Details

analyze69.0ms (3%)

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)

sample995.0ms (43.5%)

Results

943.0ms	8256×	body	256	valid
39.0ms	441×	body	256	infinite

Bogosity

preprocess6.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

60×	`fma-def`
44×	`*-commutative`
16×	`+-commutative`
14×	`distribute-lft-in`
14×	`distribute-lft-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	37	38
2	75	38
3	107	38
4	113	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 2 (+.f64 (.f64 y y) (*.f64 y x)))
(.f64 2 (.f64 y (+.f64 y x)))
(.f64 2 (.f64 y (+.f64 x y)))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

34×	`fma-def`
32×	`*-commutative`
10×	`+-commutative`
8×	`associate-r`
8×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	22	19
2	43	19
3	63	19
4	68	19

Stop Event

1×

saturated

Counts

1 → 5

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))
(.f64 x (.f64 2 (+.f64 x y)))

eval1.0ms (0%)

Compiler: Compiled 39 to 20 computations (48.7% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	4	1	5
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	5	1	6

Error

0.01%

Counts

6 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.01%	(.f64 (+.f64 x y) (.f64 2 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.01%	(.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
0.0ms	x	@	inf	(.f64 (+.f64 x y) (.f64 2 x))
0.0ms	y	@	0	(.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 (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1838×	`add-sqr-sqrt`
1818×	`*-un-lft-identity`
1700×	`add-cube-cbrt`
1680×	`add-cbrt-cube`
174×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	172	19
2	2242	19

Stop Event

1×	node limit

Counts

1 → 21

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) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (.f64 x 2)) (.f64 y (.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x 2) y) (.f64 (.f64 x 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (.f64 x 2)) (.f64 x (.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 y x))))))) (#(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 y x))))))) (#(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) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 2)) (*.f64 y (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) y) (*.f64 (*.f64 x 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (*.f64 x 2)) (*.f64 x (*.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 y x))))))) (#(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 y x))))))) (#(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))))))))

simplify53.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1098×	`associate-r`
982×	`associate-l`
878×	`associate-*r/`
786×	`associate-+l+`
760×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	943
1	193	943
2	594	943
3	3622	943

Stop Event

1×	node limit

Counts

45 → 37

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

eval7.0ms (0.3%)

Compiler: Compiled 441 to 229 computations (48.1% saved)

prune6.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	4	38

Error

Counts

38 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	25.35%	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (/.f64 (-.f64 x y) (*.f64 2 x)))
✓	0.01%	(.f64 (+.f64 x y) (.f64 2 x))
▶	52.69%	(.f64 x (.f64 2 x))
▶	33.64%	(.f64 2 (.f64 y x))

Compiler

Compiled 40 to 26 computations (35% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.01%	(.f64 2 (.f64 y x))

Compiler

Compiled 13 to 6 computations (53.8% saved)

series3.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

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

rewrite249.0ms (10.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1316×	`add-sqr-sqrt`
1302×	`*-un-lft-identity`
1206×	`add-cube-cbrt`
1190×	`add-cbrt-cube`
1176×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	141	13
2	1632	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

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

Outputs

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

simplify87.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1036×	`*-commutative`
956×	`distribute-lft-in`
914×	`distribute-rgt-in`
870×	`log-prod`
864×	`exp-sum`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	275
1	90	209
2	341	143
3	2242	143
4	6540	143

Stop Event

1×	node limit

Counts

11 → 14

Calls

Call 1

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

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

localize5.0ms (0.2%)

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

localize14.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.03%	(/.f64 (-.f64 x y) (*.f64 2 x))
✓	24.61%	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (/.f64 (-.f64 x y) (*.f64 2 x)))

Compiler

Compiled 46 to 16 computations (65.2% saved)

series165.0ms (7.2%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
160.0ms	y	@	inf	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (/.f64 (-.f64 x y) (*.f64 2 x)))
1.0ms	x	@	-inf	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (/.f64 (-.f64 x y) (*.f64 2 x)))
1.0ms	x	@	0	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (/.f64 (-.f64 x y) (*.f64 2 x)))
1.0ms	x	@	inf	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (/.f64 (-.f64 x y) (*.f64 2 x)))
1.0ms	y	@	0	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (/.f64 (-.f64 x y) (*.f64 2 x)))

rewrite152.0ms (6.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1516×	`distribute-rgt-in`
1454×	`distribute-lft-in`
324×	`associate-+l+`
306×	`add-sqr-sqrt`
300×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	62
1	288	38
2	4792	38

