Fix negative fraction simplification (issue JuliaSymbolics/Symbolic.jl#1773)

[ParthsarthiSingh-glang]

Fixes JuliaSymbolics/Symbolics.jl#1773

[github-actions]

Benchmark Results (Julia vlts)

Time benchmarks

	master	e3e56f5...	master / e3e56f5...
arithmetic/2-arg mul	12.5 ± 0.35 μs	12.9 ± 0.34 μs	0.971 ± 0.037
arithmetic/addition	0.0777 ± 0.0013 ms	0.0778 ± 0.0012 ms	0.998 ± 0.023
arithmetic/division	23.9 ± 0.72 μs	24 ± 0.64 μs	0.996 ± 0.04
arithmetic/multiplication	0.061 ± 0.0025 ms	0.0614 ± 0.0018 ms	0.994 ± 0.05
overhead/acrule/a+2	2.43 ± 0.1 μs	2.34 ± 0.1 μs	1.04 ± 0.062
overhead/acrule/a+2+b	0.06 ± 0.01 μs	0.06 ± 0.01 μs	1 ± 0.24
overhead/acrule/a+b	4.35 ± 0.18 μs	4.14 ± 0.34 μs	1.05 ± 0.097
overhead/acrule/noop:Int	0.05 ± 0.009 μs	0.05 ± 0 μs	1 ± 0.18
overhead/acrule/noop:Sym	0.05 ± 0.01 μs	0.05 ± 0.01 μs	1 ± 0.28
overhead/get_degrees/large_poly	0.08 ± 0 μs	0.08 ± 0.02 μs	1 ± 0.25
overhead/rule/noop:Int	0.06 ± 0.01 μs	0.06 ± 0.001 μs	1 ± 0.17
overhead/rule/noop:Sym	0.06 ± 0.001 μs	0.06 ± 0.01 μs	1 ± 0.17
overhead/rule/noop:Term	0.06 ± 0.001 μs	0.06 ± 0.01 μs	1 ± 0.17
overhead/ruleset/noop:Int	30 ± 0 ns	30 ± 0 ns	1 ± 0
overhead/ruleset/noop:Sym	0.24 ± 0.01 μs	0.231 ± 0.01 μs	1.04 ± 0.062
overhead/ruleset/noop:Term	1.03 ± 0.029 μs	1.03 ± 0.029 μs	1 ± 0.04
overhead/simplify/noop:Int	30 ± 0 ns	30 ± 0 ns	1 ± 0
overhead/simplify/noop:Sym	0.04 ± 0.01 μs	0.04 ± 0.01 μs	1 ± 0.35
overhead/simplify/noop:Term	27.9 ± 0.92 μs	26.8 ± 0.9 μs	1.04 ± 0.049
overhead/simplify/randterm (+, *):serial	0.274 ± 0.0032 s	0.233 ± 0.0011 s	1.18 ± 0.015
overhead/simplify/randterm (+, *):thread	0.304 ± 0.016 s	0.261 ± 0.018 s	1.17 ± 0.1
overhead/simplify/randterm (/, *):serial	0.165 ± 0.0055 ms	0.0753 ± 0.0016 ms	2.19 ± 0.087
overhead/simplify/randterm (/, *):thread	0.168 ± 0.0057 ms	0.0786 ± 0.0017 ms	2.14 ± 0.085
overhead/substitute/a	0.038 ± 0.00071 ms	0.0404 ± 0.00071 ms	0.941 ± 0.024
overhead/substitute/a,b	0.0455 ± 0.00077 ms	0.048 ± 0.00078 ms	0.947 ± 0.022
overhead/substitute/a,b,c	0.0417 ± 0.0007 ms	0.0423 ± 0.00072 ms	0.986 ± 0.024
polyform/easy_iszero	22.2 ± 0.45 μs	22.8 ± 0.44 μs	0.972 ± 0.027
polyform/isone	1.02 ± 0.028 ms	1.05 ± 0.027 ms	0.973 ± 0.037
polyform/isone:noop	0.08 ± 0 μs	0.08 ± 0 μs	1 ± 0
polyform/iszero	0.853 ± 0.025 ms	0.886 ± 0.021 ms	0.963 ± 0.037
polyform/iszero:noop	0.08 ± 0.01 μs	0.08 ± 0.001 μs	1 ± 0.13
polyform/simplify_fractions	1.1 ± 0.031 ms	1.13 ± 0.026 ms	0.98 ± 0.035
printing/large_poly	0.218 ± 0.0028 s	0.216 ± 0.0023 s	1.01 ± 0.017
time_to_load	1.59 ± 0.0073 s	1.29 ± 0.0053 s	1.24 ± 0.0077

