Details

analyze102.0ms (7.5%)

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%	87.4%	12.6%	4
6.2%	74.9%	18.8%	5
12.5%	59.3%	28.2%	6
23.4%	43.7%	32.9%	7
28.1%	33.6%	38.3%	8
35.5%	23.4%	41.1%	9
38.2%	17.8%	44%	10
42.4%	12.1%	45.5%	11
43.9%	9.1%	47%	12
46.1%	6.1%	47.7%	13
46.9%	4.6%	48.5%	14

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample691.0ms (50.8%)

Results

659.0ms	8256×	body	128	valid
19.0ms	246×	body	128	invalid

Compiler

Compiled 14 to 10 computations (28.6% saved)

preprocess15.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

1×	`swap-x-y`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	7	12
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
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (+.f64 y x))

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

Symmetry

(sort x y)

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify5.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.4%)

Counts

1 → 8

Calls

6 calls:

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

rewrite29.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`pow1_binary64`
553×	`add-log-exp_binary64`
553×	`log1p-expm1-u_binary64`
553×	`expm1-log1p-u_binary64`
58×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	109	6
2	1503	6

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

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

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

Outputs

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

simplify29.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
844×	`fma-def_binary64`
541×	`associate-l_binary64`
416×	`associate-r_binary64`
224×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	212
1	137	212
2	378	204
3	1199	198
4	4325	197

Stop Event

1×	node limit

Counts

33 → 39

Calls

Call 1

Inputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))
(-.f64 (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))

Outputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(-.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) (.f64 (.f64 -1/8 (.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (.f64 x x) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)))
(fma.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))) (sqrt.f64 y))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(-.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x x))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))) (.f64 (.f64 -1/8 (*.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (.f64 x x) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 1/16 (pow.f64 x 3)) (sqrt.f64 y))))
(fma.f64 x (fma.f64 1/2 (sqrt.f64 (/.f64 1 y)) (.f64 x (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y)))
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 y y))))
(-.f64 (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 1/8 (.f64 y y))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 y y)) -1/8 (fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)))
(fma.f64 y (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 y (*.f64 y -1/8)) (sqrt.f64 x)))
(-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 y y))))
(+.f64 (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 y y)))
(fma.f64 (pow.f64 y 3) (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 y y)) -1/8 (fma.f64 y (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))))
(fma.f64 y (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 (pow.f64 y 3) (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 y (.f64 y -1/8)) (sqrt.f64 x))))
(+.f64 (sqrt.f64 x) (fma.f64 y (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (.f64 (.f64 y y) (fma.f64 y (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)))))

prune29.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Error

Counts

40 → 3

Alt Table

Status	Error	Program
▶	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
	0.8b	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 528 to 315 computations (40.3% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x y) 1/4)
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)

series14.0ms (1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
2.0ms	y	@	-inf	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
1.0ms	x	@	0	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
1.0ms	y	@	-inf	(pow.f64 (+.f64 x y) 1/4)
1.0ms	y	@	inf	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)

rewrite38.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`pow1_binary64`
751×	`log1p-expm1-u_binary64`
751×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
85×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	182	13
2	2165	13

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
(pow.f64 (+.f64 x y) 1/4)

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

Outputs

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

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

simplify51.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

834×	`times-frac_binary64`
549×	`fma-def_binary64`
523×	`associate-/l*_binary64`
197×	`cancel-sign-sub-inv_binary64`
126×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	1962
1	482	1934
2	1690	1608