Stop Event

1×	node limit

Counts

2 → 141

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (fma.f64 (neg.f64 y) y (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 2 (fma.f64 (neg.f64 y) y (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 y y)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (fma.f64 (neg.f64 (*.f64 y y)) 1 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 (pow.f64 y 4)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (fma.f64 (neg.f64 y) y (*.f64 y y)) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (*.f64 2 (fma.f64 (neg.f64 y) y (*.f64 y y))) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 y y)) 1) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (fma.f64 (neg.f64 (*.f64 y y)) 1 (*.f64 y y)) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) (*.f64 (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 (pow.f64 y 4)) (*.f64 y y)) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (/.f64 2 (/.f64 (-.f64 x y) x))) (neg.f64 (*.f64 (*.f64 y y) (/.f64 2 (/.f64 (-.f64 x y) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (/.f64 2 (/.f64 (-.f64 x y) x))) (*.f64 1 (neg.f64 (*.f64 (*.f64 y y) (/.f64 2 (/.f64 (-.f64 x y) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (/.f64 2 (/.f64 (-.f64 x y) x))) (*.f64 (neg.f64 (*.f64 y y)) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (/.f64 2 (/.f64 (-.f64 x y) x))) (*.f64 (+.f64 (neg.f64 (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 y y))) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (/.f64 2 (/.f64 (-.f64 x y) x))) (*.f64 (*.f64 (neg.f64 (*.f64 y y)) 1) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) x) (*.f64 (*.f64 x 2) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 2)) (*.f64 y (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (*.f64 (*.f64 y y) (/.f64 2 (/.f64 (-.f64 x y) x)))) (*.f64 (*.f64 x x) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 2) y) (*.f64 (*.f64 x 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 x x)) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (neg.f64 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 x x)) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (+.f64 (neg.f64 (*.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 x x)) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 (neg.f64 (*.f64 y y)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (neg.f64 (*.f64 y y))) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (fma.f64 (neg.f64 y) y (*.f64 y y))) (*.f64 (*.f64 x 2) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 (+.f64 x y) x)) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 (+.f64 x y) (neg.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 x (+.f64 x y))) (*.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (*.f64 (neg.f64 y) (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (*.f64 x 2)) (*.f64 x (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (*.f64 x x) (/.f64 2 (/.f64 (-.f64 x y) x))) 1) (*.f64 (neg.f64 (*.f64 (*.f64 y y) (/.f64 2 (/.f64 (-.f64 x y) x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (neg.f64 (*.f64 y y)) (/.f64 2 (/.f64 (-.f64 x y) x))) (*.f64 (*.f64 x x) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 (neg.f64 y) y (*.f64 y y)) (/.f64 2 (/.f64 (-.f64 x y) x))) (*.f64 (*.f64 x 2) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (+.f64 x y) x) (/.f64 2 (/.f64 (-.f64 x y) x))) (*.f64 (*.f64 (+.f64 x y) (neg.f64 y)) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (+.f64 x y)) (/.f64 2 (/.f64 (-.f64 x y) x))) (*.f64 (*.f64 (neg.f64 y) (+.f64 x y)) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (*.f64 x x) (/.f64 2 (/.f64 (-.f64 x y) x))) (*.f64 (*.f64 y y) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 x 2) (+.f64 x y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (/.f64 2 (/.f64 (-.f64 x y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 2) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x 2) (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (*.f64 x 2) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (*.f64 x 2) (+.f64 x y))) (sqrt.f64 (*.f64 (*.f64 x 2) (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 x 2) (+.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 x 2) (+.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 x 2) (+.f64 x y))) 2) (cbrt.f64 (*.f64 (*.f64 x 2) (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) 2) (*.f64 (cbrt.f64 (-.f64 (*.f64 x x) (*.f64 y y))) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x y) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x y) (*.f64 (-.f64 x y) (/.f64 2 (/.f64 (-.f64 x y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) (-.f64 (*.f64 x x) (*.f64 y y)))))) 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simplify120.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

