fix: treat im as imaginary unit in string parsing

[MilesCranmerBot]

This ports the im parsing fix from SymbolicRegression.jl to DynamicExpressions.jl, where string expression parsing belongs.

What changed

• Normalize parsed expressions so symbol im is treated as Julia's imaginary unit constant.
• Preserve existing behavior when "im" is explicitly provided in variable_names.
• Add parser tests for both cases.

Context: requested in astroautomata/SymbolicRegression.jl#582 (comment)

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	cf03c77...	master / cf03c77...
eval/ComplexF32/evaluation	6.95 ± 0.43 ms	6.88 ± 0.43 ms	1.01 ± 0.089
eval/ComplexF64/evaluation	10.3 ± 0.83 ms	10.3 ± 0.75 ms	0.999 ± 0.11
eval/Float32/derivative	11.2 ± 1.2 ms	11.4 ± 0.97 ms	0.985 ± 0.13
eval/Float32/derivative_turbo	11.2 ± 1.1 ms	11.4 ± 0.88 ms	0.983 ± 0.12
eval/Float32/evaluation	2.49 ± 0.24 ms	2.47 ± 0.23 ms	1.01 ± 0.14
eval/Float32/evaluation_bumper	0.616 ± 0.019 ms	0.602 ± 0.016 ms	1.02 ± 0.041
eval/Float32/evaluation_turbo	0.541 ± 0.039 ms	0.527 ± 0.034 ms	1.03 ± 0.099
eval/Float32/evaluation_turbo_bumper	0.61 ± 0.018 ms	0.605 ± 0.016 ms	1.01 ± 0.04
eval/Float64/derivative	14.4 ± 1.6 ms	13.9 ± 1.5 ms	1.03 ± 0.16
eval/Float64/derivative_turbo	14.4 ± 2.1 ms	14 ± 1.3 ms	1.03 ± 0.18
eval/Float64/evaluation	2.87 ± 0.26 ms	2.87 ± 0.28 ms	1 ± 0.13
eval/Float64/evaluation_bumper	1.28 ± 0.042 ms	1.26 ± 0.039 ms	1.01 ± 0.046
eval/Float64/evaluation_turbo	1.05 ± 0.062 ms	1.02 ± 0.071 ms	1.03 ± 0.093
eval/Float64/evaluation_turbo_bumper	1.28 ± 0.045 ms	1.27 ± 0.041 ms	1.01 ± 0.049
utils/combine_operators/break_sharing	0.0422 ± 0.002 ms	0.0441 ± 0.0018 ms	0.957 ± 0.061
utils/convert/break_sharing	28 ± 3.7 μs	28.4 ± 3.8 μs	0.985 ± 0.18
utils/convert/preserve_sharing	0.108 ± 0.012 ms	0.106 ± 0.011 ms	1.01 ± 0.16
utils/copy/break_sharing	28.5 ± 4.9 μs	28.5 ± 3.9 μs	0.999 ± 0.22
utils/copy/preserve_sharing	0.11 ± 0.019 ms	0.106 ± 0.01 ms	1.04 ± 0.21
utils/count_constant_nodes/break_sharing	13.5 ± 1.8 μs	13.4 ± 1.5 μs	1.01 ± 0.17
utils/count_constant_nodes/preserve_sharing	0.09 ± 0.01 ms	0.0899 ± 0.011 ms	1 ± 0.17
utils/count_depth/break_sharing	14.1 ± 1.6 μs	14.5 ± 1.6 μs	0.971 ± 0.16
utils/count_nodes/break_sharing	12.7 ± 1.4 μs	13 ± 1.4 μs	0.981 ± 0.15
utils/count_nodes/preserve_sharing	0.0914 ± 0.01 ms	0.0909 ± 0.01 ms	1.01 ± 0.16
utils/get_set_constants!/break_sharing	0.0339 ± 0.0049 ms	0.0345 ± 0.004 ms	0.983 ± 0.18
utils/get_set_constants!/preserve_sharing	0.182 ± 0.013 ms	0.182 ± 0.013 ms	1 ± 0.1
utils/get_set_constants_parametric	0.0523 ± 0.0089 ms	0.0515 ± 0.0086 ms	1.01 ± 0.24
utils/has_constants/break_sharing	7.72 ± 1.6 μs	7.82 ± 1.7 μs	0.987 ± 0.3
utils/has_operators/break_sharing	2.69 ± 0.35 μs	2.67 ± 0.36 μs	1.01 ± 0.19
utils/hash/break_sharing	24.4 ± 1.9 μs	26.1 ± 2.7 μs	0.933 ± 0.12
utils/hash/preserve_sharing	0.107 ± 0.011 ms	0.105 ± 0.01 ms	1.02 ± 0.14
utils/index_constant_nodes/break_sharing	29.5 ± 3.1 μs	31.3 ± 4.1 μs	0.944 ± 0.16
utils/index_constant_nodes/preserve_sharing	0.108 ± 0.01 ms	0.111 ± 0.011 ms	0.974 ± 0.14
utils/is_constant/break_sharing	8.21 ± 1.7 μs	8.23 ± 1.7 μs	0.996 ± 0.29
utils/simplify_tree/break_sharing	31 ± 1.8 μs	31.5 ± 1.7 μs	0.985 ± 0.079
utils/simplify_tree/preserve_sharing	0.118 ± 0.011 ms	0.117 ± 0.0093 ms	1.01 ± 0.12
utils/string_tree/break_sharing	0.464 ± 0.037 ms	0.454 ± 0.021 ms	1.02 ± 0.093
utils/string_tree/preserve_sharing	0.557 ± 0.023 ms	0.553 ± 0.022 ms	1.01 ± 0.058
time_to_load	0.172 ± 0.0029 s	0.173 ± 0.0046 s	0.995 ± 0.031

