Details

analyze164.0ms (6.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
28.6%	25%	62.4%	0.1%	12.5%	0%	0%	6
42.9%	37.5%	50%	0.1%	12.5%	0%	0%	7
55.6%	46.8%	37.5%	0.1%	15.6%	0%	0%	8
63.6%	53.1%	30.4%	0.1%	16.4%	0%	0%	9
73.9%	58.5%	20.7%	0.1%	20.7%	0%	0%	10
79.3%	62%	16.2%	0.1%	21.7%	0%	0%	11
85.7%	65%	10.8%	0.1%	24.1%	0%	0%	12

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (42.8%)

Results

1.1s	8256×	body	256	valid
37.0ms	454×	body	256	infinite

Bogosity

preprocess66.0ms (2.5%)

Algorithm

2×	egg-herbie

Rules

1028×	`fma-def`
288×	`associate-r`
248×	`distribute-lft-in`
230×	`*-commutative`
216×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	33	38
2	77	38
3	149	38
4	267	38
5	571	38
6	1201	38
7	1671	38
8	1972	38
9	2118	38
10	2120	38
11	2120	38
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (-.f64 (.f64 y y) (*.f64 y x)))

Outputs
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (-.f64 (.f64 y y) (*.f64 y x)))
(.f64 2 (.f64 y (-.f64 y x)))
(.f64 (.f64 2 y) (-.f64 y x))
(.f64 (-.f64 y x) (.f64 2 y))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify48.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def`
372×	`associate-r`
184×	`*-commutative`
168×	`distribute-lft-in`
160×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	21	19
2	49	19
3	100	19
4	177	19
5	283	19
6	534	19
7	1043	19
8	1449	19
9	1683	19
10	1733	19

Stop Event

1×

saturated

Counts

1 → 4

Calls

Call 1

Inputs
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Outputs
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(.f64 (.f64 2 x) (-.f64 x y))
(.f64 (-.f64 x y) (.f64 2 x))

eval1.0ms (0%)

Compiler: Compiled 32 to 17 computations (46.9% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	2	2	4
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	2	3	5

Error

0.01%

Counts

5 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.04%	(.f64 (-.f64 x y) (.f64 2 x))
▶	0.02%	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 20 to 13 computations (35% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.02%	(-.f64 (.f64 x x) (.f64 x y))

Compiler

Compiled 27 to 8 computations (70.4% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(-.f64 (.f64 x x) (.f64 x y))
0.0ms	x	@	0	(-.f64 (.f64 x x) (.f64 x y))
0.0ms	y	@	inf	(-.f64 (.f64 x x) (.f64 x y))
0.0ms	y	@	0	(-.f64 (.f64 x x) (.f64 x y))
0.0ms	x	@	-inf	(-.f64 (.f64 x x) (.f64 x y))

rewrite63.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1796×	`add-sqr-sqrt`
1776×	`*-un-lft-identity`
1662×	`add-cube-cbrt`
1648×	`add-cbrt-cube`
170×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	160	13
2	2290	13

Stop Event

1×	node limit

Counts

1 → 53

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 x y))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 x (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (+.f64 (.f64 x (neg.f64 y)) (fma.f64 (neg.f64 y) x (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 (.f64 x (neg.f64 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (.f64 x (neg.f64 y)) 1 (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 x y))) (sqrt.f64 (.f64 x y)) (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 x y))) (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (neg.f64 y)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 x (-.f64 x y))) (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 x y) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (/.f64 1 (.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x (sqrt.f64 (.f64 x y))) (-.f64 x (sqrt.f64 (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 x (+.f64 x y)) (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))) (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x (neg.f64 y)) (.f64 x (neg.f64 y)))) (-.f64 (.f64 x x) (.f64 x (neg.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))) (-.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (.f64 x (neg.f64 y)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x (neg.f64 y)) (.f64 x (neg.f64 y))) (.f64 (.f64 x x) (.f64 x (neg.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) 3)) (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (-.f64 (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))) (.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))) (neg.f64 (.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (-.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x (-.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x (-.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (-.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (-.f64 x y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (.f64 x (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (.f64 x (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (.f64 x x)) (*.f64 x (neg.f64 y)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (+.f64 (*.f64 x (neg.f64 y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 (*.f64 x (neg.f64 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (+.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (*.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (*.f64 x (neg.f64 y)) 1 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 (*.f64 x y))) (sqrt.f64 (*.f64 x y)) (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (neg.f64 y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (*.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 x y) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2)) (/.f64 1 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sqrt.f64 (*.f64 x y))) (-.f64 x (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (+.f64 x y)) (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y)))) (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2)) (*.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3)) (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x (neg.f64 y)) (*.f64 x (neg.f64 y)))) (-.f64 (*.f64 x x) (*.f64 x (neg.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2) (*.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y)))) (-.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (*.f64 x (neg.f64 y)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x (neg.f64 y)) (*.f64 x (neg.f64 y))) (*.f64 (*.f64 x x) (*.f64 x (neg.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 3)) (+.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2) (-.f64 (*.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))) (*.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2))) (neg.f64 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (-.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (-.f64 x y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 x (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 x (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (*.f64 x (neg.f64 y)))))))

simplify54.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1554×	`times-frac`
1538×	`fma-def`
838×	`associate-/l*`
610×	`*-commutative`
570×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	1725
1	397	1601
2	1893	1483

Stop Event

1×	node limit

Counts

77 → 75

Calls

Call 1

Inputs
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (.f64 x x) (.f64 x (neg.f64 y)))
(+.f64 (.f64 x x) (+.f64 (.f64 x (neg.f64 y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))
(+.f64 (.f64 x x) (.f64 (*.f64 x (neg.f64 y)) 1))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))
(+.f64 (.f64 x (-.f64 x y)) (.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 1))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (.f64 x (neg.f64 y)) 1 (*.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 x y))) (sqrt.f64 (.f64 x y)) (.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 x y))) (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 x y)))
(+.f64 (.f64 x (neg.f64 y)) (.f64 x x))
(+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (.f64 x (-.f64 x y)))
(*.f64 x (-.f64 x y))
(.f64 (.f64 x (-.f64 x y)) 1)
(.f64 1 (.f64 x (-.f64 x y)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 x y)))
(.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))
(.f64 (cbrt.f64 (.f64 x x)) (*.f64 (cbrt.f64 x) (-.f64 x y)))
(.f64 (cbrt.f64 (.f64 x (-.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))))
(*.f64 (-.f64 x y) x)
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (/.f64 1 (*.f64 x (+.f64 x y))))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (*.f64 x (+.f64 x y))))))
(.f64 (+.f64 x (sqrt.f64 (.f64 x y))) (-.f64 x (sqrt.f64 (*.f64 x y))))
(/.f64 1 (/.f64 (.f64 x (+.f64 x y)) (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))) (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (.f64 x (+.f64 x y)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x (neg.f64 y)) (.f64 x (neg.f64 y)))) (-.f64 (.f64 x x) (*.f64 x (neg.f64 y))))
(/.f64 (-.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))) (-.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (.f64 x (neg.f64 y)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x (neg.f64 y)) (.f64 x (neg.f64 y))) (.f64 (.f64 x x) (*.f64 x (neg.f64 y))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) 3)) (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (-.f64 (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))) (.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))) (neg.f64 (.f64 x (+.f64 x y))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y))))))
(pow.f64 (*.f64 x (-.f64 x y)) 1)
(pow.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 3)
(pow.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2))
(log.f64 (pow.f64 (exp.f64 x) (-.f64 x y)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (-.f64 x y)))))
(cbrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (-.f64 x y))))
(exp.f64 (log.f64 (*.f64 x (-.f64 x y))))
(exp.f64 (.f64 (log.f64 (.f64 x (-.f64 x y))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (-.f64 x y))))
(fma.f64 x x (*.f64 x (neg.f64 y)))
(fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(fma.f64 1 (.f64 x x) (.f64 x (neg.f64 y)))
(fma.f64 1 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))
(fma.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (.f64 x x)) (.f64 x (neg.f64 y)))