Memory benchmarks

	master	e3e56f5...	master / e3e56f5...
arithmetic/2-arg mul	0.078 k allocs: 2.72 kB	0.077 k allocs: 2.69 kB	1.01
arithmetic/addition	0.468 k allocs: 16.9 kB	0.438 k allocs: 16 kB	1.06
arithmetic/division	0.142 k allocs: 5.47 kB	0.14 k allocs: 5.41 kB	1.01
arithmetic/multiplication	0.356 k allocs: 11.7 kB	0.356 k allocs: 11.7 kB	1
overhead/acrule/a+2	0.034 k allocs: 1.25 kB	0.033 k allocs: 1.23 kB	1.01
overhead/acrule/a+2+b	0 allocs: 0 B	0 allocs: 0 B
overhead/acrule/a+b	0.047 k allocs: 1.8 kB	0.045 k allocs: 1.77 kB	1.02
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	2 allocs: 32 B	2 allocs: 32 B	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	0.298 k allocs: 11.5 kB	0.282 k allocs: 11.4 kB	1.01
overhead/simplify/randterm (+, *):serial	2.55 M allocs: 0.0975 GB	2.22 M allocs: 0.0871 GB	1.12
overhead/simplify/randterm (+, *):thread	2.6 M allocs: 0.255 GB	2.26 M allocs: 0.245 GB	1.04
overhead/simplify/randterm (/, *):serial	2.04 k allocs: 0.0733 MB	0.781 k allocs: 29.4 kB	2.55
overhead/simplify/randterm (/, *):thread	2.07 k allocs: 0.0743 MB	0.816 k allocs: 30.5 kB	2.5
overhead/substitute/a	0.22 k allocs: 8.42 kB	0.22 k allocs: 8.42 kB	1
overhead/substitute/a,b	0.267 k allocs: 10.1 kB	0.267 k allocs: 10.1 kB	1
overhead/substitute/a,b,c	0.238 k allocs: 8.62 kB	0.238 k allocs: 8.62 kB	1
polyform/easy_iszero	0.133 k allocs: 4.58 kB	0.127 k allocs: 4.48 kB	1.02
polyform/isone	8.33 k allocs: 0.573 MB	7.98 k allocs: 0.568 MB	1.01
polyform/isone:noop	1 allocs: 16 B	1 allocs: 16 B	1
polyform/iszero	6.86 k allocs: 0.474 MB	6.7 k allocs: 0.471 MB	1.01
polyform/iszero:noop	1 allocs: 16 B	1 allocs: 16 B	1
polyform/simplify_fractions	8.81 k allocs: 0.596 MB	8.64 k allocs: 0.593 MB	1.01
printing/large_poly	1.86 M allocs: 0.082 GB	1.86 M allocs: 0.082 GB	1
time_to_load	0.153 k allocs: 14.5 kB	0.153 k allocs: 14.5 kB	1

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	e3e56f5...	master / e3e56f5...
arithmetic/2-arg mul	10.2 ± 0.27 μs	10.5 ± 0.26 μs	0.967 ± 0.035
arithmetic/addition	0.0687 ± 0.00091 ms	0.0684 ± 0.00082 ms	1.01 ± 0.018
arithmetic/division	24.8 ± 0.66 μs	24.6 ± 0.59 μs	1.01 ± 0.036
arithmetic/multiplication	0.0528 ± 0.0023 ms	0.055 ± 0.0025 ms	0.959 ± 0.06
overhead/acrule/a+2	2.2 ± 0.04 μs	2.15 ± 0.061 μs	1.02 ± 0.034
overhead/acrule/a+2+b	0.071 ± 0.01 μs	0.07 ± 0.01 μs	1.01 ± 0.2
overhead/acrule/a+b	3.73 ± 0.069 μs	3.68 ± 0.07 μs	1.01 ± 0.027
overhead/acrule/noop:Int	30 ± 0 ns	30 ± 0 ns	1 ± 0
overhead/acrule/noop:Sym	0.06 ± 0 μs	0.06 ± 0 μs	1 ± 0
overhead/get_degrees/large_poly	0.071 ± 0.01 μs	0.07 ± 0.001 μs	1.01 ± 0.14
overhead/rule/noop:Int	0.06 ± 0.01 μs	0.06 ± 0.001 μs	1 ± 0.17
overhead/rule/noop:Sym	0.07 ± 0.01 μs	0.06 ± 0.01 μs	1.17 ± 0.26
overhead/rule/noop:Term	0.07 ± 0.01 μs	0.06 ± 0.01 μs	1.17 ± 0.26
overhead/ruleset/noop:Int	30 ± 0 ns	30 ± 0 ns	1 ± 0
overhead/ruleset/noop:Sym	0.311 ± 0.001 μs	0.311 ± 0.001 μs	1 ± 0.0045
overhead/ruleset/noop:Term	1.15 ± 0.02 μs	1.13 ± 0.03 μs	1.02 ± 0.032
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	26.2 ± 0.6 μs	26.2 ± 0.6 μs	1 ± 0.033
overhead/simplify/randterm (+, *):serial	0.226 ± 0.028 s	0.196 ± 0.022 s	1.15 ± 0.19
overhead/simplify/randterm (+, *):thread	0.286 ± 0.038 s	0.253 ± 0.042 s	1.13 ± 0.24
overhead/simplify/randterm (/, *):serial	0.159 ± 0.02 ms	0.085 ± 0.0029 ms	1.87 ± 0.25
overhead/simplify/randterm (/, *):thread	0.167 ± 0.02 ms	0.0949 ± 0.0082 ms	1.76 ± 0.26
overhead/substitute/a	0.0338 ± 0.00078 ms	0.0345 ± 0.0009 ms	0.981 ± 0.034
overhead/substitute/a,b	0.0424 ± 0.0011 ms	0.043 ± 0.001 ms	0.986 ± 0.035
overhead/substitute/a,b,c	0.0406 ± 0.0011 ms	0.0405 ± 0.00094 ms	1 ± 0.036
polyform/easy_iszero	18.7 ± 0.42 μs	19.2 ± 0.4 μs	0.973 ± 0.03
polyform/isone	0.95 ± 0.024 ms	0.929 ± 0.018 ms	1.02 ± 0.032
polyform/isone:noop	0.07 ± 0 μs	0.07 ± 0 μs	1 ± 0
polyform/iszero	0.824 ± 0.023 ms	0.806 ± 0.02 ms	1.02 ± 0.039
polyform/iszero:noop	0.07 ± 0.001 μs	0.08 ± 0.01 μs	0.875 ± 0.11
polyform/simplify_fractions	1.02 ± 0.027 ms	0.999 ± 0.023 ms	1.02 ± 0.035
printing/large_poly	0.197 ± 0.013 s	0.192 ± 0.013 s	1.02 ± 0.096
time_to_load	1.74 ± 0.034 s	1.45 ± 0.018 s	1.2 ± 0.028