Stop Event

1×	node limit

Counts

94 → 106

Calls

Call 1

Inputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))
(-.f64 (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)
(+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) x)) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) x)) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (.f64 1/16 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (pow.f64 x 3))))) (.f64 1/8 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (pow.f64 x 2))))
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))
(-.f64 (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2)
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) x) y)) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) x) y)) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) (pow.f64 x 2)) (pow.f64 y 2))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) x) y)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) (.f64 1/16 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) (pow.f64 x 3)) (pow.f64 y 3))))) (.f64 1/8 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) (pow.f64 x 2)) (pow.f64 y 2))))
(pow.f64 y 1/4)
(+.f64 (pow.f64 y 1/4) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) x)))
(-.f64 (+.f64 (pow.f64 y 1/4) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) x))) (.f64 3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 2))))
(-.f64 (+.f64 (pow.f64 y 1/4) (+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) x)) (.f64 7/128 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (pow.f64 x 3))))) (.f64 3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 2))))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (.f64 1/4 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))))
(-.f64 (+.f64 (pow.f64 x 1/4) (.f64 1/4 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))) (.f64 3/32 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(-.f64 (+.f64 (.f64 7/128 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4))) (+.f64 (pow.f64 x 1/4) (.f64 1/4 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))))) (.f64 3/32 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(+.f64 (.f64 1/4 (/.f64 (.f64 y (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) x)) (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 y (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) x)) (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (.f64 3/32 (/.f64 (.f64 (pow.f64 y 2) (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 7/128 (/.f64 (.f64 (pow.f64 y 3) (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (pow.f64 x 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 y (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) x)) (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))) (.f64 3/32 (/.f64 (.f64 (pow.f64 y 2) (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (pow.f64 x 2))))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (.f64 1/4 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))))
(-.f64 (+.f64 (pow.f64 x 1/4) (.f64 1/4 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))) (.f64 3/32 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(-.f64 (+.f64 (.f64 7/128 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4))) (+.f64 (pow.f64 x 1/4) (.f64 1/4 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))))) (.f64 3/32 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(pow.f64 y 1/4)
(+.f64 (pow.f64 y 1/4) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) x)))
(-.f64 (+.f64 (pow.f64 y 1/4) (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) x))) (.f64 3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 2))))
(-.f64 (+.f64 (pow.f64 y 1/4) (+.f64 (.f64 1/4 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 3)) 1/4) x)) (.f64 7/128 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/4) (pow.f64 x 3))))) (.f64 3/32 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/4) (pow.f64 x 2))))
(exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))))
(+.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y)))
(-.f64 (+.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y))) (.f64 3/32 (/.f64 (.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 2)) (pow.f64 y 2))))
(-.f64 (+.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y)) (.f64 7/128 (/.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 3)) (pow.f64 y 3))))) (.f64 3/32 (/.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 2)) (pow.f64 y 2))))

Outputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
(fma.f64 x (*.f64 1/2 (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) (.f64 (.f64 -1/8 (.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))
(fma.f64 (.f64 -1/8 (.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (fma.f64 x (*.f64 1/2 (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y)))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))) (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x x))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))) (.f64 (.f64 -1/8 (*.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 (pow.f64 x 3) 1/16) (fma.f64 x (.f64 1/2 (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y))))
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2) (sqrt.f64 x))
(-.f64 (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (.f64 1/8 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (.f64 (.f64 -1/8 (.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) -1/8 (fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2) (sqrt.f64 x)))
(-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (.f64 -1/8 (.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (.f64 (.f64 -1/8 (*.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 (pow.f64 y 3) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16) (fma.f64 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) -1/8 (fma.f64 y (.f64 (sqrt.f64 (/.f64 1 x)) 1/2) (sqrt.f64 x))))
(pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)
(pow.f64 (*.f64 1 (exp.f64 (log.f64 x))) 1/2)
(+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) x)) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2))
(fma.f64 1/2 (/.f64 y (/.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(fma.f64 1/2 (*.f64 (/.f64 y x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(fma.f64 1/2 (.f64 (/.f64 y x) (pow.f64 (.f64 1 (exp.f64 (log.f64 x))) 1/2)) (pow.f64 (*.f64 1 (exp.f64 (log.f64 x))) 1/2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) x)) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 (/.f64 y (/.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (.f64 -1/8 (/.f64 (.f64 y y) (/.f64 (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))))
(+.f64 (fma.f64 1/2 (.f64 (/.f64 y x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (.f64 (.f64 (.f64 (/.f64 y x) (/.f64 y x)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) -1/8))
(fma.f64 (.f64 (.f64 (/.f64 y x) (pow.f64 (.f64 1 (exp.f64 (log.f64 x))) 1/2)) (/.f64 y x)) -1/8 (fma.f64 1/2 (.f64 (/.f64 y x) (pow.f64 (.f64 1 (exp.f64 (log.f64 x))) 1/2)) (pow.f64 (.f64 1 (exp.f64 (log.f64 x))) 1/2)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (.f64 1/16 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (pow.f64 x 3))))) (.f64 1/8 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (pow.f64 x 2))))
(+.f64 (+.f64 (fma.f64 1/2 (/.f64 y (/.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (.f64 1/16 (/.f64 (pow.f64 y 3) (/.f64 (pow.f64 x 3) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))))) (.f64 -1/8 (/.f64 (.f64 y y) (/.f64 (.f64 x x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))))
(+.f64 (fma.f64 1/2 (.f64 (/.f64 y x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (fma.f64 1/16 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))) (.f64 (.f64 (*.f64 (/.f64 y x) (/.f64 y x)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) -1/8))
(fma.f64 (.f64 (.f64 (/.f64 y x) (pow.f64 (.f64 1 (exp.f64 (log.f64 x))) 1/2)) (/.f64 y x)) -1/8 (fma.f64 1/2 (.f64 (/.f64 y x) (pow.f64 (.f64 1 (exp.f64 (log.f64 x))) 1/2)) (fma.f64 1/16 (.f64 (pow.f64 (/.f64 y x) 3) (pow.f64 (.f64 1 (exp.f64 (log.f64 x))) 1/2)) (pow.f64 (.f64 1 (exp.f64 (log.f64 x))) 1/2))))
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2) (sqrt.f64 x))
(-.f64 (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (.f64 1/8 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (.f64 (.f64 -1/8 (.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) -1/8 (fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2) (sqrt.f64 x)))
(-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (.f64 -1/8 (.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (.f64 (.f64 -1/8 (*.f64 y y)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 (pow.f64 y 3) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16) (fma.f64 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) -1/8 (fma.f64 y (.f64 (sqrt.f64 (/.f64 1 x)) 1/2) (sqrt.f64 x))))
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
(fma.f64 x (*.f64 1/2 (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y)) (.f64 (.f64 -1/8 (.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))
(fma.f64 (.f64 -1/8 (.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (fma.f64 x (*.f64 1/2 (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y)))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))) (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 x x))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)) (sqrt.f64 y))) (.f64 (.f64 -1/8 (*.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) -1/8) (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 (pow.f64 x 3) 1/16) (fma.f64 x (.f64 1/2 (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y))))
(pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)
(pow.f64 (*.f64 1 (exp.f64 (log.f64 y))) 1/2)
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) x) y)) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) (/.f64 y x)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2))
(fma.f64 1/2 (.f64 (/.f64 x y) (pow.f64 (.f64 1 (exp.f64 (log.f64 y))) 1/2)) (pow.f64 (*.f64 1 (exp.f64 (log.f64 y))) 1/2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) x) y)) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) (pow.f64 x 2)) (pow.f64 y 2))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) (/.f64 y x)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)) (.f64 -1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) (/.f64 (.f64 y y) (*.f64 x x)))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2) (/.f64 y x)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)) (/.f64 (.f64 -1/8 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) 2)) (.f64 (/.f64 y x) (/.f64 y x))))
(fma.f64 (.f64 (.f64 (/.f64 x y) (pow.f64 (.f64 1 (exp.f64 (log.f64 y))) 1/2)) (/.f64 x y)) -1/8 (fma.f64 1/2 (.f64 (/.f64 x y) (pow.f64 (.f64 1 (exp.f64 (log.f64 y))) 1/2)) (pow.f64 (.f64 1 (exp.f64 (log.f64 y))) 1/2)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) x) y)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) (.f64 1/16 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) (pow.f64 x 3)) (pow.f64 y 3))))) (.f64 1/8 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) 2) (pow.f64 x 2)) (pow.f64 y 2))))
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(fma.f64 1/4 (*.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 0 (log.f64 y))) y) x) (pow.f64 (exp.f64 1/4) (+.f64 0 (log.f64 y))))
(-.f64 (+.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y))) (.f64 3/32 (/.f64 (.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 2)) (pow.f64 y 2))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (-.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 y x))) (.f64 3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 (.f64 y y) (.f64 x x))))))
(+.f64 (fma.f64 1/4 (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y) x) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (*.f64 (/.f64 y x) (/.f64 y x))) -3/32))
(fma.f64 (.f64 (.f64 (/.f64 x y) (/.f64 x y)) (pow.f64 (exp.f64 1/4) (+.f64 0 (log.f64 y)))) -3/32 (fma.f64 1/4 (*.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 0 (log.f64 y))) y) x) (pow.f64 (exp.f64 1/4) (+.f64 0 (log.f64 y)))))
(-.f64 (+.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y)) (.f64 7/128 (/.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 3)) (pow.f64 y 3))))) (.f64 3/32 (/.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 2)) (pow.f64 y 2))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (-.f64 (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 y x)) (.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 (pow.f64 y 3) (pow.f64 x 3))))) (.f64 3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 (.f64 y y) (.f64 x x))))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (+.f64 (fma.f64 1/4 (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y) x) (/.f64 (.f64 7/128 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (/.f64 (pow.f64 y 3) (pow.f64 x 3)))) (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (.f64 (/.f64 y x) (/.f64 y x))) -3/32)))
(fma.f64 (.f64 (.f64 (/.f64 x y) (/.f64 x y)) (pow.f64 (exp.f64 1/4) (+.f64 0 (log.f64 y)))) -3/32 (fma.f64 1/4 (*.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 0 (log.f64 y))) y) x) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 0 (log.f64 y))) (pow.f64 (/.f64 y x) 3)) (pow.f64 (exp.f64 1/4) (+.f64 0 (log.f64 y))))))