Outputs
(.f64 -1 (.f64 y x))
(*.f64 x (neg.f64 y))
(*.f64 y (neg.f64 x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(.f64 -1 (.f64 y x))
(*.f64 x (neg.f64 y))
(*.f64 y (neg.f64 x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(.f64 -1 (.f64 y x))
(*.f64 x (neg.f64 y))
(*.f64 y (neg.f64 x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x x) (.f64 x (neg.f64 y)))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x x) (+.f64 (.f64 x (neg.f64 y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x x) (.f64 (*.f64 x (neg.f64 y)) 1))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 1))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (.f64 x y)))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (.f64 x (neg.f64 y)) 1 (*.f64 x y)))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 x y))) (sqrt.f64 (.f64 x y)) (.f64 x y)))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 x y))) (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 x y)))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (neg.f64 y)) (.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (.f64 x (-.f64 x y)))
(*.f64 x (-.f64 x y))
(*.f64 x (-.f64 x y))
(.f64 (.f64 x (-.f64 x y)) 1)
(*.f64 x (-.f64 x y))
(.f64 1 (.f64 x (-.f64 x y)))
(*.f64 x (-.f64 x y))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 x y)))
(*.f64 x (-.f64 x y))
(.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))
(*.f64 x (-.f64 x y))
(.f64 (cbrt.f64 (.f64 x x)) (*.f64 (cbrt.f64 x) (-.f64 x y)))
(.f64 (.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x)) (-.f64 x y))
(.f64 (-.f64 x y) (.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x)))
(.f64 (cbrt.f64 (.f64 x (-.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2))
(*.f64 x (-.f64 x y))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))))
(*.f64 x (-.f64 x y))
(*.f64 (-.f64 x y) x)
(*.f64 x (-.f64 x y))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (/.f64 1 (*.f64 x (+.f64 x y))))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 (/.f64 1 x) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(.f64 (/.f64 x 1) (/.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 y x)))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (*.f64 x (+.f64 x y))))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 (.f64 y x) (*.f64 x (+.f64 y x)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 x (*.f64 y x)) (+.f64 y x) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 x (.f64 (*.f64 y x) (+.f64 y x)) (pow.f64 x 4)))
(.f64 (+.f64 x (sqrt.f64 (.f64 x y))) (-.f64 x (sqrt.f64 (*.f64 x y))))
(*.f64 x (-.f64 x y))
(/.f64 1 (/.f64 (.f64 x (+.f64 x y)) (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 (/.f64 1 x) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(.f64 (/.f64 x 1) (/.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 y x)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))) (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 (.f64 y x) (*.f64 x (+.f64 y x)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 x (*.f64 y x)) (+.f64 y x) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 x (.f64 (*.f64 y x) (+.f64 y x)) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (.f64 x (+.f64 x y)))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 (/.f64 1 x) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(.f64 (/.f64 x 1) (/.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 (.f64 y x) (*.f64 x (+.f64 y x)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 x (*.f64 y x)) (+.f64 y x) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 x (.f64 (*.f64 y x) (+.f64 y x)) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x (neg.f64 y)) (.f64 x (neg.f64 y)))) (-.f64 (.f64 x x) (*.f64 x (neg.f64 y))))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 (/.f64 1 x) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(.f64 (/.f64 x 1) (/.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))) (-.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))
(/.f64 (-.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) (fma.f64 (neg.f64 y) x (.f64 y x)))) (-.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 y x))))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (.f64 0 (.f64 y x)) (.f64 0 (.f64 y x)))) (fma.f64 x (-.f64 x y) (.f64 0 (.f64 y x))))
(/.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 x (-.f64 x y)))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (.f64 x (neg.f64 y)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x (neg.f64 y)) (.f64 x (neg.f64 y))) (.f64 (.f64 x x) (*.f64 x (neg.f64 y))))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 (.f64 y x) (*.f64 x (+.f64 y x)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 x (*.f64 y x)) (+.f64 y x) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 x (.f64 (*.f64 y x) (+.f64 y x)) (pow.f64 x 4)))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) 3)) (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (-.f64 (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))) (.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) 3)) (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) (-.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) (*.f64 x (-.f64 x y))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (.f64 0 (.f64 y x)) 3)) (fma.f64 (.f64 0 (.f64 y x)) (-.f64 (.f64 0 (.f64 y x)) (.f64 x (-.f64 x y))) (pow.f64 (*.f64 x (-.f64 x y)) 2)))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) 0) (pow.f64 (.f64 x (-.f64 x y)) 2))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))) (neg.f64 (.f64 x (+.f64 x y))))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 (/.f64 1 x) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(.f64 (/.f64 x 1) (/.f64 (-.f64 (.f64 x x) (*.f64 y y)) (+.f64 y x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y))))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 (.f64 y x) (*.f64 x (+.f64 y x)))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 x (*.f64 y x)) (+.f64 y x) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 x (.f64 (*.f64 y x) (+.f64 y x)) (pow.f64 x 4)))
(pow.f64 (*.f64 x (-.f64 x y)) 1)
(*.f64 x (-.f64 x y))
(pow.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) 2)
(*.f64 x (-.f64 x y))
(pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 3)
(*.f64 x (-.f64 x y))
(pow.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) 1/3)
(*.f64 x (-.f64 x y))
(sqrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2))
(*.f64 x (-.f64 x y))
(log.f64 (pow.f64 (exp.f64 x) (-.f64 x y)))
(*.f64 x (-.f64 x y))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (-.f64 x y)))))
(*.f64 x (-.f64 x y))
(cbrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3))
(*.f64 x (-.f64 x y))
(expm1.f64 (log1p.f64 (*.f64 x (-.f64 x y))))
(*.f64 x (-.f64 x y))
(exp.f64 (log.f64 (*.f64 x (-.f64 x y))))
(*.f64 x (-.f64 x y))
(exp.f64 (.f64 (log.f64 (.f64 x (-.f64 x y))) 1))
(*.f64 x (-.f64 x y))
(log1p.f64 (expm1.f64 (*.f64 x (-.f64 x y))))
(*.f64 x (-.f64 x y))
(fma.f64 x x (*.f64 x (neg.f64 y)))
(*.f64 x (-.f64 x y))
(fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(*.f64 x (-.f64 x y))
(fma.f64 1 (.f64 x x) (.f64 x (neg.f64 y)))
(*.f64 x (-.f64 x y))
(fma.f64 1 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))
(*.f64 x (-.f64 x y))
(fma.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(*.f64 x (-.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(*.f64 x (-.f64 x y))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (.f64 x x)) (.f64 x (neg.f64 y)))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (.f64 x x)) (.f64 y (neg.f64 x)))
(-.f64 (.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 (pow.f64 x 4))) (*.f64 y x))

localize10.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.04%	(.f64 (-.f64 x y) (.f64 2 x))

