Details

analyze161.0ms (3.5%)

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)

sample1.1s (25%)

Results

986.0ms	8256×	body	256	valid
138.0ms	1022×	body	256	invalid

preprocess19.0ms (0.4%)

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

0.0b

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)

localize15.0ms (0.3%)

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)

series7.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite85.0ms (1.9%)

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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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (.f64 x (.f64 2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (.f64 2 y) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) 1 (.f64 x (.f64 2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (.f64 x y) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x x) y (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (+.f64 x x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (.f64 2 y)) 1 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (.f64 x (.f64 2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x (.f64 2 y)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (.f64 x x) 4)) (.f64 (cbrt.f64 (+.f64 x x)) y) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (+.f64 x 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 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)))))))

simplify199.0ms (4.4%)

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

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 (0.2%)

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))
0.0ms	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 (1.3%)

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)))))))))

simplify199.0ms (4.4%)

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)))

eval68.0ms (1.5%)

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

prune40.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	222	8	230
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	224	8	232

Error

Counts

232 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	30.5b	(+.f64 (.f64 y (.f64 2 x)) (*.f64 y y))
▶	25.6b	(*.f64 x x)
	25.4b	(fma.f64 x x (.f64 y (.f64 2 x)))
	30.5b	(*.f64 y y)
▶	0.9b	(+.f64 (.f64 x x) (.f64 y y))
▶	0.0b	(fma.f64 x x (+.f64 (.f64 (.f64 x 2) y) (*.f64 y y)))
▶	0.0b	(fma.f64 y y (*.f64 x (fma.f64 2 y x)))
▶	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))

Compiler

Compiled 156 to 92 computations (41% saved)

localize16.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 37 to 18 computations (51.4% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite61.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

478×	`log-prod_binary64`
416×	`prod-exp_binary64`
381×	`fma-def_binary64`
346×	`pow-prod-down_binary64`
342×	`exp-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	194	12
2	2561	12

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

Outputs

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

simplify185.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

947×	`sqr-pow_binary64`
615×	`fma-def_binary64`
553×	`fabs-mul_binary64`
539×	`cube-prod_binary64`
372×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	294
1	32	267
2	69	222
3	151	216
4	418	216
5	1562	216
6	2826	216
7	3098	216
8	3284	216
9	3528	216
10	3831	216
11	4224	216
12	4729	216
13	5307	216
14	6055	216
15	6607	216
16	6943	216
17	7263	216
18	7349	216
19	7379	216

Stop Event

1×	node limit

Counts

62 → 48

Calls

Call 1

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

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	y	@	-inf	(+.f64 (.f64 x x) (.f64 y y))

rewrite52.0ms (1.1%)

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))))))

simplify166.0ms (3.6%)

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))

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)

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite80.0ms (1.8%)

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 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (*.f64 x (+.f64 y y)))))))

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(#(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 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(*.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 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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))))))

simplify207.0ms (4.5%)

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)))

localize12.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 24 to 12 computations (50% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite211.0ms (4.6%)

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 x (fma.f64 2 y x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 2 y) x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 2 y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (fma.f64 2 y x))) 1)))) (#(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)) 3) 1/3)))) (#(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 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 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))))))))

simplify179.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	213
2	41	177
3	79	177
4	170	177
5	476	177
6	1590	177
7	2828	177
8	3175	177
9	3398	177
10	3620	177
11	3938	177
12	4358	177
13	4847	177
14	5421	177
15	6115	177
16	6969	177
17	7366	177
18	7656	177
19	7936	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 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))

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

eval291.0ms (6.4%)

Compiler: Compiled 3500 to 1700 computations (51.4% saved)

prune107.0ms (2.3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	1	2	3
Picked	1	0	1
Done	0	4	4
Total	244	8	252

Error

Counts

252 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.5b	(+.f64 (.f64 y (.f64 2 x)) (*.f64 y y))
✓	25.6b	(*.f64 x x)
▶	0.0b	(fma.f64 y y (+.f64 (.f64 (.f64 2 y) x) (*.f64 x x)))
▶	25.4b	(fma.f64 x x (.f64 y (.f64 2 x)))
✓	0.9b	(+.f64 (.f64 x x) (.f64 y y))
✓	0.0b	(fma.f64 x x (+.f64 (.f64 (.f64 x 2) y) (*.f64 y y)))
✓	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
▶	30.5b	(*.f64 y y)

Compiler

Compiled 81 to 48 computations (40.7% saved)

localize133.0ms (2.9%)

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

localize20.0ms (0.4%)

Compiler: Compiled 25 to 13 computations (48% saved)

localize18.0ms (0.4%)

Compiler: Compiled 21 to 12 computations (42.9% saved)

localize28.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 37 to 18 computations (51.4% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite81.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

890×	`pow1_binary64`
828×	`add-log-exp_binary64`
827×	`log1p-expm1-u_binary64`
827×	`expm1-log1p-u_binary64`
809×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	174	8
2	2324	8

