another mechanism for rules

[Bumblebee00]

In terms of performance the two biggest problem of rule macro are:

• creating the rule object: calls recursively a lor of functions that return other functions (that are closures)
• type inference: first time executing the rule takes some time

So i tought of a simpler approach: instead of creating the a rule object we just store the quoted expression, and then we check if it's equal to the input expression with a simple recursive function. And problem 1 goes away. For problem 2 I tried to write this recursive function specifying the types but I am not sure I made it corrrectly. I made a test in wich 100 rules are created and 100 random expressions are compared to the rules, both using the old @ rule macro and this new approach, and it seems 25 times faster.

[github-actions]

Benchmark Results (Julia vlts)

Time benchmarks

	master	366fd3e...	master / 366fd3e...
arithmetic/addition	0.0752 ± 0.00088 ms	0.076 ± 0.00099 ms	0.989 ± 0.017
arithmetic/division	28.3 ± 0.69 μs	30 ± 0.85 μs	0.941 ± 0.035
arithmetic/multiplication	0.06 ± 0.0016 ms	0.0636 ± 0.0017 ms	0.943 ± 0.035
overhead/acrule/a+2	2.73 ± 0.051 μs	2.85 ± 0.061 μs	0.961 ± 0.027
overhead/acrule/a+2+b	0.07 ± 0 μs	0.07 ± 0 μs	1 ± 0
overhead/acrule/a+b	4.89 ± 0.11 μs	5.13 ± 0.12 μs	0.953 ± 0.031
overhead/acrule/noop:Int	0.05 ± 0.01 μs	0.05 ± 0.01 μs	1 ± 0.28
overhead/acrule/noop:Sym	0.06 ± 0.01 μs	0.06 ± 0.01 μs	1 ± 0.24
overhead/get_degrees/large_poly	0.0994 ± 0.0039 s	0.103 ± 0.004 s	0.968 ± 0.054
overhead/rule/noop:Int	0.07 ± 0 μs	0.07 ± 0 μs	1 ± 0
overhead/rule/noop:Sym	0.06 ± 0.01 μs	0.06 ± 0.01 μs	1 ± 0.24
overhead/rule/noop:Term	0.06 ± 0.01 μs	0.06 ± 0.01 μs	1 ± 0.24
overhead/ruleset/noop:Int	30 ± 0 ns	30 ± 0 ns	1 ± 0
overhead/ruleset/noop:Sym	0.31 ± 0.01 μs	0.301 ± 0.01 μs	1.03 ± 0.048
overhead/ruleset/noop:Term	1.2 ± 0.02 μs	1.21 ± 0.029 μs	0.992 ± 0.029
overhead/simplify/noop:Int	30 ± 0 ns	30 ± 0 ns	1 ± 0
overhead/simplify/noop:Sym	30 ± 10 ns	30 ± 10 ns	1 ± 0.47
overhead/simplify/noop:Term	0.0324 ± 0.00095 ms	0.0331 ± 0.0013 ms	0.977 ± 0.047
overhead/simplify/randterm (+, *):serial	0.259 ± 0.0057 s	0.27 ± 0.0058 s	0.959 ± 0.029
overhead/simplify/randterm (+, *):thread	0.323 ± 0.15 s	0.322 ± 0.11 s	1 ± 0.58
overhead/simplify/randterm (/, *):serial	0.0907 ± 0.0021 ms	0.0939 ± 0.0021 ms	0.965 ± 0.031
overhead/simplify/randterm (/, *):thread	0.0941 ± 0.0019 ms	0.0962 ± 0.0021 ms	0.978 ± 0.029
overhead/substitute/a	0.0509 ± 0.0011 ms	0.0501 ± 0.0012 ms	1.02 ± 0.033
overhead/substitute/a,b	0.0638 ± 0.0014 ms	0.0624 ± 0.0013 ms	1.02 ± 0.03
overhead/substitute/a,b,c	0.0579 ± 0.0012 ms	0.0558 ± 0.0014 ms	1.04 ± 0.034
polyform/easy_iszero	23.2 ± 0.45 μs	23.8 ± 0.5 μs	0.974 ± 0.028
polyform/isone	1.07 ± 0.027 ms	1.09 ± 0.02 ms	0.981 ± 0.031
polyform/isone:noop	0.15 ± 0.001 μs	0.231 ± 0.01 μs	0.649 ± 0.028
polyform/iszero	0.909 ± 0.024 ms	0.926 ± 0.015 ms	0.981 ± 0.03
polyform/iszero:noop	0.15 ± 0.01 μs	0.23 ± 0.01 μs	0.652 ± 0.052
polyform/simplify_fractions	1.18 ± 0.03 ms	1.21 ± 0.026 ms	0.98 ± 0.032
time_to_load	1.17 ± 0.0046 s	1.18 ± 0.0094 s	0.994 ± 0.0088