Compiler

Compiled 18 to 9 computations (50% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(.f64 (-.f64 x y) (.f64 2 x))
0.0ms	x	@	inf	(.f64 (-.f64 x y) (.f64 2 x))
0.0ms	x	@	0	(.f64 (-.f64 x y) (.f64 2 x))
0.0ms	y	@	inf	(.f64 (-.f64 x y) (.f64 2 x))
0.0ms	x	@	-inf	(.f64 (-.f64 x y) (.f64 2 x))

rewrite58.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1858×	`add-sqr-sqrt`
1838×	`*-un-lft-identity`
1718×	`add-cube-cbrt`
1698×	`add-cbrt-cube`
176×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	173	19
2	2255	19

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

Inputs
(.f64 (-.f64 x y) (.f64 2 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x 2) x) (.f64 (.f64 x 2) (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (.f64 x 2)) (.f64 (neg.f64 y) (.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 x 2) (-.f64 (.f64 x x) (.f64 y y))) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 x 2) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (.f64 y (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 x 2)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 x 2)) (fma.f64 x x (.f64 y (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (-.f64 x y)) (.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (.f64 (-.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (.f64 (-.f64 x y) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) x) (*.f64 (*.f64 x 2) (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 2)) (*.f64 (neg.f64 y) (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 (-.f64 x y) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x 2) (-.f64 (*.f64 x x) (*.f64 y y))) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x 2) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (*.f64 x 2)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (*.f64 x 2)) (fma.f64 x x (*.f64 y (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 (-.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 (-.f64 x y) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 (-.f64 x y) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 (-.f64 x y) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 (-.f64 x y) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (-.f64 x y)) (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 (-.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 (-.f64 x y) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 (-.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 (-.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 (-.f64 x y) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 (-.f64 x y) 2))))))))

simplify55.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1686×	`associate-*r/`
1386×	`associate-*l/`
1122×	`associate-r`
984×	`associate-l`
784×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	69	1137
1	187	857
2	599	857
3	3686	857

Stop Event

1×	node limit

Counts

43 → 32

Calls

Call 1

Inputs
(.f64 -2 (.f64 y x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(.f64 -2 (.f64 y x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(.f64 -2 (.f64 y x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 (.f64 x 2) x) (.f64 (.f64 x 2) (neg.f64 y)))
(+.f64 (.f64 x (.f64 x 2)) (.f64 (neg.f64 y) (.f64 x 2)))
(-.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2)))) 1)
(/.f64 (.f64 (.f64 x 2) (-.f64 (.f64 x x) (.f64 y y))) (+.f64 x y))
(/.f64 (.f64 (.f64 x 2) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 x 2)) (+.f64 x y))
(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 x 2)) (fma.f64 x x (*.f64 y (+.f64 x y))))
(pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 1)
(pow.f64 (sqrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 2)
(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3) 1/3)
(sqrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 2))
(log.f64 (pow.f64 (exp.f64 (-.f64 x y)) (*.f64 x 2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2)))))
(cbrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3))
(expm1.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(exp.f64 (log.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 (-.f64 x y) 2))) 1))
(log1p.f64 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2))))

Outputs
(.f64 -2 (.f64 y x))
(.f64 x (.f64 -2 y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(*.f64 2 (pow.f64 x 2))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(*.f64 2 (pow.f64 x 2))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(*.f64 2 (pow.f64 x 2))
(.f64 x (.f64 x 2))
(.f64 2 (.f64 x x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(.f64 -2 (.f64 y x))
(.f64 x (.f64 -2 y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(.f64 -2 (.f64 y x))
(.f64 x (.f64 -2 y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 (.f64 x 2) x) (.f64 (.f64 x 2) (neg.f64 y)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(+.f64 (.f64 x (.f64 x 2)) (.f64 (neg.f64 y) (.f64 x 2)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(-.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2)))) 1)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(/.f64 (.f64 (.f64 x 2) (-.f64 (.f64 x x) (.f64 y y))) (+.f64 x y))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(/.f64 (.f64 (.f64 x 2) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 x 2) (/.f64 (fma.f64 x x (.f64 y (+.f64 y x))) (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 (fma.f64 x x (.f64 y (+.f64 y x))) (.f64 x 2)))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (.f64 x 2)))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 (.f64 x 2) (fma.f64 y (+.f64 y x) (*.f64 x x))))
(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 x 2)) (+.f64 x y))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 x 2)) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 x 2) (/.f64 (fma.f64 x x (.f64 y (+.f64 y x))) (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 (fma.f64 x x (.f64 y (+.f64 y x))) (.f64 x 2)))
(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (.f64 x 2)))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 (.f64 x 2) (fma.f64 y (+.f64 y x) (*.f64 x x))))
(pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 1)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(pow.f64 (sqrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 2)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(pow.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3) 1/3)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(sqrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 2))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(log.f64 (pow.f64 (exp.f64 (-.f64 x y)) (*.f64 x 2)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2)))))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(cbrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(expm1.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(exp.f64 (log.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 (-.f64 x y) 2))) 1))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))
(log1p.f64 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 (.f64 x 2) (-.f64 x y))

eval21.0ms (0.8%)

Compiler: Compiled 1665 to 690 computations (58.6% saved)

prune15.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	103	6	109

Error

Counts

109 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.9%	(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
✓	0.04%	(.f64 (-.f64 x y) (.f64 2 x))
▶	52.72%	(.f64 x (.f64 x 2))
▶	33.65%	(.f64 x (.f64 -2 y))
▶	0.01%	(.f64 2 (fma.f64 x x (.f64 x (neg.f64 y))))
✓	0.02%	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 57 to 39 computations (31.6% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.01%	(fma.f64 x x (*.f64 x (neg.f64 y)))

Compiler

Compiled 27 to 8 computations (70.4% saved)

series1.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(fma.f64 x x (*.f64 x (neg.f64 y)))
0.0ms	x	@	-inf	(fma.f64 x x (*.f64 x (neg.f64 y)))
0.0ms	y	@	0	(fma.f64 x x (*.f64 x (neg.f64 y)))
0.0ms	x	@	inf	(fma.f64 x x (*.f64 x (neg.f64 y)))
0.0ms	y	@	inf	(fma.f64 x x (*.f64 x (neg.f64 y)))

rewrite58.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1538×	`add-sqr-sqrt`
1526×	`*-un-lft-identity`
1408×	`add-cube-cbrt`
1388×	`add-cbrt-cube`
1370×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	180	13
2	2228	13