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

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

Outputs

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

simplify193.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	213
2	41	177
3	79	177
4	170	177
5	485	177
6	1619	177
7	2847	177
8	3194	177
9	3416	177
10	3638	177
11	3954	177
12	4374	177
13	4863	177
14	5437	177
15	6127	177
16	6979	177
17	7370	177
18	7660	177
19	7942	177

Stop Event

1×	node limit

Counts

64 → 45

Calls

Call 1

Inputs
(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))
(.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))

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

eval30.0ms (0.6%)

Compiler: Compiled 748 to 419 computations (44% saved)

prune18.0ms (0.4%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	45	8	53

Error

Counts

53 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.5b	(+.f64 (.f64 y (.f64 2 x)) (*.f64 y y))
✓	25.6b	(*.f64 x x)
✓	0.0b	(fma.f64 y y (+.f64 (.f64 (.f64 2 y) x) (*.f64 x x)))
✓	25.4b	(fma.f64 x x (.f64 y (.f64 2 x)))
✓	0.9b	(+.f64 (.f64 x x) (.f64 y y))
✓	0.0b	(fma.f64 x x (+.f64 (.f64 (.f64 x 2) y) (*.f64 y y)))
✓	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
✓	30.5b	(*.f64 y y)

Compiler

Compiled 81 to 48 computations (40.7% saved)

regimes56.0ms (1.2%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

19.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))
15.0ms	y
15.0ms	x

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 122 to 54 computations (55.7% saved)

regimes39.0ms (0.9%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

12.0ms	y
12.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))
11.0ms	x

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 92 to 41 computations (55.4% saved)

regimes11.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	x
4.0ms	y

Results

Error	Segments	Branch
0.9b	1	`x`
0.9b	1	`y`

Compiler

Compiled 33 to 13 computations (60.6% saved)

regimes40.0ms (0.9%)

Accuracy

Total -48.5b remaining (-715.6%)

Threshold costs -48.5b (-715.6%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

2 calls:

32.0ms	y
7.0ms	x

Results

Error	Segments	Branch
7.0b	2	`x`
6.8b	2	`y`

Compiler

Compiled 17 to 8 computations (52.9% saved)

bsearch21.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
21.0ms	2.550945691437359e-62	3.312985615332654e-59

Compiler

Compiled 20 to 13 computations (35% saved)

simplify148.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	61
1	27	61

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x x (+.f64 (.f64 (.f64 x 2) y) (*.f64 y y)))
(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
(+.f64 (.f64 x x) (.f64 y y))
(if (<=.f64 y 5907586622849239/231584178474632390847141970017375815706539969331281128078915168015826259279872) (.f64 x x) (.f64 y y))
(*.f64 y y)

Outputs
(fma.f64 x x (+.f64 (.f64 (.f64 x 2) y) (*.f64 y y)))
(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
(+.f64 (.f64 y y) (.f64 x (+.f64 x (*.f64 2 y))))
(+.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 y y) (.f64 x x))
(if (<=.f64 y 5907586622849239/231584178474632390847141970017375815706539969331281128078915168015826259279872) (.f64 x x) (.f64 y y))
(*.f64 y y)

Compiler

Compiled 53 to 31 computations (41.5% saved)

soundness11.0ms (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

Compiler

Compiled 67 to 39 computations (41.8% saved)

end79.0ms (1.7%)

Compiler: Compiled 73 to 34 computations (53.4% saved)

Details

analyze161.0ms (3.5%)

sample1.1s (25%)

preprocess19.0ms (0.4%)

simplify8.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize15.0ms (0.3%)

series7.0ms (0.1%)

rewrite85.0ms (1.9%)

simplify199.0ms (4.4%)

localize11.0ms (0.2%)

series6.0ms (0.1%)

rewrite61.0ms (1.3%)

simplify199.0ms (4.4%)

eval68.0ms (1.5%)

prune40.0ms (0.9%)

localize16.0ms (0.4%)

series2.0ms (0%)

rewrite61.0ms (1.4%)

simplify185.0ms (4.1%)

localize3.0ms (0.1%)

localize7.0ms (0.2%)

series2.0ms (0%)

rewrite52.0ms (1.1%)

simplify166.0ms (3.6%)

localize14.0ms (0.3%)

series6.0ms (0.1%)

rewrite80.0ms (1.8%)

simplify207.0ms (4.5%)

localize12.0ms (0.3%)

series2.0ms (0.1%)

rewrite211.0ms (4.6%)

simplify179.0ms (3.9%)

eval291.0ms (6.4%)

prune107.0ms (2.3%)

localize133.0ms (2.9%)

localize20.0ms (0.4%)

localize18.0ms (0.4%)

localize28.0ms (0.6%)

series3.0ms (0.1%)

rewrite81.0ms (1.8%)

simplify193.0ms (4.2%)

eval30.0ms (0.6%)

prune18.0ms (0.4%)

regimes56.0ms (1.2%)

regimes39.0ms (0.9%)

regimes11.0ms (0.2%)

regimes40.0ms (0.9%)

bsearch21.0ms (0.5%)

simplify148.0ms (3.2%)

soundness11.0ms (0.2%)

end79.0ms (1.7%)

Profiling