Details

analyze99.0ms (2.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
25%	53.1%	22%	7
31.2%	43.7%	25.1%	8
39%	32.8%	28.2%	9
42.9%	25.4%	31.7%	10
47.2%	18%	34.8%	11
49.4%	13.6%	37.1%	12

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample1.5s (37.1%)

Results

1.3s	8256×	body	256	valid
152.0ms	960×	body	256	invalid

preprocess19.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

48×	`fma-def_binary64`
9×	`*-commutative_binary64`
7×	`+-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	32	28
2	62	24
3	100	24
4	102	24
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Call 2

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

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

Symmetry

(sort x y)

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

33×	`fma-def_binary64`
8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	14
2	47	12
3	81	12
4	83	12

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 24 to 13 computations (45.8% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(fma.f64 x x (*.f64 y (fma.f64 x 2 y)))
▶	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

Compiler

Compiled 26 to 15 computations (42.3% saved)

localize16.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))
✓	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))

Compiler

Compiled 41 to 19 computations (53.7% saved)

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite80.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

667×	`fma-def_binary64`
542×	`log-prod_binary64`
437×	`pow-prod-down_binary64`
292×	`fma-neg_binary64`
288×	`pow2_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	223	24
2	3185	20

Stop Event

1×	node limit

Counts

2 → 174

Calls

Call 1

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

Outputs
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(2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) x) (.f64 x (.f64 2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 2 y)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 x) x) (pow.f64 (cbrt.f64 x) 2) (.f64 x (.f64 2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x (.f64 2 y))) (pow.f64 (cbrt.f64 (.f64 x (.f64 2 y))) 2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 2 y))) 2) (cbrt.f64 (.f64 x (.f64 2 y))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x x)) (.f64 (sqrt.f64 (+.f64 x x)) y) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 x (sqrt.f64 x)) (.f64 x (.f64 2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 2 y)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (.f64 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(.f64 x x))))))
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Outputs

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

simplify192.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

947×	`sqr-pow_binary64`
615×	`fma-def_binary64`
550×	`fabs-mul_binary64`
539×	`cube-prod_binary64`
375×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	525
1	32	480
2	69	399
3	151	393
4	418	393
5	1568	393
6	2841	393
7	3113	393
8	3299	393
9	3543	393
10	3842	393
11	4235	393
12	4740	393
13	5318	393
14	6064	393
15	6612	393
16	6946	393
17	7272	393
18	7360	393
19	7388	393

Stop Event

1×	node limit

Counts

222 → 184

Calls

Call 1

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

Outputs
(.f64 2 (.f64 y x))
(.f64 (.f64 2 y) x)
(.f64 y (.f64 x 2))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(.f64 2 (.f64 y x))
(.f64 (.f64 2 y) x)
(.f64 y (.f64 x 2))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(.f64 2 (.f64 y x))
(.f64 (.f64 2 y) x)
(.f64 y (.f64 x 2))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y (fma.f64 x 2 y)))
✓	0.0b	(*.f64 y (fma.f64 x 2 y))

Compiler

Compiled 24 to 12 computations (50% saved)

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite61.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

654×	`pow1_binary64`
600×	`add-log-exp_binary64`
600×	`log1p-expm1-u_binary64`
600×	`expm1-log1p-u_binary64`
588×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	140	20
2	1605	20

Stop Event

1×	node limit

Counts

2 → 34

Calls

Call 1

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

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

Outputs

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

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

simplify187.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

947×	`sqr-pow_binary64`
615×	`fma-def_binary64`
552×	`fabs-mul_binary64`
539×	`cube-prod_binary64`
375×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	525
1	32	498
2	69	435
3	151	393
4	418	393
5	1565	393
6	2837	393
7	3109	393
8	3296	393
9	3540	393
10	3839	393
11	4234	393
12	4743	393
13	5321	393
14	6061	393
15	6611	393
16	6947	393
17	7271	393
18	7359	393
19	7391	393