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(fma.f64 x x (*.f64 x (neg.f64 y)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x y) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1) (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x x) (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (+.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x y))) (sqrt.f64 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x y))) 2) (cbrt.f64 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (pow.f64 (*.f64 x y) 2)) (*.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (*.f64 x y) 3)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (pow.f64 (*.f64 x y) 2) (*.f64 (*.f64 x x) (*.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (+.f64 x y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (+.f64 x y))))))))

simplify64.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

798×	`*-commutative`
776×	`+-commutative`
740×	`associate-/l*`
654×	`associate-+r+`
646×	`associate-/r*`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	722
1	179	690
2	1034	680
3	3964	674
4	6704	674

Stop Event

1×	node limit

Counts

48 → 38

Calls

Call 1

Inputs
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (.f64 x y) (.f64 x x))
(+.f64 (.f64 x x) (.f64 x y))
(+.f64 (.f64 (.f64 x x) 1) (*.f64 x y))
(-.f64 (.f64 x x) (.f64 x y))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x y))) 1)
(*.f64 x (+.f64 x y))
(.f64 (.f64 x (+.f64 x y)) 1)
(.f64 1 (.f64 x (+.f64 x y)))
(.f64 (sqrt.f64 (.f64 x (+.f64 x y))) (sqrt.f64 (*.f64 x (+.f64 x y))))
(.f64 (cbrt.f64 (.f64 x (+.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x y))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x y))) 2) (cbrt.f64 (*.f64 x (+.f64 x y))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 (.f64 x y) 2)) (*.f64 x (+.f64 x y)))
(/.f64 (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (pow.f64 (.f64 x y) 2) (.f64 (.f64 x x) (*.f64 x y)))))
(pow.f64 (*.f64 x (+.f64 x y)) 1)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x y))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x y))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x y)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x y)) 2))
(log.f64 (exp.f64 (*.f64 x (+.f64 x y))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x y)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x y))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x y))))
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 x y))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x y))))

Outputs
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 y (neg.f64 x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 y (neg.f64 x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 y (neg.f64 x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x y) (.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (.f64 x x) (.f64 x y))
(*.f64 x (+.f64 y x))
(+.f64 (.f64 (.f64 x x) 1) (*.f64 x y))
(*.f64 x (+.f64 y x))
(-.f64 (.f64 x x) (.f64 x y))
(*.f64 x (-.f64 x y))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x y))) 1)
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(*.f64 x (+.f64 y x))
(.f64 (.f64 x (+.f64 x y)) 1)
(*.f64 x (+.f64 y x))
(.f64 1 (.f64 x (+.f64 x y)))
(*.f64 x (+.f64 y x))
(.f64 (sqrt.f64 (.f64 x (+.f64 x y))) (sqrt.f64 (*.f64 x (+.f64 x y))))
(*.f64 x (+.f64 y x))
(.f64 (cbrt.f64 (.f64 x (+.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x y))) 2))
(*.f64 x (+.f64 y x))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x y))) 2) (cbrt.f64 (*.f64 x (+.f64 x y))))
(*.f64 x (+.f64 y x))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 (.f64 x y) 2)) (*.f64 x (+.f64 x y)))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 (.f64 y x) 2)) (*.f64 x (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x 3) (.f64 y (.f64 y x))) (+.f64 y x))
(/.f64 (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (pow.f64 (.f64 x y) 2) (.f64 (.f64 x x) (*.f64 x y)))))
(/.f64 (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 x x) (.f64 x x) (-.f64 (pow.f64 (.f64 y x) 2) (.f64 (.f64 (.f64 x x) x) y))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 (.f64 y x) 2) (*.f64 y (pow.f64 x 3)))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 y x) (*.f64 x (-.f64 y x)) (pow.f64 x 4)))
(pow.f64 (*.f64 x (+.f64 x y)) 1)
(*.f64 x (+.f64 y x))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x y))) 2)
(*.f64 x (+.f64 y x))
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x y))) 3)
(*.f64 x (+.f64 y x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x y)) 3) 1/3)
(*.f64 x (+.f64 y x))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x y)) 2))
(*.f64 x (+.f64 y x))
(log.f64 (exp.f64 (*.f64 x (+.f64 x y))))
(*.f64 x (+.f64 y x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x y)) 3))
(*.f64 x (+.f64 y x))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x y))))
(*.f64 x (+.f64 y x))
(exp.f64 (log.f64 (*.f64 x (+.f64 x y))))
(*.f64 x (+.f64 y x))
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 x y))) 1))
(*.f64 x (+.f64 y x))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x y))))
(*.f64 x (+.f64 y x))

localize5.0ms (0.2%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

localize5.0ms (0.2%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

localize14.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.04%	(.f64 x (.f64 (-.f64 x y) 2))
✓	1.02%	(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
✓	11.52%	(cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2)))

Compiler

Compiled 39 to 20 computations (48.7% saved)

series10.0ms (0.4%)

Counts

3 → 32

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	y	@	0	(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
2.0ms	y	@	0	(cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2)))
1.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
1.0ms	x	@	0	(cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2)))

rewrite119.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1060×	`*-commutative`
966×	`unswap-sqr`
660×	`associate-*r/`
650×	`swap-sqr`
548×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	61
1	257	61
2	2978	61

Stop Event

1×	node limit

Counts

3 → 175

Calls

Call 1

Inputs
(cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2)))
(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
(.f64 x (.f64 (-.f64 x y) 2))

Outputs

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simplify169.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

1084×	`associate-r`
956×	`associate-l`
878×	`associate-/l*`
812×	`associate-/r*`
714×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	419	9197
1	1195	7841
2	4604	7841

