Array-based storage for expression objects

[MilesCranmer]

Related to the CUDA implementation in #65. However the difference here is that this is a full AbstractNode type, capable of being used in all existing functions. It's also fully writeable, rather than just read-only and generated for the CUDA kernel.

In fact I think this is probably useful to rewrite the CUDA implementation to be a bit leaner. The existing CUDA kernel has a lot of redundancies.

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	76e9a5b...	master / 76e9a5b...
eval/ComplexF32/evaluation	7.3 ± 0.58 ms	7.3 ± 0.55 ms	1 ± 0.11
eval/ComplexF64/evaluation	10.9 ± 1.1 ms	11 ± 1.1 ms	0.996 ± 0.14
eval/Float32/derivative	12.1 ± 0.88 ms	13 ± 1.4 ms	0.928 ± 0.12
eval/Float32/derivative_turbo	12.1 ± 1 ms	13.1 ± 1.6 ms	0.925 ± 0.14
eval/Float32/evaluation	2.77 ± 0.26 ms	2.8 ± 0.26 ms	0.988 ± 0.13
eval/Float32/evaluation_bumper	0.586 ± 0.019 ms	0.583 ± 0.017 ms	1 ± 0.043
eval/Float32/evaluation_turbo	0.544 ± 0.03 ms	0.543 ± 0.038 ms	1 ± 0.09
eval/Float32/evaluation_turbo_bumper	0.586 ± 0.018 ms	0.583 ± 0.018 ms	1 ± 0.044
eval/Float64/derivative	15.3 ± 1.3 ms	16.2 ± 0.87 ms	0.945 ± 0.094
eval/Float64/derivative_turbo	15.5 ± 0.95 ms	16.3 ± 0.85 ms	0.953 ± 0.077
eval/Float64/evaluation	3.21 ± 0.32 ms	3.2 ± 0.33 ms	1 ± 0.15
eval/Float64/evaluation_bumper	1.2 ± 0.044 ms	1.2 ± 0.042 ms	0.998 ± 0.05
eval/Float64/evaluation_turbo	1.06 ± 0.062 ms	1.06 ± 0.062 ms	0.996 ± 0.082
eval/Float64/evaluation_turbo_bumper	1.21 ± 0.046 ms	1.2 ± 0.044 ms	1 ± 0.053
utils/combine_operators/break_sharing	0.0433 ± 0.0036 ms	0.0415 ± 0.002 ms	1.04 ± 0.1
utils/convert/break_sharing	31.2 ± 8 μs	0.0328 ± 0.0078 ms	0.952 ± 0.33
utils/convert/preserve_sharing	0.111 ± 0.013 ms	0.103 ± 0.0099 ms	1.07 ± 0.16
utils/copy/break_sharing	31.6 ± 8.7 μs	30.5 ± 6.1 μs	1.04 ± 0.35
utils/copy/preserve_sharing	0.111 ± 0.013 ms	0.107 ± 0.012 ms	1.04 ± 0.17
utils/count_constant_nodes/break_sharing	14.4 ± 3.3 μs	13.7 ± 2.8 μs	1.05 ± 0.33
utils/count_constant_nodes/preserve_sharing	0.093 ± 0.01 ms	0.0928 ± 0.0099 ms	1 ± 0.15
utils/count_depth/break_sharing	16.4 ± 4.1 μs	16.7 ± 3.4 μs	0.979 ± 0.31
utils/count_nodes/break_sharing	13.7 ± 2.9 μs	13.6 ± 3.2 μs	1.01 ± 0.32
utils/count_nodes/preserve_sharing	0.0931 ± 0.01 ms	0.0939 ± 0.011 ms	0.991 ± 0.16
utils/get_set_constants!/break_sharing	0.0359 ± 0.0054 ms	0.0338 ± 0.0028 ms	1.06 ± 0.18
utils/get_set_constants!/preserve_sharing	0.19 ± 0.015 ms	0.181 ± 0.012 ms	1.05 ± 0.11
utils/get_set_constants_parametric	0.0501 ± 0.0059 ms	0.0515 ± 0.01 ms	0.973 ± 0.23
utils/has_constants/break_sharing	8.66 ± 2.5 μs	9.9 ± 3 μs	0.875 ± 0.37
utils/has_operators/break_sharing	2.78 ± 0.49 μs	2.9 ± 0.51 μs	0.959 ± 0.24
utils/hash/break_sharing	25.8 ± 4.8 μs	26.4 ± 5.1 μs	0.975 ± 0.26
utils/hash/preserve_sharing	0.106 ± 0.01 ms	0.0993 ± 0.0083 ms	1.07 ± 0.14
utils/index_constant_nodes/break_sharing	0.0324 ± 0.0069 ms	0.0328 ± 0.0059 ms	0.988 ± 0.28
utils/index_constant_nodes/preserve_sharing	0.113 ± 0.011 ms	0.112 ± 0.014 ms	1.01 ± 0.16
utils/is_constant/break_sharing	10.8 ± 3.3 μs	10.7 ± 3.4 μs	1.01 ± 0.44
utils/simplify_tree/break_sharing	28.3 ± 5.1 μs	27.4 ± 4.6 μs	1.03 ± 0.25
utils/simplify_tree/preserve_sharing	0.112 ± 0.012 ms	0.115 ± 0.012 ms	0.978 ± 0.14
utils/string_tree/break_sharing	0.523 ± 0.04 ms	0.524 ± 0.039 ms	0.997 ± 0.11
utils/string_tree/preserve_sharing	0.619 ± 0.028 ms	0.617 ± 0.024 ms	1 ± 0.06
time_to_load	0.242 ± 0.0077 s	0.292 ± 0.0073 s	0.83 ± 0.034