Memory benchmarks

	master	366fd3e...	master / 366fd3e...
arithmetic/addition	0.438 k allocs: 16 kB	0.438 k allocs: 16 kB	1
arithmetic/division	0.198 k allocs: 6.89 kB	0.198 k allocs: 6.89 kB	1
arithmetic/multiplication	0.357 k allocs: 11.7 kB	0.357 k allocs: 11.7 kB	1
overhead/acrule/a+2	0.037 k allocs: 1.29 kB	0.037 k allocs: 1.29 kB	1
overhead/acrule/a+2+b	0 allocs: 0 B	0 allocs: 0 B
overhead/acrule/a+b	0.053 k allocs: 1.88 kB	0.053 k allocs: 1.88 kB	1
overhead/acrule/noop:Int	0 allocs: 0 B	0 allocs: 0 B
overhead/acrule/noop:Sym	0 allocs: 0 B	0 allocs: 0 B
overhead/get_degrees/large_poly	0.712 M allocs: 20.6 MB	0.712 M allocs: 20.6 MB	1
overhead/rule/noop:Int	2 allocs: 0.0625 kB	2 allocs: 0.0625 kB	1
overhead/rule/noop:Sym	2 allocs: 0.0625 kB	2 allocs: 0.0625 kB	1
overhead/rule/noop:Term	2 allocs: 0.0625 kB	2 allocs: 0.0625 kB	1
overhead/ruleset/noop:Int	0 allocs: 0 B	0 allocs: 0 B
overhead/ruleset/noop:Sym	3 allocs: 0.109 kB	3 allocs: 0.109 kB	1
overhead/ruleset/noop:Term	12 allocs: 0.391 kB	12 allocs: 0.391 kB	1
overhead/simplify/noop:Int	0 allocs: 0 B	0 allocs: 0 B
overhead/simplify/noop:Sym	0 allocs: 0 B	0 allocs: 0 B
overhead/simplify/noop:Term	0.388 k allocs: 14.4 kB	0.388 k allocs: 14.4 kB	1
overhead/simplify/randterm (+, *):serial	2.96 M allocs: 0.106 GB	2.96 M allocs: 0.106 GB	1
overhead/simplify/randterm (+, *):thread	2.96 M allocs: 0.263 GB	2.96 M allocs: 0.263 GB	1
overhead/simplify/randterm (/, *):serial	0.869 k allocs: 30.8 kB	0.869 k allocs: 30.8 kB	1
overhead/simplify/randterm (/, *):thread	0.894 k allocs: 31.5 kB	0.894 k allocs: 31.5 kB	1
overhead/substitute/a	0.308 k allocs: 11 kB	0.308 k allocs: 11 kB	1
overhead/substitute/a,b	0.394 k allocs: 13.9 kB	0.394 k allocs: 13.9 kB	1
overhead/substitute/a,b,c	0.355 k allocs: 12.1 kB	0.355 k allocs: 12.1 kB	1
polyform/easy_iszero	0.146 k allocs: 4.92 kB	0.146 k allocs: 4.92 kB	1
polyform/isone	9.22 k allocs: 0.589 MB	9.22 k allocs: 0.589 MB	1
polyform/isone:noop	2 allocs: 32 B	2 allocs: 32 B	1
polyform/iszero	7.58 k allocs: 0.484 MB	7.58 k allocs: 0.484 MB	1
polyform/iszero:noop	2 allocs: 32 B	2 allocs: 32 B	1
polyform/simplify_fractions	10.3 k allocs: 0.627 MB	10.3 k allocs: 0.627 MB	1
time_to_load	0.153 k allocs: 14.5 kB	0.153 k allocs: 14.5 kB	1