Stop Event

1×	node limit

Counts

207 → 237

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (cbrt.f64 2))
(+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (cbrt.f64 2)) (.f64 -1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/9) (.f64 (cbrt.f64 2) y))))
(+.f64 (.f64 -1/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 4)) 1/9) (.f64 (cbrt.f64 2) (pow.f64 y 2)))) (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (cbrt.f64 2)) (.f64 -1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/9) (.f64 (cbrt.f64 2) y)))))
(+.f64 (.f64 -1/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 4)) 1/9) (.f64 (cbrt.f64 2) (pow.f64 y 2)))) (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (cbrt.f64 2)) (+.f64 (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3) (.f64 (cbrt.f64 2) (.f64 (pow.f64 y 3) (+.f64 (.f64 -1/27 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/3)) (.f64 2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 x 5) 1/3)))))))) (.f64 -1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/9) (.f64 (cbrt.f64 2) y))))))
(.f64 2 (.f64 (pow.f64 1 1/3) (pow.f64 x 2)))
(+.f64 (.f64 2 (.f64 (pow.f64 1 1/3) (pow.f64 x 2))) (.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 17)) 1/9)) (.f64 -4/3 (pow.f64 (*.f64 1 (pow.f64 x 17)) 1/9))) y))
(+.f64 (.f64 2 (.f64 (pow.f64 1 1/3) (pow.f64 x 2))) (+.f64 (.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 17)) 1/9)) (.f64 -4/3 (pow.f64 (.f64 1 (pow.f64 x 17)) 1/9))) y) (.f64 (pow.f64 y 2) (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (.f64 (cbrt.f64 2) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 10)) 1/9) (pow.f64 (cbrt.f64 2) 2))) (.f64 1/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 10)) 1/9) (pow.f64 (cbrt.f64 2) 2)))))) (+.f64 (.f64 -2/9 (pow.f64 (.f64 1 (pow.f64 x 16)) 1/9)) (.f64 4/9 (pow.f64 (*.f64 1 (pow.f64 x 16)) 1/9)))))))
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(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) (pow.f64 (sqrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 1/3)) (.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) (pow.f64 (sqrt.f64 (.f64 x (*.f64 (-.f64 x y) 2))) 1/3)))
(/.f64 (.f64 x (.f64 2 (-.f64 (.f64 x x) (.f64 y y)))) (+.f64 x y))
(/.f64 (.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 2 (.f64 x (-.f64 (.f64 x x) (.f64 y y)))) (+.f64 x y))
(/.f64 (.f64 2 (.f64 x (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (.f64 x 2) 1) (/.f64 1 (-.f64 x y)))
(/.f64 (.f64 (.f64 x 2) (-.f64 (.f64 x x) (.f64 y y))) (+.f64 x y))
(/.f64 (.f64 (.f64 x 2) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (.f64 x 2) (+.f64 (pow.f64 x 3) (pow.f64 (neg.f64 y) 3))) (+.f64 (.f64 x x) (.f64 (neg.f64 y) (-.f64 (neg.f64 y) x))))
(/.f64 (.f64 (.f64 x 2) (+.f64 (neg.f64 (.f64 x x)) (.f64 y y))) (neg.f64 (+.f64 x y)))
(/.f64 (.f64 (.f64 x 2) (neg.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (neg.f64 (fma.f64 x x (*.f64 y (+.f64 x y)))))
(/.f64 (.f64 1 (.f64 x 2)) (/.f64 1 (-.f64 x y)))
(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 x 2)) (+.f64 x y))
(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 x 2)) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 (neg.f64 y) 3)) (.f64 x 2)) (+.f64 (.f64 x x) (.f64 (neg.f64 y) (-.f64 (neg.f64 y) x))))
(/.f64 (.f64 (+.f64 (neg.f64 (.f64 x x)) (.f64 y y)) (.f64 x 2)) (neg.f64 (+.f64 x y)))
(/.f64 (.f64 (neg.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 x 2)) (neg.f64 (fma.f64 x x (*.f64 y (+.f64 x y)))))
(/.f64 (.f64 (.f64 2 (-.f64 (.f64 x x) (.f64 y y))) x) (+.f64 x y))
(/.f64 (.f64 (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) x) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (.f64 x (-.f64 (.f64 x x) (.f64 y y))) 2) (+.f64 x y))
(/.f64 (.f64 (.f64 x (-.f64 (pow.f64 x 3) (pow.f64 y 3))) 2) (fma.f64 x x (*.f64 y (+.f64 x y))))
(sqrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) (-.f64 x y)) x))
(log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2)))))
(cbrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 (-.f64 x y) 2) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(exp.f64 (log.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(+.f64 (.f64 x (.f64 (-.f64 x y) 2)) (.f64 (.f64 x 2) (fma.f64 (neg.f64 y) 1 y)))
(+.f64 (.f64 x (.f64 (-.f64 x y) 2)) (.f64 (.f64 x 2) (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y)))
(+.f64 (.f64 x (.f64 (-.f64 x y) 2)) (.f64 (.f64 x 2) (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y)))
(+.f64 (.f64 x (.f64 (-.f64 x y) 2)) (.f64 (fma.f64 (neg.f64 y) 1 y) (.f64 x 2)))
(+.f64 (.f64 x (.f64 (-.f64 x y) 2)) (.f64 (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y) (.f64 x 2)))
(+.f64 (.f64 x (.f64 (-.f64 x y) 2)) (.f64 (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y) (.f64 x 2)))
(+.f64 (.f64 x (.f64 x 2)) (.f64 x (.f64 2 (neg.f64 y))))
(+.f64 (.f64 x (.f64 x 2)) (.f64 (neg.f64 y) (.f64 x 2)))
(+.f64 (.f64 2 (.f64 x x)) (.f64 2 (.f64 x (neg.f64 y))))
(+.f64 (.f64 (.f64 x 2) x) (.f64 (.f64 x 2) (neg.f64 y)))
(+.f64 (.f64 (.f64 x 2) x) (.f64 (.f64 2 (neg.f64 y)) x))
(+.f64 (.f64 (.f64 x 2) (neg.f64 y)) (.f64 (.f64 x 2) x))
(+.f64 (.f64 (.f64 x x) 2) (.f64 (.f64 x (neg.f64 y)) 2))
(+.f64 (.f64 (neg.f64 y) (.f64 x 2)) (.f64 x (.f64 x 2)))
(-.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2)))) 1)
(/.f64 (.f64 x (.f64 2 (-.f64 (.f64 x x) (.f64 y y)))) (+.f64 x y))
(/.f64 (.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 2 (.f64 x (-.f64 (.f64 x x) (.f64 y y)))) (+.f64 x y))
(/.f64 (.f64 2 (.f64 x (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (.f64 x 2) 1) (/.f64 1 (-.f64 x y)))
(/.f64 (.f64 (.f64 x 2) (-.f64 (.f64 x x) (.f64 y y))) (+.f64 x y))
(/.f64 (.f64 (.f64 x 2) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (.f64 x 2) (+.f64 (pow.f64 x 3) (pow.f64 (neg.f64 y) 3))) (+.f64 (.f64 x x) (.f64 (neg.f64 y) (-.f64 (neg.f64 y) x))))
(/.f64 (.f64 (.f64 x 2) (+.f64 (neg.f64 (.f64 x x)) (.f64 y y))) (neg.f64 (+.f64 x y)))
(/.f64 (.f64 (.f64 x 2) (neg.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (neg.f64 (fma.f64 x x (*.f64 y (+.f64 x y)))))
(/.f64 (.f64 1 (.f64 x 2)) (/.f64 1 (-.f64 x y)))
(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 x 2)) (+.f64 x y))
(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 x 2)) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 (neg.f64 y) 3)) (.f64 x 2)) (+.f64 (.f64 x x) (.f64 (neg.f64 y) (-.f64 (neg.f64 y) x))))
(/.f64 (.f64 (+.f64 (neg.f64 (.f64 x x)) (.f64 y y)) (.f64 x 2)) (neg.f64 (+.f64 x y)))
(/.f64 (.f64 (neg.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 x 2)) (neg.f64 (fma.f64 x x (*.f64 y (+.f64 x y)))))
(/.f64 (.f64 (.f64 2 (-.f64 (.f64 x x) (.f64 y y))) x) (+.f64 x y))
(/.f64 (.f64 (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) x) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (.f64 x (-.f64 (.f64 x x) (.f64 y y))) 2) (+.f64 x y))
(/.f64 (.f64 (.f64 x (-.f64 (pow.f64 x 3) (pow.f64 y 3))) 2) (fma.f64 x x (*.f64 y (+.f64 x y))))
(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
(pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 1)
(pow.f64 (sqrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 2)
(pow.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 2) 3/2)
(pow.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3) 1/3)
(sqrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) (-.f64 x y)) x))
(log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2)))))
(cbrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 (-.f64 x y) 2) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(exp.f64 (log.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2))))