Memory benchmarks

	master	76e9a5b...	master / 76e9a5b...
eval/ComplexF32/evaluation	0.978 k allocs: 2.5 MB	0.981 k allocs: 2.51 MB	0.997
eval/ComplexF64/evaluation	0.99 k allocs: 5.04 MB	1.01 k allocs: 5.15 MB	0.979
eval/Float32/derivative	4.69 k allocs: 17.7 MB	4.58 k allocs: 17.2 MB	1.02
eval/Float32/derivative_turbo	4.66 k allocs: 17.5 MB	4.68 k allocs: 17.6 MB	0.996
eval/Float32/evaluation	0.972 k allocs: 1.27 MB	0.969 k allocs: 1.26 MB	1
eval/Float32/evaluation_bumper	0.303 k allocs: 0.393 MB	0.303 k allocs: 0.393 MB	1
eval/Float32/evaluation_turbo	0.969 k allocs: 1.26 MB	0.981 k allocs: 1.28 MB	0.988
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	4.84 k allocs: 0.0354 GB	0.991
eval/Float64/derivative_turbo	4.78 k allocs: 0.0349 GB	4.77 k allocs: 0.0349 GB	1
eval/Float64/evaluation	0.981 k allocs: 2.51 MB	1.01 k allocs: 2.58 MB	0.973
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	0.999 k allocs: 2.56 MB	0.988
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	4 allocs: 0.953 kB	4 allocs: 0.953 kB	1
utils/simplify_tree/preserve_sharing	0.404 k allocs: 0.0696 MB	0.404 k allocs: 0.0696 MB	1
utils/string_tree/break_sharing	11.8 k allocs: 1.04 MB	11.8 k allocs: 1.04 MB	1
utils/string_tree/preserve_sharing	12.2 k allocs: 1.11 MB	12.2 k allocs: 1.11 MB	1
time_to_load	0.159 k allocs: 11.2 kB	0.159 k allocs: 11.2 kB	1

[codecov]

Codecov Report

❌ Patch coverage is 0% with 245 lines in your changes missing coverage. Please review.
✅ Project coverage is 3.06%. Comparing base (2c8d3ca) to head (76e9a5b).

Files with missing lines	Patch %	Lines
src/ArrayNode.jl	0.00%	245 Missing ⚠️

❗ There is a different number of reports uploaded between BASE (2c8d3ca) and HEAD (76e9a5b). Click for more details.

HEAD has 4 uploads less than BASE

Flag	BASE (2c8d3ca)	HEAD (76e9a5b)
	5	1

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #138       +/-   ##
==========================================
- Coverage   96.66%   3.06%   -93.61%     
==========================================
  Files          30      31        +1     
  Lines        2612    2745      +133     
==========================================
- Hits         2525      84     -2441     
- Misses         87    2661     +2574     

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