Switch to immutable nodes in expressions

[MilesCranmer]

Finally got things working with immutable Node{T} types. This makes the codebase much safer and hopefully also more memory efficient. The fields :val, :l, and :r are now RefValue and can be updated, but the others are set at construction time.

[coveralls]

Pull Request Test Coverage Report for Build 8216463658

Details

• 40 of 42 (95.24%) changed or added relevant lines in 3 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-0.06%) to 94.625%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
src/Equation.jl	24	25	96.0%
src/SimplifyEquation.jl	14	15	93.33%
<!--	Total:	40	42	95.24%	-->

Totals
Change from base Build 7996123220:	-0.06%
Covered Lines:	1602
Relevant Lines:	1693

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💛 - Coveralls

[github-actions[bot]]

Benchmark Results

	master	ad4b372f7eb972...	master/ad4b372f7eb972...
eval/ComplexF32/evaluation	6.97 ± 0.47 ms	7.15 ± 0.45 ms	0.975
eval/ComplexF64/evaluation	9.1 ± 0.69 ms	9.36 ± 0.78 ms	0.972
eval/Float32/derivative	10 ± 1.5 ms	10.4 ± 1.5 ms	0.965
eval/Float32/derivative_turbo	9.98 ± 1.4 ms	10.2 ± 1.5 ms	0.979
eval/Float32/evaluation	2.58 ± 0.24 ms	2.69 ± 0.25 ms	0.96
eval/Float32/evaluation_bumper	0.511 ± 0.019 ms	0.567 ± 0.043 ms	0.901
eval/Float32/evaluation_turbo	0.638 ± 0.039 ms	0.657 ± 0.048 ms	0.97
eval/Float32/evaluation_turbo_bumper	0.511 ± 0.019 ms	0.565 ± 0.042 ms	0.904
eval/Float64/derivative	13.1 ± 0.6 ms	13.2 ± 0.58 ms	0.995
eval/Float64/derivative_turbo	13 ± 0.51 ms	13.3 ± 0.6 ms	0.982
eval/Float64/evaluation	2.79 ± 0.23 ms	2.84 ± 0.25 ms	0.985
eval/Float64/evaluation_bumper	1.12 ± 0.06 ms	1.22 ± 0.067 ms	0.917
eval/Float64/evaluation_turbo	1.1 ± 0.072 ms	1.11 ± 0.071 ms	0.989
eval/Float64/evaluation_turbo_bumper	1.12 ± 0.056 ms	1.22 ± 0.067 ms	0.913
utils/combine_operators/break_sharing	0.0378 ± 0.0022 ms	0.0605 ± 0.0051 ms	0.625
utils/convert/break_sharing	25.7 ± 1.4 μs	0.0516 ± 0.0038 ms	0.498
utils/convert/preserve_sharing	0.118 ± 0.0038 ms	0.259 ± 0.012 ms	0.455
utils/copy/break_sharing	26.6 ± 1.2 μs	0.0518 ± 0.004 ms	0.513
utils/copy/preserve_sharing	0.118 ± 0.0074 ms	0.258 ± 0.018 ms	0.458
utils/count_constants/break_sharing	9.33 ± 0.19 μs	12.4 ± 0.79 μs	0.754
utils/count_constants/preserve_sharing	0.102 ± 0.0034 ms	0.217 ± 0.012 ms	0.471
utils/count_depth/break_sharing	11.6 ± 0.28 μs	18.5 ± 1.5 μs	0.628
utils/count_nodes/break_sharing	9.27 ± 0.27 μs	11.7 ± 0.65 μs	0.794
utils/count_nodes/preserve_sharing	0.104 ± 0.0054 ms	0.221 ± 0.0081 ms	0.472
utils/get_set_constants!/break_sharing	0.0472 ± 0.00098 ms	0.0531 ± 0.0044 ms	0.888
utils/get_set_constants!/preserve_sharing	0.294 ± 0.0095 ms	0.628 ± 0.048 ms	0.469
utils/has_constants/break_sharing	4.38 ± 0.26 μs	5.9 ± 0.47 μs	0.742
utils/has_operators/break_sharing	1.94 ± 0.022 μs	1.91 ± 0.074 μs	1.02
utils/hash/break_sharing	28 ± 0.74 μs	30.4 ± 2.5 μs	0.921
utils/hash/preserve_sharing	0.122 ± 0.0038 ms	0.237 ± 0.019 ms	0.514
utils/index_constants/break_sharing	24.9 ± 0.77 μs	28.5 ± 2.3 μs	0.873
utils/index_constants/preserve_sharing	0.117 ± 0.0068 ms	0.233 ± 0.018 ms	0.503
utils/is_constant/break_sharing	4.36 ± 0.23 μs	5.83 ± 0.5 μs	0.748
utils/simplify_tree/break_sharing	0.169 ± 0.017 ms	0.0924 ± 0.0087 ms	1.83
utils/simplify_tree/preserve_sharing	0.275 ± 0.02 ms	0.304 ± 0.016 ms	0.906
utils/string_tree/break_sharing	0.457 ± 0.029 ms	0.472 ± 0.033 ms	0.968
utils/string_tree/preserve_sharing	0.591 ± 0.029 ms	0.71 ± 0.048 ms	0.833
time_to_load	0.177 ± 0.0018 s	0.189 ± 0.0037 s	0.938

[MilesCranmer]

Wow, this hurts performance by quite a bit! Nevermind then, seems like it's not a good approach.