-11.11%	2,800 (-4)	-0.14%
regression_struct_array_conditional	70 (-5)	-6.67%	3,253 (-5)	-0.15%
regression_4709	72 (-6)	-7.69%	2,920 (-6)	-0.21%
bit_shifts_runtime	2,611 (-12)	-0.46%	5,706 (-12)	-0.21%
array_dynamic	111 (-8)	-6.72%	3,764 (-8)	-0.21%
array_sort	55 (-8)	-12.70%	2,927 (-8)	-0.27%
signed_division	167 (-16)	-8.74%	3,646 (-16)	-0.44%
nested_array_in_slice	1,094 (-32)	-2.84%	6,789 (-34)	-0.50%
signed_arithmetic	179 (-22)	-10.95%	2,929 (-22)	-0.75%
signed_comparison	143 (-3)	-2.05%	298 (-3)	-1.00%
7_function	234 (-31)	-11.70%	3,007 (-31)	-1.02%
u128	782 (-50)	-6.01%	4,783 (-50)	-1.03%
nested_array_dynamic	4,406 (-189)	-4.11%	15,943 (-189)	-1.17%
debug_logs	46 (-1)	-2.13%	74 (-1)	-1.33%
hashmap	209,999 (-5,898)	-2.73%	415,302 (-5,898)	-1.40%
slice_dynamic_index	1,279 (-148)	-10.37%	7,088 (-148)	-2.05%
slices	311 (-79)	-20.26%	3,487 (-104)	-2.90%
references	6 (-2)	-25.00%	21 (-2)	-8.70%