Outputs
(.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (cbrt.f64 2))
(.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2))
(+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (cbrt.f64 2)) (.f64 -1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/9) (.f64 (cbrt.f64 2) y))))
(fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2) (.f64 -1/3 (.f64 (.f64 (pow.f64 (pow.f64 x 5) 1/18) (pow.f64 (pow.f64 x 5) 1/18)) (*.f64 (cbrt.f64 2) y))))
(fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2) (.f64 (.f64 (cbrt.f64 2) y) (.f64 (*.f64 -1/3 (pow.f64 (pow.f64 x 5) 1/18)) (pow.f64 (pow.f64 x 5) 1/18))))
(fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2) (.f64 (.f64 (cbrt.f64 2) y) (.f64 -1/3 (*.f64 (pow.f64 (pow.f64 x 5) 1/18) (pow.f64 (pow.f64 x 5) 1/18)))))
(+.f64 (.f64 -1/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 4)) 1/9) (.f64 (cbrt.f64 2) (pow.f64 y 2)))) (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (cbrt.f64 2)) (.f64 -1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/9) (.f64 (cbrt.f64 2) y)))))
(fma.f64 -1/9 (.f64 (.f64 (pow.f64 (pow.f64 x 4) 1/18) (pow.f64 (pow.f64 x 4) 1/18)) (.f64 (cbrt.f64 2) (.f64 y y))) (fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2) (.f64 -1/3 (.f64 (.f64 (pow.f64 (pow.f64 x 5) 1/18) (pow.f64 (pow.f64 x 5) 1/18)) (*.f64 (cbrt.f64 2) y)))))
(fma.f64 -1/9 (.f64 (cbrt.f64 2) (.f64 (.f64 y y) (.f64 (pow.f64 (pow.f64 x 4) 1/18) (pow.f64 (pow.f64 x 4) 1/18)))) (fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2) (.f64 (.f64 (cbrt.f64 2) y) (.f64 (*.f64 -1/3 (pow.f64 (pow.f64 x 5) 1/18)) (pow.f64 (pow.f64 x 5) 1/18)))))
(fma.f64 -1/9 (.f64 (cbrt.f64 2) (.f64 (.f64 y y) (.f64 (pow.f64 (pow.f64 x 4) 1/18) (pow.f64 (pow.f64 x 4) 1/18)))) (fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2) (.f64 (.f64 (cbrt.f64 2) y) (.f64 -1/3 (*.f64 (pow.f64 (pow.f64 x 5) 1/18) (pow.f64 (pow.f64 x 5) 1/18))))))
(+.f64 (.f64 -1/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 4)) 1/9) (.f64 (cbrt.f64 2) (pow.f64 y 2)))) (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (cbrt.f64 2)) (+.f64 (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3) (.f64 (cbrt.f64 2) (.f64 (pow.f64 y 3) (+.f64 (.f64 -1/27 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/3)) (.f64 2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 x 5) 1/3)))))))) (.f64 -1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/9) (.f64 (cbrt.f64 2) y))))))
(fma.f64 -1/9 (.f64 (.f64 (pow.f64 (pow.f64 x 4) 1/18) (pow.f64 (pow.f64 x 4) 1/18)) (.f64 (cbrt.f64 2) (.f64 y y))) (fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2) (.f64 -1/3 (+.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (.f64 (.f64 (cbrt.f64 2) (pow.f64 y 3)) (fma.f64 -1/27 (cbrt.f64 (pow.f64 x 5)) (.f64 2/9 (cbrt.f64 (pow.f64 x 5)))))) (.f64 (.f64 (pow.f64 (pow.f64 x 5) 1/18) (pow.f64 (pow.f64 x 5) 1/18)) (*.f64 (cbrt.f64 2) y))))))
(fma.f64 -1/9 (.f64 (cbrt.f64 2) (.f64 (.f64 y y) (.f64 (pow.f64 (pow.f64 x 4) 1/18) (pow.f64 (pow.f64 x 4) 1/18)))) (fma.f64 -1/3 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (.f64 (cbrt.f64 2) (.f64 (pow.f64 y 3) (.f64 (cbrt.f64 (pow.f64 x 5)) 5/27))) (.f64 (cbrt.f64 2) (.f64 y (.f64 (pow.f64 (pow.f64 x 5) 1/18) (pow.f64 (pow.f64 x 5) 1/18))))) (.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2))))
(fma.f64 -1/9 (.f64 (cbrt.f64 2) (.f64 (.f64 y y) (.f64 (pow.f64 (pow.f64 x 4) 1/18) (pow.f64 (pow.f64 x 4) 1/18)))) (fma.f64 -1/3 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (.f64 (pow.f64 y 3) (.f64 (.f64 (cbrt.f64 (pow.f64 x 5)) 5/27) (cbrt.f64 2))) (.f64 (cbrt.f64 2) (.f64 y (.f64 (pow.f64 (pow.f64 x 5) 1/18) (pow.f64 (pow.f64 x 5) 1/18))))) (.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 2))))
(.f64 2 (.f64 (pow.f64 1 1/3) (pow.f64 x 2)))
(.f64 2 (.f64 x x))
(.f64 x (.f64 x 2))
(+.f64 (.f64 2 (.f64 (pow.f64 1 1/3) (pow.f64 x 2))) (.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 17)) 1/9)) (.f64 -4/3 (pow.f64 (*.f64 1 (pow.f64 x 17)) 1/9))) y))
(fma.f64 2 (.f64 x x) (.f64 y (.f64 (.f64 (pow.f64 (pow.f64 x 17) 1/18) (pow.f64 (pow.f64 x 17) 1/18)) -2)))
(fma.f64 x (.f64 x 2) (.f64 y (.f64 (.f64 (pow.f64 (pow.f64 x 17) 1/18) (pow.f64 (pow.f64 x 17) 1/18)) -2)))
(fma.f64 x (.f64 x 2) (.f64 (.f64 (pow.f64 (pow.f64 x 17) 1/18) (pow.f64 (pow.f64 x 17) 1/18)) (.f64 y -2)))
(+.f64 (.f64 2 (.f64 (pow.f64 1 1/3) (pow.f64 x 2))) (+.f64 (.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 17)) 1/9)) (.f64 -4/3 (pow.f64 (.f64 1 (pow.f64 x 17)) 1/9))) y) (.f64 (pow.f64 y 2) (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (.f64 (cbrt.f64 2) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 10)) 1/9) (pow.f64 (cbrt.f64 2) 2))) (.f64 1/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 10)) 1/9) (pow.f64 (cbrt.f64 2) 2)))))) (+.f64 (.f64 -2/9 (pow.f64 (.f64 1 (pow.f64 x 16)) 1/9)) (.f64 4/9 (pow.f64 (*.f64 1 (pow.f64 x 16)) 1/9)))))))