Stop Event

1×	node limit

Counts

82 → 46

Calls

Call 1

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

Outputs
(.f64 2 (.f64 y x))
(.f64 (.f64 2 y) x)
(.f64 y (.f64 x 2))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(.f64 2 (.f64 y x))
(.f64 (.f64 2 y) x)
(.f64 y (.f64 x 2))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(.f64 2 (.f64 y x))
(.f64 (.f64 2 y) x)
(.f64 y (.f64 x 2))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(fma.f64 y y (.f64 y (.f64 x 2)))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(fma.f64 2 (.f64 y x) (+.f64 (.f64 y y) (*.f64 x x)))
(fma.f64 2 (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))

eval69.0ms (1.7%)

Compiler: Compiled 3674 to 1776 computations (51.7% saved)

prune37.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	224	6	230
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	225	7	232

Error

Counts

232 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	25.0b	(*.f64 x x)
▶	29.4b	(+.f64 (.f64 2 (.f64 y x)) (*.f64 y y))
▶	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))
	29.4b	(*.f64 y (fma.f64 2 x y))
▶	29.6b	(*.f64 y y)
▶	1.6b	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 117 to 71 computations (39.3% saved)

localize14.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
✓	0.0b	(.f64 x (+.f64 x (.f64 2 y)))

Compiler

Compiled 34 to 18 computations (47.1% saved)

series35.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
31.0ms	x	@	-inf	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
1.0ms	x	@	0	(.f64 x (+.f64 x (.f64 2 y)))
1.0ms	x	@	-inf	(.f64 x (+.f64 x (.f64 2 y)))
0.0ms	y	@	inf	(.f64 x (+.f64 x (.f64 2 y)))
0.0ms	y	@	0	(.f64 x (+.f64 x (.f64 2 y)))

rewrite195.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

549×	`fma-def_binary64`
489×	`log-prod_binary64`
376×	`pow-prod-down_binary64`
264×	`pow2_binary64`
242×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	203	20
2	2942	20