1420×	`unswap-sqr`
538×	`associate-l`
534×	`associate-+r+`
518×	`+-commutative`
500×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	3995
1	1083	3763
2	4471	3759

Stop Event

1×	node limit

Counts

189 → 178

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

Outputs
(.f64 2 (.f64 y x))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 (*.f64 y x)))
(.f64 x (.f64 2 (+.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 (*.f64 y x)))
(.f64 x (.f64 2 (+.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 (*.f64 y x)))
(.f64 x (.f64 2 (+.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(+.f64 (.f64 2 (.f64 y x)) (*.f64 2 (pow.f64 x 2)))
(.f64 x (.f64 2 (+.f64 y x)))
(+.f64 (.f64 2 (.f64 y x)) (*.f64 2 (pow.f64 x 2)))
(.f64 x (.f64 2 (+.f64 y x)))
(+.f64 (.f64 2 (.f64 y x)) (*.f64 2 (pow.f64 x 2)))
(.f64 x (.f64 2 (+.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(+.f64 (.f64 2 (.f64 y x)) (*.f64 2 (pow.f64 x 2)))
(.f64 x (.f64 2 (+.f64 y x)))
(+.f64 (.f64 2 (.f64 y x)) (*.f64 2 (pow.f64 x 2)))
(.f64 x (.f64 2 (+.f64 y x)))
(+.f64 (.f64 2 (.f64 y x)) (*.f64 2 (pow.f64 x 2)))
(.f64 x (.f64 2 (+.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(+.f64 (.f64 2 (.f64 y x)) (*.f64 2 (pow.f64 x 2)))
(.f64 x (.f64 2 (+.f64 y x)))
(+.f64 (.f64 2 (.f64 y x)) (*.f64 2 (pow.f64 x 2)))
(.f64 x (.f64 2 (+.f64 y x)))
(+.f64 (.f64 2 (.f64 y x)) (*.f64 2 (pow.f64 x 2)))
(.f64 x (.f64 2 (+.f64 y x)))
(.f64 2 (.f64 y x))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 (*.f64 y x)))
(.f64 x (.f64 2 (+.f64 y x)))
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(cbrt.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3) (pow.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x)) 3)))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3) (pow.f64 (*.f64 1/2 (/.f64 (-.f64 x y) x)) 3)))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) (.f64 y y)) 3) (pow.f64 (fma.f64 -1/2 (/.f64 y x) 1/2) 3)))
(expm1.f64 (log1p.f64 (.f64 (.f64 x 2) (+.f64 x y))))
(.f64 x (.f64 2 (+.f64 y x)))
(exp.f64 (log.f64 (.f64 (.f64 x 2) (+.f64 x y))))
(.f64 x (.f64 2 (+.f64 y x)))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x 2) (+.f64 x y))) 1))
(.f64 x (.f64 2 (+.f64 y x)))
(log1p.f64 (expm1.f64 (.f64 (.f64 x 2) (+.f64 x y))))
(.f64 x (.f64 2 (+.f64 y x)))
(+.f64 (.f64 (-.f64 x y) (/.f64 1/2 x)) (.f64 (/.f64 1/2 x) (fma.f64 (neg.f64 y) 1 y)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 (-.f64 x y) (/.f64 1/2 x)) (.f64 (/.f64 1/2 x) (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y)))
(*.f64 (/.f64 1/2 x) (+.f64 (-.f64 x y) (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y)))
(+.f64 (.f64 (-.f64 x y) (/.f64 1/2 x)) (.f64 (/.f64 1/2 x) (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y)))
(*.f64 (/.f64 1/2 x) (+.f64 (-.f64 x y) (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y)))
(+.f64 (.f64 (-.f64 x y) (/.f64 1/2 x)) (.f64 (fma.f64 (neg.f64 y) 1 y) (/.f64 1/2 x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 (-.f64 x y) (/.f64 1/2 x)) (.f64 (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y) (/.f64 1/2 x)))
(*.f64 (/.f64 1/2 x) (+.f64 (-.f64 x y) (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y)))
(+.f64 (.f64 (-.f64 x y) (/.f64 1/2 x)) (.f64 (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y) (/.f64 1/2 x)))
(*.f64 (/.f64 1/2 x) (+.f64 (-.f64 x y) (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y)))