(fma.f64 2 (.f64 x x) (fma.f64 (.f64 (.f64 (pow.f64 (pow.f64 x 17) 1/18) (pow.f64 (pow.f64 x 17) 1/18)) -2) y (.f64 (.f64 y y) (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 2) (.f64 (.f64 (.f64 (pow.f64 (pow.f64 x 10) 1/18) (pow.f64 (pow.f64 x 10) 1/18)) (pow.f64 (cbrt.f64 2) 2)) -1/9)) (.f64 (.f64 (pow.f64 (pow.f64 x 16) 1/18) (pow.f64 (pow.f64 x 16) 1/18)) 2/9)))))
(fma.f64 x (.f64 x 2) (fma.f64 y (.f64 (.f64 (pow.f64 (pow.f64 x 17) 1/18) (pow.f64 (pow.f64 x 17) 1/18)) -2) (.f64 y (.f64 y (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (.f64 (pow.f64 (pow.f64 x 10) 1/18) (.f64 (pow.f64 (pow.f64 x 10) 1/18) (pow.f64 (cbrt.f64 2) 2))) (.f64 -1/9 (cbrt.f64 2))) (.f64 2/9 (.f64 (pow.f64 (pow.f64 x 16) 1/18) (pow.f64 (pow.f64 x 16) 1/18))))))))
(fma.f64 x (.f64 x 2) (fma.f64 (.f64 y y) (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (.f64 (pow.f64 (pow.f64 x 10) 1/18) (.f64 (pow.f64 (pow.f64 x 10) 1/18) (pow.f64 (cbrt.f64 2) 2))) (.f64 -1/9 (cbrt.f64 2))) (.f64 2/9 (.f64 (pow.f64 (pow.f64 x 16) 1/18) (pow.f64 (pow.f64 x 16) 1/18)))) (.f64 (.f64 (pow.f64 (pow.f64 x 17) 1/18) (pow.f64 (pow.f64 x 17) 1/18)) (.f64 y -2))))
(+.f64 (.f64 2 (.f64 (pow.f64 1 1/3) (pow.f64 x 2))) (+.f64 (.f64 (+.f64 (.f64 -2/3 (pow.f64 (.f64 1 (pow.f64 x 17)) 1/9)) (.f64 -4/3 (pow.f64 (.f64 1 (pow.f64 x 17)) 1/9))) y) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3) (.f64 (cbrt.f64 2) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 10)) 1/9) (pow.f64 (cbrt.f64 2) 2))) (.f64 1/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 10)) 1/9) (pow.f64 (cbrt.f64 2) 2)))))) (+.f64 (.f64 -2/9 (pow.f64 (.f64 1 (pow.f64 x 16)) 1/9)) (.f64 4/9 (pow.f64 (.f64 1 (pow.f64 x 16)) 1/9))))) (.f64 (pow.f64 y 3) (+.f64 (.f64 -2/3 (.f64 (pow.f64 1 1/3) (+.f64 (.f64 -1/27 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/3)) (.f64 2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 x 5) 1/3)))))) (+.f64 (.f64 (.f64 (+.f64 (.f64 2/27 (.f64 (pow.f64 1 1/9) (.f64 (pow.f64 (cbrt.f64 2) 2) x))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3) (.f64 (pow.f64 (cbrt.f64 2) 2) (+.f64 (.f64 -1/27 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/3)) (.f64 2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 x 5) 1/3)))))))) (cbrt.f64 2)) (pow.f64 (.f64 1 (pow.f64 x 2)) 1/3)) (+.f64 (.f64 4/27 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 x 5) 1/3))) (.f64 -1/3 (.f64 (pow.f64 (.f64 1 (pow.f64 x 5)) 1/9) (.f64 (cbrt.f64 2) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (.f64 1 (pow.f64 x 10)) 1/9) (pow.f64 (cbrt.f64 2) 2))) (.f64 1/9 (.f64 (pow.f64 (*.f64 1 (pow.f64 x 10)) 1/9) (pow.f64 (cbrt.f64 2) 2))))))))))))))
(fma.f64 2 (.f64 x x) (fma.f64 (.f64 (.f64 (pow.f64 (pow.f64 x 17) 1/18) (pow.f64 (pow.f64 x 17) 1/18)) -2) y (fma.f64 (.f64 y y) (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 2) (.f64 (.f64 (.f64 (pow.f64 (pow.f64 x 10) 1/18) (pow.f64 (pow.f64 x 10) 1/18)) (pow.f64 (cbrt.f64 2) 2)) -1/9)) (.f64 (.f64 (pow.f64 (pow.f64 x 16) 1/18) (pow.f64 (pow.f64 x 16) 1/18)) 2/9)) (.f64 (pow.f64 y 3) (+.f64 (.f64 -2/3 (fma.f64 -1/27 (cbrt.f64 (pow.f64 x 5)) (.f64 2/9 (cbrt.f64 (pow.f64 x 5))))) (fma.f64 (.f64 (cbrt.f64 2) (+.f64 (.f64 2/27 (.f64 x (pow.f64 (cbrt.f64 2) 2))) (.f64 (.f64 -2/3 (cbrt.f64 (/.f64 1 (.f64 x x)))) (.f64 (fma.f64 -1/27 (cbrt.f64 (pow.f64 x 5)) (.f64 2/9 (cbrt.f64 (pow.f64 x 5)))) (pow.f64 (cbrt.f64 2) 2))))) (cbrt.f64 (.f64 x x)) (+.f64 (.f64 4/27 (cbrt.f64 (pow.f64 x 5))) (.f64 -1/3 (.f64 (.f64 (pow.f64 (pow.f64 x 5) 1/18) (pow.f64 (pow.f64 x 5) 1/18)) (.f64 (cbrt.f64 2) (.f64 (.f64 (*.f64 (pow.f64 (pow.f64 x 10) 1/18) (pow.f64 (pow.f64 x 10) 1/18)) (pow.f64 (cbrt.f64 2) 2)) -1/9)))))))))))
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(*.f64 x (log.f64 (pow.f64 (exp.f64 2) (-.f64 x y))))
(.f64 x (.f64 (-.f64 x y) (log.f64 (exp.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2)))))
(fma.f64 2 (.f64 x x) (.f64 (*.f64 -2 y) x))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) 2)) 3))
(fma.f64 2 (.f64 x x) (.f64 (*.f64 -2 y) x))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(cbrt.f64 (.f64 (pow.f64 (.f64 (-.f64 x y) 2) 3) (pow.f64 x 3)))
(fma.f64 2 (.f64 x x) (.f64 (*.f64 -2 y) x))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(expm1.f64 (log1p.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(fma.f64 2 (.f64 x x) (.f64 (*.f64 -2 y) x))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(exp.f64 (log.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(fma.f64 2 (.f64 x x) (.f64 (*.f64 -2 y) x))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(log1p.f64 (expm1.f64 (.f64 x (.f64 (-.f64 x y) 2))))
(fma.f64 2 (.f64 x x) (.f64 (*.f64 -2 y) x))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))