Stop Event

1×	node limit

Counts

2 → 128

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (+.f64 y y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1) (*.f64 (*.f64 x (+.f64 y y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 2 y x))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 2 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 2 y x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 2 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 2 y x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (*.f64 x (+.f64 y y)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 (*.f64 x (+.f64 y y)) 2) (*.f64 (*.f64 x x) (*.f64 x (+.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x (+.f64 y y)) 2)) (-.f64 (*.f64 x x) (*.f64 x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 8 (pow.f64 y 3) (pow.f64 x 3)) x) (fma.f64 (+.f64 y y) (-.f64 (+.f64 y y) x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4)) x) (+.f64 x (*.f64 -2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (fma.f64 8 (pow.f64 y 3) (pow.f64 x 3))) (fma.f64 (+.f64 y y) (-.f64 (+.f64 y y) x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (-.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) (+.f64 x (*.f64 -2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 2 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 2 y x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 2 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 2 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 2 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 2 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 2 y x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (fma.f64 2 y x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 x (fma.f64 2 y x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 2 y x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 2 y x))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 x (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 y y) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (*.f64 y x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (*.f64 2 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 y y) x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 x (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (+.f64 y y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1 (*.f64 (*.f64 x (+.f64 y y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 y y)) 2) (*.f64 (cbrt.f64 (+.f64 y y)) x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) x) (*.f64 x (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 y y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 y y)) (*.f64 (sqrt.f64 (+.f64 y y)) x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (*.f64 x (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 y y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (*.f64 x (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (pow.f64 (cbrt.f64 x) 2) (*.f64 x (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 y y))) 2) (cbrt.f64 (*.f64 x (+.f64 y y))) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (+.f64 y y))) (sqrt.f64 (*.f64 x (+.f64 y y))) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 2) y (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x y) 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (+.f64 y y)) 2)) (cbrt.f64 (+.f64 y y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (+.f64 y y))) (sqrt.f64 (+.f64 y y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 y y) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (*.f64 x (+.f64 y y)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 2) (-.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))) (/.f64 (pow.f64 y 4) (-.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) 2) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 y (sqrt.f64 (*.f64 x (fma.f64 2 y x)))) (hypot.f64 y (sqrt.f64 (*.f64 x (fma.f64 2 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 (*.f64 y y) (-.f64 (*.f64 y y) (*.f64 x (fma.f64 2 y x))) (pow.f64 (*.f64 x (fma.f64 2 y x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 2) (pow.f64 y 4)) (/.f64 1 (-.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (*.f64 y y) (-.f64 (*.f64 y y) (*.f64 x (fma.f64 2 y x))) (pow.f64 (*.f64 x (fma.f64 2 y x)) 2)) (+.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 3) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y)) (-.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 2) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 3) (pow.f64 y 6)) (fma.f64 (*.f64 y y) (-.f64 (*.f64 y y) (*.f64 x (fma.f64 2 y x))) (pow.f64 (*.f64 x (fma.f64 2 y x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 3) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 2) (*.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 2) (pow.f64 y 4)) (-.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 3) (pow.f64 y 6))) (neg.f64 (fma.f64 (*.f64 y y) (-.f64 (*.f64 y y) (*.f64 x (fma.f64 2 y x))) (pow.f64 (*.f64 x (fma.f64 2 y x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 2) (pow.f64 y 4))) (neg.f64 (-.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 x (fma.f64 2 y x)) 2)) (-.f64 (*.f64 y y) (*.f64 x (fma.f64 2 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 y (sqrt.f64 (*.f64 x (fma.f64 2 y x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (*.f64 y y) (-.f64 (*.f64 y y) (*.f64 x (fma.f64 2 y x))) (pow.f64 (*.f64 x (fma.f64 2 y x)) 2)) (+.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 3) (pow.f64 y 6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (*.f64 x (fma.f64 2 y x)) (*.f64 y y)) (-.f64 (pow.f64 (*.f64 x (fma.f64 2 y x)) 2) (pow.f64 y 4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 2 y x)))) (exp.f64 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 x) (fma.f64 2 y x)) (+.f64 1 (expm1.f64 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 2 y x)))) (+.f64 1 (expm1.f64 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 y y))) (pow.f64 (exp.f64 x) (fma.f64 2 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 y y)) (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 2 y x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 y y))) (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 2 y x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 y (sqrt.f64 (*.f64 x (fma.f64 2 y x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (fma.f64 x (+.f64 y y) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (fma.f64 2 y x) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (*.f64 x (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 2 y x) x (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (fma.f64 2 y x)) 1 (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y y) 1 (*.f64 x (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (fma.f64 2 y x)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y y) (*.f64 x (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (fma.f64 x (+.f64 y y) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) y) (*.f64 x (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 y) y) (pow.f64 (cbrt.f64 y) 2) (*.f64 x (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) x) (fma.f64 x (+.f64 y y) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (fma.f64 2 y x)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 y x)) 2) (*.f64 (cbrt.f64 (fma.f64 2 y x)) x) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x (fma.f64 2 y x))) (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 2 y x))) 2) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 2 y x))) 2) (cbrt.f64 (*.f64 x (fma.f64 2 y x))) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (fma.f64 x (+.f64 y y) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (fma.f64 2 y x)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 2 y x)) (*.f64 (sqrt.f64 (fma.f64 2 y x)) x) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (sqrt.f64 (*.f64 x (fma.f64 2 y x))) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (pow.f64 y 3/2) (*.f64 x (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (fma.f64 x (+.f64 y y) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (pow.f64 (cbrt.f64 x) 2) (fma.f64 x (+.f64 y y) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 y 3/2) (sqrt.f64 y) (*.f64 x (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 5) (cbrt.f64 y) (*.f64 x (fma.f64 2 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (fma.f64 x (+.f64 y y) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (fma.f64 2 y x)) 2)) (cbrt.f64 (fma.f64 2 y x)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (fma.f64 2 y x))) (sqrt.f64 (fma.f64 2 y x)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 2 y x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 2 y x) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 y y))))))

simplify215.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

947×	`sqr-pow_binary64`
615×	`fma-def_binary64`
550×	`fabs-mul_binary64`
539×	`cube-prod_binary64`
375×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	525
1	32	480
2	69	399
3	151	393
4	418	393
5	1568	393
6	2841	393
7	3113	393
8	3299	393
9	3543	393
10	3842	393
11	4235	393
12	4740	393
13	5318	393
14	6064	393
15	6612	393
16	6946	393
17	7272	393
18	7360	393
19	7388	393