(+.f64 (.f64 x (/.f64 1/2 x)) (neg.f64 (.f64 1/2 (/.f64 y x))))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 x (/.f64 1/2 x)) (.f64 1 (neg.f64 (*.f64 1/2 (/.f64 y x)))))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 x (/.f64 1/2 x)) (.f64 (neg.f64 y) (/.f64 1/2 x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 x (/.f64 1/2 x)) (.f64 (*.f64 (neg.f64 y) 1) (/.f64 1/2 x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (neg.f64 (.f64 1/2 (/.f64 y x))) (.f64 x (/.f64 1/2 x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 (/.f64 1/2 x) x) (.f64 (/.f64 1/2 x) (neg.f64 y)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 (/.f64 1/2 x) x) (.f64 (/.f64 1/2 x) (*.f64 (neg.f64 y) 1)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 (/.f64 1/2 x) (neg.f64 y)) (.f64 (/.f64 1/2 x) x))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 (.f64 x (/.f64 1/2 x)) 1) (.f64 (neg.f64 (.f64 1/2 (/.f64 y x))) 1))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(+.f64 (.f64 (neg.f64 y) (/.f64 1/2 x)) (.f64 x (/.f64 1/2 x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(-.f64 (.f64 x (/.f64 1/2 x)) (.f64 1/2 (/.f64 y x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(-.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x)))) 1)
(fma.f64 -1/2 (/.f64 y x) 1/2)
(*.f64 (-.f64 x y) (/.f64 1/2 x))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (.f64 (-.f64 x y) (/.f64 1/2 x)) 1)
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 1 (.f64 (-.f64 x y) (/.f64 1/2 x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (sqrt.f64 (.f64 (-.f64 x y) (/.f64 1/2 x))) (sqrt.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x))))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (sqrt.f64 (-.f64 x y)) (.f64 (sqrt.f64 (-.f64 x y)) (/.f64 1/2 x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (cbrt.f64 (.f64 (-.f64 x y) (/.f64 1/2 x))) (pow.f64 (cbrt.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x))) 2))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 x y) (/.f64 1/2 x))) 2) (cbrt.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x))))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (.f64 (cbrt.f64 (-.f64 x y)) (/.f64 1/2 x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (.f64 (-.f64 x y) 1/2) (/.f64 1 x))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(*.f64 (/.f64 1/2 x) (-.f64 x y))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (neg.f64 (-.f64 x y)) (/.f64 1 (.f64 x -2)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (/.f64 1 x) (.f64 (-.f64 x y) 1/2))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(*.f64 1/2 (/.f64 (-.f64 x y) x))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(.f64 (/.f64 1 (sqrt.f64 (.f64 x 2))) (/.f64 (-.f64 x y) (sqrt.f64 (*.f64 x 2))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 2 x))) (/.f64 (-.f64 x y) (sqrt.f64 (*.f64 2 x))))
(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (.f64 2 x))) (sqrt.f64 (.f64 2 x)))
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 x 2)) 2)) (/.f64 (-.f64 x y) (cbrt.f64 (*.f64 x 2))))
(/.f64 (.f64 1 (/.f64 (-.f64 x y) (cbrt.f64 (.f64 2 x)))) (pow.f64 (cbrt.f64 (*.f64 2 x)) 2))
(/.f64 (/.f64 (-.f64 x y) (pow.f64 (cbrt.f64 (.f64 2 x)) 2)) (cbrt.f64 (.f64 2 x)))
(/.f64 (/.f64 (-.f64 x y) (cbrt.f64 (.f64 2 x))) (pow.f64 (cbrt.f64 (.f64 2 x)) 2))
(*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) x) (/.f64 (sqrt.f64 (-.f64 x y)) 2))
(/.f64 (-.f64 x y) (*.f64 2 x))
(*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 2) (/.f64 (sqrt.f64 (-.f64 x y)) x))
(*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) x) (/.f64 (sqrt.f64 (-.f64 x y)) 2))
(/.f64 (-.f64 x y) (*.f64 2 x))
