ArenaNode: stabilize cursor typing and allocation checks

[MilesCranmerBot]

Summary

• add ArenaNode-specific / helpers to avoid ambiguity/inference issues
• make traversal return and update call sites for concrete typing
• tighten ArenaNode child-setting dispatch and a few Int32 construction paths
• add explicit Arena allocation regression checks in using a fresh Julia subprocess

Validation

• Test Summary: | Pass Total Time
  Arena-backed node prototype | 43 43 23.5s (43/43 pass)
• (3011/3011 pass)

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	847c2c6...	master / 847c2c6...
eval/ComplexF32/evaluation	6.86 ± 0.47 ms	6.91 ± 0.47 ms	0.993 ± 0.096
eval/ComplexF64/evaluation	10.3 ± 0.84 ms	10.2 ± 0.86 ms	1.01 ± 0.12
eval/Float32/derivative	11.4 ± 1.6 ms	11.3 ± 1 ms	1.01 ± 0.17
eval/Float32/derivative_turbo	11.3 ± 1.3 ms	11.2 ± 1.1 ms	1.01 ± 0.15
eval/Float32/evaluation	2.48 ± 0.25 ms	2.47 ± 0.23 ms	1.01 ± 0.14
eval/Float32/evaluation_bumper	0.604 ± 0.016 ms	0.602 ± 0.016 ms	1 ± 0.037
eval/Float32/evaluation_turbo	0.522 ± 0.032 ms	0.522 ± 0.031 ms	1 ± 0.085
eval/Float32/evaluation_turbo_bumper	0.604 ± 0.016 ms	0.603 ± 0.015 ms	1 ± 0.037
eval/Float64/derivative	14.2 ± 1.6 ms	14.3 ± 1.8 ms	0.997 ± 0.17
eval/Float64/derivative_turbo	14.1 ± 1.7 ms	14.3 ± 1.6 ms	0.987 ± 0.16
eval/Float64/evaluation	2.85 ± 0.28 ms	2.87 ± 0.27 ms	0.993 ± 0.14
eval/Float64/evaluation_bumper	1.27 ± 0.041 ms	1.26 ± 0.042 ms	1 ± 0.046
eval/Float64/evaluation_turbo	1.02 ± 0.06 ms	1.02 ± 0.061 ms	1 ± 0.084
eval/Float64/evaluation_turbo_bumper	1.27 ± 0.043 ms	1.27 ± 0.043 ms	1 ± 0.048
utils/combine_operators/break_sharing	0.0413 ± 0.00087 ms	0.0409 ± 0.00091 ms	1.01 ± 0.031
utils/convert/break_sharing	27.8 ± 3.1 μs	27.7 ± 3.2 μs	1 ± 0.16
utils/convert/preserve_sharing	0.0989 ± 0.0079 ms	0.1 ± 0.0086 ms	0.985 ± 0.12
utils/copy/break_sharing	27.5 ± 3.1 μs	28.1 ± 3.2 μs	0.978 ± 0.16
utils/copy/preserve_sharing	0.0999 ± 0.0091 ms	0.0994 ± 0.0084 ms	1.01 ± 0.12
utils/count_constant_nodes/break_sharing	12.8 ± 0.71 μs	12.8 ± 0.74 μs	0.993 ± 0.08
utils/count_constant_nodes/preserve_sharing	0.084 ± 0.0064 ms	0.0839 ± 0.0065 ms	1 ± 0.11
utils/count_depth/break_sharing	13.8 ± 0.79 μs	13.4 ± 0.94 μs	1.04 ± 0.094
utils/count_nodes/break_sharing	12.2 ± 0.77 μs	12.7 ± 0.75 μs	0.96 ± 0.084
utils/count_nodes/preserve_sharing	0.0856 ± 0.0069 ms	0.0843 ± 0.0069 ms	1.01 ± 0.12
utils/get_set_constants!/break_sharing	0.0325 ± 0.0028 ms	0.0322 ± 0.0031 ms	1.01 ± 0.13
utils/get_set_constants!/preserve_sharing	0.172 ± 0.01 ms	0.171 ± 0.0097 ms	1.01 ± 0.083
utils/get_set_constants_parametric	0.0473 ± 0.0062 ms	0.0466 ± 0.0061 ms	1.01 ± 0.19
utils/has_constants/break_sharing	7.39 ± 0.71 μs	7.41 ± 0.62 μs	0.997 ± 0.13
utils/has_operators/break_sharing	2.56 ± 0.15 μs	2.62 ± 0.12 μs	0.98 ± 0.073
utils/hash/break_sharing	23.3 ± 1.5 μs	24 ± 1.8 μs	0.972 ± 0.095
utils/hash/preserve_sharing	0.1 ± 0.0073 ms	0.0998 ± 0.0077 ms	1.01 ± 0.11
utils/index_constant_nodes/break_sharing	28.7 ± 2.4 μs	29 ± 2.1 μs	0.988 ± 0.11
utils/index_constant_nodes/preserve_sharing	0.101 ± 0.008 ms	0.101 ± 0.0075 ms	1 ± 0.11
utils/is_constant/break_sharing	8 ± 0.83 μs	7.91 ± 0.68 μs	1.01 ± 0.14
utils/simplify_tree/break_sharing	31.3 ± 1.2 μs	0.0321 ± 0.0014 ms	0.973 ± 0.055
utils/simplify_tree/preserve_sharing	0.113 ± 0.0076 ms	0.113 ± 0.0072 ms	1 ± 0.093
utils/string_tree/break_sharing	0.443 ± 0.018 ms	0.446 ± 0.018 ms	0.993 ± 0.056
utils/string_tree/preserve_sharing	0.542 ± 0.022 ms	0.541 ± 0.02 ms	1 ± 0.055
time_to_load	0.169 ± 0.0026 s	0.175 ± 0.0024 s	0.965 ± 0.02

Memory benchmarks

	master	847c2c6...	master / 847c2c6...
eval/ComplexF32/evaluation	0.981 k allocs: 2.51 MB	0.99 k allocs: 2.53 MB	0.991
eval/ComplexF64/evaluation	0.969 k allocs: 4.94 MB	0.996 k allocs: 5.07 MB	0.973
eval/Float32/derivative	4.69 k allocs: 17.7 MB	4.55 k allocs: 17.1 MB	1.03
eval/Float32/derivative_turbo	4.64 k allocs: 17.5 MB	4.71 k allocs: 17.7 MB	0.984
eval/Float32/evaluation	0.987 k allocs: 1.29 MB	0.975 k allocs: 1.27 MB	1.01
eval/Float32/evaluation_bumper	0.303 k allocs: 0.393 MB	0.303 k allocs: 0.393 MB	1
eval/Float32/evaluation_turbo	0.963 k allocs: 1.25 MB	0.96 k allocs: 1.25 MB	1
eval/Float32/evaluation_turbo_bumper	0.303 k allocs: 0.393 MB	0.303 k allocs: 0.393 MB	1
eval/Float64/derivative	4.8 k allocs: 0.0351 GB	4.83 k allocs: 0.0353 GB	0.994
eval/Float64/derivative_turbo	4.72 k allocs: 0.0345 GB	4.83 k allocs: 0.0353 GB	0.978
eval/Float64/evaluation	1.01 k allocs: 2.58 MB	0.972 k allocs: 2.49 MB	1.04
eval/Float64/evaluation_bumper	0.303 k allocs: 0.771 MB	0.303 k allocs: 0.771 MB	1
eval/Float64/evaluation_turbo	0.99 k allocs: 2.53 MB	1.01 k allocs: 2.57 MB	0.985
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