Memory benchmarks

	master	e3e56f5...	master / e3e56f5...
arithmetic/2-arg mul	0.056 k allocs: 1.78 kB	0.056 k allocs: 1.78 kB	1
arithmetic/addition	0.33 k allocs: 11.3 kB	0.3 k allocs: 10.3 kB	1.09
arithmetic/division	0.132 k allocs: 4.77 kB	0.132 k allocs: 4.77 kB	1
arithmetic/multiplication	0.252 k allocs: 6.5 kB	0.252 k allocs: 6.5 kB	1
overhead/acrule/a+2	0.034 k allocs: 1.12 kB	0.034 k allocs: 1.12 kB	1
overhead/acrule/a+2+b	0 allocs: 0 B	0 allocs: 0 B
overhead/acrule/a+b	0.046 k allocs: 1.55 kB	0.046 k allocs: 1.55 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	2 allocs: 32 B	2 allocs: 32 B	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	0.284 k allocs: 9.91 kB	0.284 k allocs: 10 kB	0.989
overhead/simplify/randterm (+, *):serial	2.39 M allocs: 0.0828 GB	2.16 M allocs: 0.0755 GB	1.1
overhead/simplify/randterm (+, *):thread	2.54 M allocs: 0.245 GB	2.32 M allocs: 0.237 GB	1.03
overhead/simplify/randterm (/, *):serial	1.91 k allocs: 0.0655 MB	0.783 k allocs: 28.2 kB	2.37
overhead/simplify/randterm (/, *):thread	2.05 k allocs: 0.0704 MB	0.918 k allocs: 0.0325 MB	2.17
overhead/substitute/a	0.172 k allocs: 6.05 kB	0.172 k allocs: 6.05 kB	1
overhead/substitute/a,b	0.223 k allocs: 7.69 kB	0.223 k allocs: 7.69 kB	1
overhead/substitute/a,b,c	0.229 k allocs: 7.81 kB	0.229 k allocs: 7.81 kB	1
polyform/easy_iszero	0.092 k allocs: 2.94 kB	0.092 k allocs: 2.94 kB	1
polyform/isone	10.9 k allocs: 0.578 MB	10.9 k allocs: 0.578 MB	1
polyform/isone:noop	1 allocs: 16 B	1 allocs: 16 B	1
polyform/iszero	8.96 k allocs: 0.48 MB	8.96 k allocs: 0.48 MB	1
polyform/iszero:noop	1 allocs: 16 B	1 allocs: 16 B	1
polyform/simplify_fractions	11.4 k allocs: 0.595 MB	11.4 k allocs: 0.595 MB	1
printing/large_poly	2.15 M allocs: 0.079 GB	2.15 M allocs: 0.079 GB	1
time_to_load	0.145 k allocs: 11 kB	0.145 k allocs: 11 kB	1