Stop Event

1×	node limit

Counts

176 → 139

Calls

Call 1

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

Outputs
(.f64 2 (.f64 y x))
(.f64 (.f64 2 y) x)
(.f64 y (.f64 x 2))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(.f64 2 (.f64 y x))
(.f64 (.f64 2 y) x)
(.f64 y (.f64 x 2))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(.f64 2 (.f64 y x))
(.f64 (.f64 2 y) x)
(.f64 y (.f64 x 2))
(.f64 y (.f64 2 x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 x 2))
(fma.f64 2 (.f64 y x) (.f64 x x))
(.f64 x (+.f64 (.f64 2 y) x))
(*.f64 x (fma.f64 2 y x))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 (.f64 y x) (.f64 y y)) (*.f64 x x))
(fma.f64 2 (.f64 y x) (fma.f64 x x (.f64 y y)))
(fma.f64 y y (*.f64 x (fma.f64 2 y x)))

localize3.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 17 to 5 computations (70.6% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite186.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`pow1_binary64`
606×	`add-log-exp_binary64`
606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
589×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	129	7
2	1751	7

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

Inputs
(+.f64 (.f64 x x) (.f64 y y))

Outputs

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

simplify168.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1204×	`sqr-pow_binary64`
754×	`cube-prod_binary64`
743×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
346×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	204
1	16	168
2	29	168
3	47	168
4	99	168
5	295	168
6	1113	168
7	1389	168
8	1679	168
9	1930	168
10	2269	168
11	2762	168
12	3421	168
13	4211	168
14	5133	168
15	5654	168
16	6071	168
17	6462	168
18	6583	168
19	6627	168
20	7796	168

Stop Event

1×	node limit

Counts

57 → 38

Calls

Call 1

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

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 y x))
✓	0.0b	(+.f64 (.f64 2 (.f64 y x)) (*.f64 y y))

Compiler

Compiled 25 to 10 computations (60% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite180.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

872×	`pow1_binary64`
811×	`add-log-exp_binary64`
810×	`log1p-expm1-u_binary64`
810×	`expm1-log1p-u_binary64`
793×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	172	18
2	2275	18

Stop Event

1×	node limit

Counts

2 → 47

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 2 (*.f64 y x) (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (-.f64 (*.f64 2 (*.f64 y x)) (*.f64 y y))) (/.f64 (pow.f64 y 4) (-.f64 (*.f64 2 (*.f64 y x)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 2 (*.f64 y x) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y))) (pow.f64 (cbrt.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y))) 2) (cbrt.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 y (sqrt.f64 (*.f64 2 (*.f64 y x)))) (hypot.f64 y (sqrt.f64 (*.f64 2 (*.f64 y x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 (*.f64 y x) 3) 8) (pow.f64 y 6)) (/.f64 1 (+.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 (*.f64 y x) (*.f64 y y)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (pow.f64 y 4)) (/.f64 1 (-.f64 (*.f64 2 (*.f64 y x)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 (*.f64 y x) (*.f64 y y))))) (+.f64 (*.f64 (pow.f64 (*.f64 y x) 3) 8) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 2 (*.f64 y x)) (*.f64 y y)) (-.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (*.f64 y x) 3) 8) (pow.f64 y 6)) (+.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 (*.f64 y x) (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (*.f64 y x) 3) 8) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (*.f64 2 (*.f64 (*.f64 y x) (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (pow.f64 y 4)) (-.f64 (*.f64 2 (*.f64 y x)) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 (*.f64 y x) 3) 8) (pow.f64 y 6))) (neg.f64 (+.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 (*.f64 y x) (*.f64 y y)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2) (pow.f64 y 4))) (neg.f64 (-.f64 (*.f64 2 (*.f64 y x)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 2 (*.f64 y x)) 2)) (-.f64 (*.f64 y y) (*.f64 2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 y (sqrt.f64 (*.f64 2 (*.f64 y x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 2 (*.f64 y x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (*.f64 y x) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (*.f64 2 (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y x) 2 (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 2 (*.f64 y x)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y y) (*.f64 2 (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 y x))) 2) (cbrt.f64 (*.f64 2 (*.f64 y x))) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 y 4)) (cbrt.f64 (*.f64 y y)) (*.f64 2 (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 2 (*.f64 y x))) (sqrt.f64 (*.f64 2 (*.f64 y x))) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 y) x (*.f64 y y))))))