Memory benchmarks

	master	cf03c77...	master / cf03c77...
eval/ComplexF32/evaluation	0.987 k allocs: 2.53 MB	0.978 k allocs: 2.5 MB	1.01
eval/ComplexF64/evaluation	1 k allocs: 5.11 MB	0.993 k allocs: 5.06 MB	1.01
eval/Float32/derivative	4.63 k allocs: 17.4 MB	4.68 k allocs: 17.6 MB	0.99
eval/Float32/derivative_turbo	4.69 k allocs: 17.7 MB	4.67 k allocs: 17.6 MB	1
eval/Float32/evaluation	0.957 k allocs: 1.25 MB	0.966 k allocs: 1.26 MB	0.991
eval/Float32/evaluation_bumper	0.303 k allocs: 0.393 MB	0.303 k allocs: 0.393 MB	1
eval/Float32/evaluation_turbo	0.978 k allocs: 1.27 MB	0.945 k allocs: 1.23 MB	1.03
eval/Float32/evaluation_turbo_bumper	0.303 k allocs: 0.393 MB	0.303 k allocs: 0.393 MB	1
eval/Float64/derivative	4.78 k allocs: 0.0349 GB	4.79 k allocs: 0.035 GB	0.997
eval/Float64/derivative_turbo	4.81 k allocs: 0.0352 GB	4.78 k allocs: 0.035 GB	1.01
eval/Float64/evaluation	1.01 k allocs: 2.58 MB	1 k allocs: 2.57 MB	1.01
eval/Float64/evaluation_bumper	0.303 k allocs: 0.771 MB	0.303 k allocs: 0.771 MB	1
eval/Float64/evaluation_turbo	0.987 k allocs: 2.53 MB	0.996 k allocs: 2.55 MB	0.991
eval/Float64/evaluation_turbo_bumper	0.303 k allocs: 0.771 MB	0.303 k allocs: 0.771 MB	1
utils/combine_operators/break_sharing	4 allocs: 0.953 kB	4 allocs: 0.953 kB	1
utils/convert/break_sharing	2 k allocs: 0.123 MB	2 k allocs: 0.123 MB	1
utils/convert/preserve_sharing	2.4 k allocs: 0.192 MB	2.4 k allocs: 0.192 MB	1
utils/copy/break_sharing	2 k allocs: 0.123 MB	2 k allocs: 0.123 MB	1
utils/copy/preserve_sharing	2.4 k allocs: 0.192 MB	2.4 k allocs: 0.192 MB	1
utils/count_constant_nodes/break_sharing	4 allocs: 0.953 kB	4 allocs: 0.953 kB	1
utils/count_constant_nodes/preserve_sharing	0.404 k allocs: 0.0696 MB	0.404 k allocs: 0.0696 MB	1
utils/count_depth/break_sharing	4 allocs: 0.953 kB	4 allocs: 0.953 kB	1
utils/count_nodes/break_sharing	4 allocs: 0.953 kB	4 allocs: 0.953 kB	1
utils/count_nodes/preserve_sharing	0.404 k allocs: 0.0696 MB	0.404 k allocs: 0.0696 MB	1
utils/get_set_constants!/break_sharing	0.898 k allocs: 25.2 kB	0.898 k allocs: 25.2 kB	1
utils/get_set_constants!/preserve_sharing	1.7 k allocs: 0.138 MB	1.7 k allocs: 0.138 MB	1
utils/get_set_constants_parametric	1.42 k allocs: 0.0663 MB	1.42 k allocs: 0.0663 MB	1
utils/has_constants/break_sharing	4 allocs: 0.203 kB	4 allocs: 0.203 kB	1
utils/has_operators/break_sharing	4 allocs: 0.203 kB	4 allocs: 0.203 kB	1