(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (/.f64 (sqrt.f64 (-.f64 x y)) (.f64 x 2)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) x) (/.f64 (sqrt.f64 (-.f64 x y)) 2))
(/.f64 (-.f64 x y) (*.f64 2 x))
(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (pow.f64 (cbrt.f64 (.f64 x 2)) 2)) (/.f64 (sqrt.f64 (-.f64 x y)) (cbrt.f64 (*.f64 x 2))))
(/.f64 (.f64 1 (/.f64 (-.f64 x y) (cbrt.f64 (.f64 2 x)))) (pow.f64 (cbrt.f64 (*.f64 2 x)) 2))
(/.f64 (/.f64 (-.f64 x y) (pow.f64 (cbrt.f64 (.f64 2 x)) 2)) (cbrt.f64 (.f64 2 x)))
(/.f64 (/.f64 (-.f64 x y) (cbrt.f64 (.f64 2 x))) (pow.f64 (cbrt.f64 (.f64 2 x)) 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) x) (/.f64 (cbrt.f64 (-.f64 x y)) 2))
(*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) x) (/.f64 (sqrt.f64 (-.f64 x y)) 2))
(/.f64 (-.f64 x y) (*.f64 2 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) 2) (/.f64 (cbrt.f64 (-.f64 x y)) x))
(*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) x) (/.f64 (sqrt.f64 (-.f64 x y)) 2))
(/.f64 (-.f64 x y) (*.f64 2 x))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) 1) (/.f64 (cbrt.f64 (-.f64 x y)) (.f64 x 2)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 x y)) x) (/.f64 (sqrt.f64 (-.f64 x y)) 2))
(/.f64 (-.f64 x y) (*.f64 2 x))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (sqrt.f64 (.f64 x 2))) (/.f64 (cbrt.f64 (-.f64 x y)) (sqrt.f64 (*.f64 x 2))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 2 x))) (/.f64 (-.f64 x y) (sqrt.f64 (*.f64 2 x))))
(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (.f64 2 x))) (sqrt.f64 (.f64 2 x)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (pow.f64 (cbrt.f64 (.f64 x 2)) 2)) (cbrt.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x))))
(.f64 (cbrt.f64 (.f64 1/2 (/.f64 (-.f64 x y) x))) (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (pow.f64 (cbrt.f64 (*.f64 2 x)) 2)))
(.f64 (cbrt.f64 (fma.f64 -1/2 (/.f64 y x) 1/2)) (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (pow.f64 (cbrt.f64 (.f64 2 x)) 2)))
(pow.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x)) 1)
(fma.f64 -1/2 (/.f64 y x) 1/2)
(pow.f64 (sqrt.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x))) 2)
(fma.f64 -1/2 (/.f64 y x) 1/2)
(pow.f64 (cbrt.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x))) 3)
(fma.f64 -1/2 (/.f64 y x) 1/2)
(pow.f64 (pow.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x)) 3) 1/3)
(fma.f64 -1/2 (/.f64 y x) 1/2)
(pow.f64 (/.f64 2 (/.f64 (-.f64 x y) x)) -1)
(fma.f64 -1/2 (/.f64 y x) 1/2)
(neg.f64 (/.f64 (-.f64 x y) (*.f64 x -2)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(sqrt.f64 (pow.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x)) 2))
(sqrt.f64 (pow.f64 (*.f64 1/2 (/.f64 (-.f64 x y) x)) 2))
(fabs.f64 (fma.f64 -1/2 (/.f64 y x) 1/2))
(log.f64 (pow.f64 (exp.f64 (-.f64 x y)) (/.f64 1/2 x)))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x)))))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(cbrt.f64 (pow.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x)) 3))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(cbrt.f64 (/.f64 (pow.f64 (-.f64 x y) 3) (pow.f64 (*.f64 x 2) 3)))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 x y) 3) (*.f64 (pow.f64 x 3) 8)))
(expm1.f64 (log1p.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x))))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(exp.f64 (log.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x))))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(exp.f64 (.f64 (log.f64 (.f64 (-.f64 x y) (/.f64 1/2 x))) 1))
(fma.f64 -1/2 (/.f64 y x) 1/2)
(log1p.f64 (expm1.f64 (*.f64 (-.f64 x y) (/.f64 1/2 x))))
(fma.f64 -1/2 (/.f64 y x) 1/2)