((#(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 (cbrt.f64 (*.f64 2 (*.f64 y x))) 3)))) (#(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 (*.f64 (pow.f64 (*.f64 y x) 3) 8) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 2 (*.f64 y x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 y) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 y x) 3) 8))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (*.f64 y x))))))))

simplify168.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
582×	`fma-def_binary64`
555×	`cube-prod_binary64`
550×	`fabs-mul_binary64`
473×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	231
2	37	213
3	75	177
4	167	177
5	467	177
6	1572	177
7	2818	177
8	3173	177
9	3395	177
10	3617	177
11	3935	177
12	4357	177
13	4870	177
14	5442	177
15	6136	177
16	6986	177
17	7379	177
18	7667	177
19	7947	177

Stop Event

1×	node limit

Counts

71 → 53

Calls

Call 1

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

Outputs
(.f64 2 (.f64 y x))
(.f64 x (.f64 2 y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(.f64 2 (.f64 y x))
(.f64 x (.f64 2 y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(.f64 2 (.f64 y x))
(.f64 x (.f64 2 y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))

eval91.0ms (2.3%)

Compiler: Compiled 3421 to 1610 computations (52.9% saved)

prune39.0ms (1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	1	0	1
Picked	0	1	1
Done	0	5	5
Total	230	7	237

Error

Counts

237 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.4b	(*.f64 y (fma.f64 2 x y))
✓	25.0b	(*.f64 x x)
✓	29.4b	(+.f64 (.f64 2 (.f64 y x)) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))
✓	29.6b	(*.f64 y y)
✓	1.6b	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 66 to 40 computations (39.4% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (fma.f64 2 x y))

Compiler

Compiled 15 to 8 computations (46.7% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	0	(*.f64 y (fma.f64 2 x y))
0.0ms	y	@	-inf	(*.f64 y (fma.f64 2 x y))
0.0ms	x	@	0	(*.f64 y (fma.f64 2 x y))
0.0ms	x	@	-inf	(*.f64 y (fma.f64 2 x y))
0.0ms	x	@	inf	(*.f64 y (fma.f64 2 x y))

rewrite77.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`pow1_binary64`
531×	`add-sqr-sqrt_binary64`
507×	`add-log-exp_binary64`
507×	`log1p-expm1-u_binary64`
507×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	120	8
2	1364	8

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify166.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
582×	`fma-def_binary64`
555×	`cube-prod_binary64`
550×	`fabs-mul_binary64`
473×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	231
2	37	213
3	75	177
4	167	177
5	467	177
6	1572	177
7	2818	177
8	3173	177
9	3395	177
10	3617	177
11	3935	177
12	4357	177
13	4870	177
14	5442	177
15	6136	177
16	6986	177
17	7379	177
18	7667	177
19	7947	177