utils/hash/break_sharing	0.104 k allocs: 2.52 kB	0.104 k allocs: 2.52 kB	1
utils/hash/preserve_sharing	0.504 k allocs: 0.0711 MB	0.504 k allocs: 0.0711 MB	1
utils/index_constant_nodes/break_sharing	2.1 k allocs: 0.094 MB	2.1 k allocs: 0.094 MB	1
utils/index_constant_nodes/preserve_sharing	2.5 k allocs: 0.163 MB	2.5 k allocs: 0.163 MB	1
utils/is_constant/break_sharing	4 allocs: 0.203 kB	4 allocs: 0.203 kB	1
utils/simplify_tree/break_sharing	0.104 k allocs: 2.52 kB	0.104 k allocs: 2.52 kB	1
utils/simplify_tree/preserve_sharing	0.504 k allocs: 0.0711 MB	0.504 k allocs: 0.0711 MB	1
utils/string_tree/break_sharing	11.9 k allocs: 0.999 MB	11.9 k allocs: 0.999 MB	1
utils/string_tree/preserve_sharing	12.3 k allocs: 1.07 MB	12.3 k allocs: 1.07 MB	1
time_to_load	0.145 k allocs: 11 kB	0.145 k allocs: 11 kB	1

[codecov]

Codecov Report

❌ Patch coverage is 88.88889% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 59.43%. Comparing base (68d60d4) to head (cf03c77).
⚠️ Report is 2 commits behind head on master.

Files with missing lines	Patch %	Lines
src/Parse.jl	88.88%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #168      +/-   ##
==========================================
+ Coverage   59.33%   59.43%   +0.09%     
==========================================
  Files          30       30              
  Lines        2673     2682       +9     
==========================================
+ Hits         1586     1594       +8     
- Misses       1087     1088       +1     

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[MilesCranmer]

@MilesCranmerBot please implement the suggestions

[MilesCranmerBot]

Implemented review suggestions:

• Updated the im parsing test to evaluate on real/complex inputs and assert output eltype/values.
• Dropped @unstable on _replace_imaginary_unit_symbol(::Expr) (always an Expr).

Commit: ec8cb53

[MilesCranmer]

@MilesCranmerBot formatter check failed

[MilesCranmer]

@MilesCranmerBot please backport to release-v1

[MilesCranmerBot]

Done — opened release-v1 backport PR: #169

• PR: fix: backport im string parsing fix to release-v1 #169
• Branch: MilesCranmerBot:bot/backport-fix-im-string-parse-release-v1
• Commits: 741031c, c5f6bba, 63d7900, e835279, 59815bb

I ran a targeted local validation for the im parse paths (0.1im + x and im + x2). Full Pkg.test() is heavier and was not re-run after the final compatibility patch.