[WIP] Hierarchical printing of graph-like expressions

[MilesCranmer]

Say we create an expression:

julia> using DynamicExpressions

julia> x1, x2, x3 = (GraphNode{Float64}(feature=i) for i=1:3);

julia> operators = OperatorEnum(
           binary_operators=[+, -, *, /, ^],
           unary_operators=[cos, sin, exp],
       );

julia> base_tree = cos(x1 - 3.2) * x2 - x3 * x3
(cos(x1 - 3.2) * x2) - (x3 * {x3})

julia> base_tree2 = exp(x3 * x2) - base_tree
exp(x3 * x2) - ((cos(x1 - 3.2) * {x2}) - ({x3} * {x3}))

julia> tree = cos(base_tree * base_tree2) - base_tree * base_tree2 ^ 2
cos(((cos(x1 - 3.2) * x2) - (x3 * {x3})) * (exp({x3} * {x2}) - {((cos(x1 - 3.2) * x2) - (x3 * {x3}))})) - ({((cos(x1 - 3.2) * x2) - (x3 * {x3}))} * ({(exp({x3} * {x2}) - {((cos(x1 - 3.2) * x2) - (x3 * {x3}))})} ^ 2.0))

Note that the normal behavior is to encapsulate with {} when a node is shared.

However, we can print this with less redundancy with pretty_string_graph:

julia> print(pretty_string_graph(tree, operators))
┌─── z1 = (cos(x1 - 3.2) * x2) - (x3 * x3)
├─── z2 = exp(x3 * x2) - z1
│
= cos(z1 * z2) - (z1 * (z2 ^ 2.0))

which finds the shared nodes, assigns variable names based on their depth, and then prints the program in this hierarchical fashion.

This is only 2x slower than the regular string_tree method, so I'm considering have this as the default for GraphNode types. For consistency I might need to prepend the = to regular print statements though...

Curious to hear your thoughts @AlCap23 @Vaibhavdixit02 @ChrisRackauckas! I played around with a few different ideas for how to visualize this in the REPL and this one seemed like a good option. But interested in more.

[github-actions]

Pull Request Test Coverage Report for Build 7344448443

• 70 of 135 (51.85%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-4.2%) to 90.064%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
src/Strings.jl	70	135	51.85%

Totals
Change from base Build 7337169551:	-4.2%
Covered Lines:	1269
Relevant Lines:	1409

---

💛 - Coveralls

[github-actions]

Benchmark Results

	master	9cd35ff...	t[master]/t[9cd35ff...]
eval/ComplexF32/evaluation	7.37 ± 0.52 ms	7.31 ± 0.46 ms	1.01
eval/ComplexF64/evaluation	9.58 ± 0.7 ms	9.5 ± 0.64 ms	1.01
eval/Float32/derivative	10.5 ± 1.3 ms	10.8 ± 1.3 ms	0.972
eval/Float32/derivative_turbo	12.1 ± 1.4 ms	12.3 ± 1.3 ms	0.986
eval/Float32/evaluation	2.65 ± 0.24 ms	2.62 ± 0.22 ms	1.01
eval/Float32/evaluation_turbo	0.618 ± 0.025 ms	0.603 ± 0.026 ms	1.02
eval/Float64/derivative	13.7 ± 0.54 ms	13.3 ± 0.55 ms	1.03
eval/Float64/derivative_turbo	14.5 ± 0.56 ms	14.6 ± 0.54 ms	0.992
eval/Float64/evaluation	2.82 ± 0.24 ms	2.82 ± 0.24 ms	0.999
eval/Float64/evaluation_turbo	1.12 ± 0.058 ms	1.11 ± 0.059 ms	1.01
utils/combine_operators/break_sharing	0.0415 ± 0.0028 ms	0.0409 ± 0.0026 ms	1.01
utils/convert/break_sharing	28.1 ± 0.56 μs	28.4 ± 0.72 μs	0.99
utils/convert/preserve_sharing	0.127 ± 0.0025 ms	0.128 ± 0.0026 ms	0.995
utils/copy/break_sharing	28.9 ± 0.58 μs	28.6 ± 0.63 μs	1.01
utils/copy/preserve_sharing	0.128 ± 0.0027 ms	0.127 ± 0.0025 ms	1
utils/count_constants/break_sharing	11.8 ± 0.22 μs	10.8 ± 0.17 μs	1.09
utils/count_constants/preserve_sharing	0.11 ± 0.0023 ms	0.111 ± 0.0023 ms	0.997
utils/count_depth/break_sharing	12.8 ± 0.22 μs	12.7 ± 0.21 μs	1
utils/count_nodes/break_sharing	10.5 ± 0.18 μs	10.1 ± 0.16 μs	1.03
utils/count_nodes/preserve_sharing	0.114 ± 0.0022 ms	0.114 ± 0.0022 ms	1
utils/get_set_constants!/break_sharing	0.0539 ± 0.00088 ms	0.0523 ± 0.00081 ms	1.03
utils/get_set_constants!/preserve_sharing	0.318 ± 0.0051 ms	0.32 ± 0.0048 ms	0.994
utils/has_constants/break_sharing	4.47 ± 0.22 μs	4.31 ± 0.21 μs	1.04
utils/has_operators/break_sharing	1.78 ± 0.017 μs	1.77 ± 0.016 μs	1
utils/hash/break_sharing	30.4 ± 0.46 μs	30 ± 0.48 μs	1.01
utils/hash/preserve_sharing	0.133 ± 0.0025 ms	0.133 ± 0.0025 ms	1
utils/index_constants/break_sharing	27.5 ± 0.68 μs	27.4 ± 0.76 μs	1
utils/index_constants/preserve_sharing	0.127 ± 0.0024 ms	0.127 ± 0.0024 ms	0.997
utils/is_constant/break_sharing	5.51 ± 0.21 μs	4.77 ± 0.22 μs	1.16
utils/simplify_tree/break_sharing	0.251 ± 0.02 ms	0.248 ± 0.02 ms	1.01
utils/simplify_tree/preserve_sharing	0.377 ± 0.022 ms	0.386 ± 0.022 ms	0.977
utils/string_tree/break_sharing	0.558 ± 0.011 ms	0.582 ± 0.015 ms	0.959
utils/string_tree/preserve_sharing	0.693 ± 0.013 ms	0.7 ± 0.022 ms	0.99
time_to_load	0.683 ± 0.0083 s	0.701 ± 0.0079 s	0.974