Stop Event

1×	node limit

Counts

37 → 19

Calls

Call 1

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

Outputs
(.f64 2 (.f64 y x))
(.f64 x (.f64 2 y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(.f64 2 (.f64 y x))
(.f64 x (.f64 2 y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(.f64 2 (.f64 y x))
(.f64 x (.f64 2 y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))
(+.f64 (.f64 2 (.f64 y x)) (pow.f64 y 2))
(fma.f64 2 (.f64 y x) (.f64 y y))
(.f64 y (+.f64 (.f64 2 x) y))
(*.f64 y (fma.f64 2 x y))

eval4.0ms (0.1%)

Compiler: Compiled 147 to 90 computations (38.8% saved)

prune7.0ms (0.2%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	19	0	19
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	19	7	26

Error

Counts

26 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.4b	(*.f64 y (fma.f64 2 x y))
✓	25.0b	(*.f64 x x)
✓	29.4b	(+.f64 (.f64 2 (.f64 y x)) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))
✓	29.6b	(*.f64 y y)
✓	1.6b	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 66 to 40 computations (39.4% saved)

regimes21.0ms (0.5%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	y
6.0ms	x
5.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))`

Compiler

Compiled 90 to 42 computations (53.3% saved)

regimes10.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	y
4.0ms	x

Results

Error	Segments	Branch
1.6b	1	`x`
1.6b	1	`y`

Compiler

Compiled 30 to 13 computations (56.7% saved)

regimes17.0ms (0.4%)

Accuracy

Total -47.9b remaining (-926.8%)

Threshold costs -47.9b (-926.8%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

10.0ms	x
6.0ms	y

Results

Error	Segments	Branch
5.2b	2	`x`
8.6b	2	`y`

Compiler

Compiled 14 to 8 computations (42.9% saved)

bsearch25.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
25.0ms	-1.3171660527988144e-152	-9.53095087398779e-154

Compiler

Compiled 20 to 13 computations (35% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	20	44

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
(+.f64 (.f64 x x) (.f64 y y))
(if (<=.f64 x -1553417247035385/117936325775673167257548580655883402841153788138013763386756446882675755074754651627691460161801836485670886719711370153117830769685149769767544820357271751364043603968) (.f64 x x) (.f64 y y))
(*.f64 x x)

Outputs
(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
(+.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 y y) (.f64 x x))
(if (<=.f64 x -1553417247035385/117936325775673167257548580655883402841153788138013763386756446882675755074754651627691460161801836485670886719711370153117830769685149769767544820357271751364043603968) (.f64 x x) (.f64 y y))
(*.f64 x x)

Compiler

Compiled 39 to 23 computations (41% saved)

soundness0.0ms (0%)

end60.0ms (1.5%)

Remove: (sort x y)
Compiler: Compiled 59 to 29 computations (50.8% saved)

Details

analyze99.0ms (2.5%)

sample1.5s (37.1%)

preprocess19.0ms (0.5%)

simplify8.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize16.0ms (0.4%)

series6.0ms (0.1%)

rewrite80.0ms (2%)

simplify192.0ms (4.8%)

localize11.0ms (0.3%)

series6.0ms (0.1%)

rewrite61.0ms (1.5%)

simplify187.0ms (4.7%)

eval69.0ms (1.7%)

prune37.0ms (0.9%)

localize14.0ms (0.3%)

series35.0ms (0.9%)

rewrite195.0ms (4.9%)

simplify215.0ms (5.4%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize7.0ms (0.2%)

series2.0ms (0%)

rewrite186.0ms (4.6%)

simplify168.0ms (4.2%)

localize9.0ms (0.2%)

series4.0ms (0.1%)

rewrite180.0ms (4.5%)

simplify168.0ms (4.2%)

eval91.0ms (2.3%)

prune39.0ms (1%)

localize8.0ms (0.2%)

series4.0ms (0.1%)

rewrite77.0ms (1.9%)

simplify166.0ms (4.1%)

eval4.0ms (0.1%)

prune7.0ms (0.2%)

regimes21.0ms (0.5%)

regimes10.0ms (0.3%)

regimes17.0ms (0.4%)

bsearch25.0ms (0.6%)

simplify9.0ms (0.2%)

soundness0.0ms (0%)

end60.0ms (1.5%)

Profiling