eval200.0ms (7.5%)

Compiler: Compiled 6123 to 3809 computations (37.8% saved)

prune41.0ms (1.5%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	275	6	281

Error

Counts

281 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.9%	(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)
✓	0.04%	(.f64 (-.f64 x y) (.f64 2 x))
✓	52.72%	(.f64 x (.f64 x 2))
✓	33.65%	(.f64 x (.f64 -2 y))
✓	0.01%	(.f64 2 (fma.f64 x x (.f64 x (neg.f64 y))))
✓	0.02%	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 57 to 39 computations (31.6% saved)

regimes54.0ms (2%)

Counts

6 → 1

Calls

Call 1

Inputs
(.f64 x (.f64 -2 y))
(.f64 x (.f64 x 2))
(.f64 (-.f64 x y) (.f64 2 x))
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (fma.f64 x x (.f64 x (neg.f64 y))))
(pow.f64 (cbrt.f64 (.f64 x (.f64 (-.f64 x y) 2))) 3)

Outputs
(.f64 2 (fma.f64 x x (.f64 x (neg.f64 y))))

Calls

4 calls:

39.0ms	(-.f64 (.f64 x x) (.f64 x y))
5.0ms	y
4.0ms	x
4.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Results

Error	Segments	Branch
0.01%	1	`x`
0.01%	1	`y`
0.01%	1	`(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))`
0.01%	1	`(-.f64 (.f64 x x) (.f64 x y))`

Compiler

Compiled 73 to 44 computations (39.7% saved)

regimes41.0ms (1.6%)

Counts

4 → 1

Calls

Call 1

Inputs
(.f64 x (.f64 -2 y))
(.f64 x (.f64 x 2))
(.f64 (-.f64 x y) (.f64 2 x))
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Outputs
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Calls

4 calls:

29.0ms	(-.f64 (.f64 x x) (.f64 x y))
4.0ms	y
4.0ms	x
4.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Results

Error	Segments	Branch
0.02%	1	`x`
0.02%	1	`y`
0.02%	1	`(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))`
0.02%	1	`(-.f64 (.f64 x x) (.f64 x y))`

Compiler

Compiled 54 to 33 computations (38.9% saved)

regimes9.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

Inputs
(.f64 x (.f64 -2 y))
(.f64 x (.f64 x 2))
(.f64 (-.f64 x y) (.f64 2 x))

Outputs
(.f64 (-.f64 x y) (.f64 2 x))

Calls

2 calls:

4.0ms	x
3.0ms	y

Results

Error	Segments	Branch
0.04%	1	`x`
0.04%	1	`y`

Compiler

Compiled 25 to 16 computations (36% saved)

regimes50.0ms (1.9%)

Accuracy

Total -46.3b remaining (-573.2%)

Threshold costs -46.3b (-573.2%)

Counts

2 → 3

Calls

Call 1

Inputs
(.f64 x (.f64 -2 y))
(.f64 x (.f64 x 2))

Outputs
(.f64 x (.f64 -2 y))
(.f64 x (.f64 x 2))
(.f64 x (.f64 -2 y))

Calls

2 calls:

39.0ms	x
10.0ms	y

Results

Error	Segments	Branch
18.14%	5	`x`
12.61%	3	`y`

Compiler

Compiled 18 to 12 computations (33.3% saved)

bsearch26.0ms (1%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	3.92583789783825e-78	4.521180231128852e-77
16.0ms	-9.371014309806121e-32	-3.371896335487179e-42

Results

23.0ms

256×

body

256

valid

Compiler

Compiled 272 to 203 computations (25.4% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative`
12×	`+-commutative`
8×	`sub-neg`
6×	`neg-mul-1`
6×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	133
1	56	133
2	66	133
3	71	133
4	73	133

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 2 (fma.f64 x x (.f64 x (neg.f64 y))))
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 (-.f64 x y) (.f64 2 x))
(if (<=.f64 y -6590956822156015/1569275433846670190958947355801916604025588861116008628224) (.f64 x (.f64 -2 y)) (if (<=.f64 y 5997033914328727/260740604970814219042361048116400404614587954389239840081425977517360806369707098391474864128) (.f64 x (.f64 x 2)) (.f64 x (.f64 -2 y))))
(.f64 x (.f64 -2 y))

Outputs
(.f64 2 (fma.f64 x x (.f64 x (neg.f64 y))))
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 (-.f64 x y) (.f64 2 x))
(if (<=.f64 y -6590956822156015/1569275433846670190958947355801916604025588861116008628224) (.f64 x (.f64 -2 y)) (if (<=.f64 y 5997033914328727/260740604970814219042361048116400404614587954389239840081425977517360806369707098391474864128) (.f64 x (.f64 x 2)) (.f64 x (.f64 -2 y))))
(if (or (<=.f64 y -6590956822156015/1569275433846670190958947355801916604025588861116008628224) (not (<=.f64 y 5997033914328727/260740604970814219042361048116400404614587954389239840081425977517360806369707098391474864128))) (.f64 x (.f64 y -2)) (.f64 x (.f64 2 x)))
(.f64 x (.f64 -2 y))
(.f64 x (.f64 y -2))

Compiler

Compiled 59 to 40 computations (32.2% saved)

soundness0.0ms (0%)

end71.0ms (2.7%)

Compiler: Compiled 51 to 32 computations (37.3% saved)

Details

analyze164.0ms (6.2%)

sample1.1s (42.8%)

preprocess66.0ms (2.5%)

simplify48.0ms (1.8%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize8.0ms (0.3%)

series2.0ms (0.1%)

rewrite63.0ms (2.4%)

simplify54.0ms (2%)

localize10.0ms (0.4%)

series3.0ms (0.1%)

rewrite58.0ms (2.2%)

simplify55.0ms (2.1%)

eval21.0ms (0.8%)

prune15.0ms (0.6%)

localize8.0ms (0.3%)

series1.0ms (0.1%)

rewrite58.0ms (2.2%)

simplify64.0ms (2.4%)

localize5.0ms (0.2%)

localize5.0ms (0.2%)

localize14.0ms (0.5%)

series10.0ms (0.4%)

rewrite119.0ms (4.5%)

simplify169.0ms (6.4%)

eval200.0ms (7.5%)

prune41.0ms (1.5%)

regimes54.0ms (2%)

regimes41.0ms (1.6%)

regimes9.0ms (0.3%)

regimes50.0ms (1.9%)

bsearch26.0ms (1%)

simplify7.0ms (0.3%)

soundness0.0ms (0%)

end71.0ms (2.7%)

Profiling