eval69.0ms (3%)

Compiler: Compiled 3609 to 1457 computations (59.6% saved)

prune35.0ms (1.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	192	4	196

Error

Counts

196 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	25.35%	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (/.f64 (-.f64 x y) (*.f64 2 x)))
✓	0.01%	(.f64 (+.f64 x y) (.f64 2 x))
✓	52.69%	(.f64 x (.f64 2 x))
✓	33.64%	(.f64 2 (.f64 y x))

Compiler

Compiled 40 to 26 computations (35% saved)

regimes18.0ms (0.8%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
4.0ms	x
4.0ms	y
4.0ms	(+.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 69 to 40 computations (42% saved)

regimes56.0ms (2.4%)

Accuracy

Total -46b remaining (-551.1%)

Threshold costs -46b (-551.1%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

38.0ms	y
17.0ms	x

Results

Error	Segments	Branch
16.56%	5	`x`
13.04%	3	`y`

Compiler

Compiled 18 to 12 computations (33.3% saved)

bsearch25.0ms (1.1%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	3.92583789783825e-78	4.521180231128852e-77
15.0ms	-9.371014309806121e-32	-4.26228628830826e-37

Results

22.0ms

240×

body

256

valid

Compiler

Compiled 256 to 191 computations (25.4% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative`
2×	`+-commutative`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	83
1	31	83

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(*.f64 (+.f64 x y) (*.f64 2 x))

(if (<=.f64 y -3507603929594167/730750818665451459101842416358141509827966271488) (*.f64 2 (*.f64 y x)) (if (<=.f64 y 439999770888249/16296287810675888690147565507275025288411747149327490005089123594835050398106693649467179008) (*.f64 x (*.f64 2 x)) (*.f64 2 (*.f64 y x))))

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

Outputs
(.f64 (+.f64 x y) (.f64 2 x))
(.f64 (+.f64 x y) (.f64 x 2))
(if (<=.f64 y -3507603929594167/730750818665451459101842416358141509827966271488) (.f64 2 (.f64 y x)) (if (<=.f64 y 439999770888249/16296287810675888690147565507275025288411747149327490005089123594835050398106693649467179008) (.f64 x (.f64 2 x)) (.f64 2 (.f64 y x))))
(if (or (<=.f64 y -3507603929594167/730750818665451459101842416358141509827966271488) (not (<=.f64 y 439999770888249/16296287810675888690147565507275025288411747149327490005089123594835050398106693649467179008))) (.f64 2 (.f64 x y)) (.f64 x (.f64 x 2)))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 x y))

Compiler

Compiled 37 to 26 computations (29.7% saved)

soundness37.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

34×	`fma-def`
32×	`*-commutative`
10×	`+-commutative`
8×	`associate-r`
8×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	22	19
2	43	19
3	63	19
4	68	19

Stop Event

1×

saturated

Compiler

Compiled 32 to 17 computations (46.9% saved)

end24.0ms (1%)

Compiler: Compiled 33 to 21 computations (36.4% saved)

Details

analyze69.0ms (3%)

sample995.0ms (43.5%)

preprocess6.0ms (0.3%)

simplify13.0ms (0.6%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize7.0ms (0.3%)

series3.0ms (0.1%)

rewrite58.0ms (2.5%)

simplify53.0ms (2.3%)

eval7.0ms (0.3%)

prune6.0ms (0.3%)

localize7.0ms (0.3%)

series3.0ms (0.1%)

rewrite249.0ms (10.9%)

simplify87.0ms (3.8%)

localize5.0ms (0.2%)

localize14.0ms (0.6%)

series165.0ms (7.2%)

rewrite152.0ms (6.6%)

simplify120.0ms (5.3%)

eval69.0ms (3%)

prune35.0ms (1.5%)

regimes18.0ms (0.8%)

regimes56.0ms (2.4%)

bsearch25.0ms (1.1%)

simplify5.0ms (0.2%)

soundness37.0ms (1.6%)

end24.0ms (1%)

Profiling