prune63.0ms (4.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	106	3	109

Error

Counts

109 → 3

Alt Table

Status	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
▶	0.8b	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 2312 to 1628 computations (29.6% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.4b	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))
✓	0.5b	(cbrt.f64 (sqrt.f64 (+.f64 x y)))
✓	0.6b	(cbrt.f64 (+.f64 x y))

series12.0ms (0.9%)

Counts

3 → 40

Calls

18 calls:

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

rewrite50.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`pow1_binary64`
686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
83×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	166	19
2	2115	19

Stop Event

1×	node limit

Counts

3 → 71

Calls

Call 1

Inputs
(cbrt.f64 (+.f64 x y))
(cbrt.f64 (sqrt.f64 (+.f64 x y)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))

Outputs

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

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

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

simplify38.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

659×	`associate-l_binary64`
619×	`fma-def_binary64`
388×	`times-frac_binary64`
253×	`associate-/r*_binary64`
242×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	1576
1	510	1546
2	1706	1398

Stop Event

1×	node limit

Counts

111 → 131

Calls

Call 1

Inputs
(pow.f64 y 1/3)
(+.f64 (pow.f64 y 1/3) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/9) x)))
(-.f64 (+.f64 (pow.f64 y 1/3) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/9) x))) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/9) (pow.f64 x 2))))
(-.f64 (+.f64 (pow.f64 y 1/3) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/9) x)) (.f64 5/81 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 4)) 1/3) (pow.f64 x 3))))) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/9) (pow.f64 x 2))))
(pow.f64 x 1/3)
(+.f64 (pow.f64 x 1/3) (.f64 1/3 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9))))
(-.f64 (+.f64 (pow.f64 x 1/3) (.f64 1/3 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)))) (.f64 1/9 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/9))))
(-.f64 (+.f64 (.f64 5/81 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3))) (+.f64 (pow.f64 x 1/3) (.f64 1/3 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9))))) (.f64 1/9 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/9))))
(pow.f64 y 1/6)
(+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)))
(-.f64 (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x))) (.f64 5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (pow.f64 x 3))) (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)))) (.f64 5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))))
(pow.f64 x 1/6)
(+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6))
(-.f64 (+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6)) (.f64 5/72 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(-.f64 (+.f64 (.f64 55/1296 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6))) (+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6))) (.f64 5/72 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(+.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) y) x)))
(-.f64 (+.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) y) x))) (.f64 5/72 (/.f64 (.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 y 2)) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 55/1296 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 y 3)) (pow.f64 x 3))) (+.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) y) x)))) (.f64 5/72 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 y 2)) (pow.f64 x 2))))
(pow.f64 x 1/6)
(+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6))
(-.f64 (+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6)) (.f64 5/72 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(-.f64 (+.f64 (.f64 55/1296 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6))) (+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6))) (.f64 5/72 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(pow.f64 y 1/6)
(+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)))
(-.f64 (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x))) (.f64 5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (pow.f64 x 3))) (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)))) (.f64 5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))))
(+.f64 (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y)) (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y)) (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))))) (.f64 5/72 (/.f64 (.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 2)) (pow.f64 y 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y)) (+.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 55/1296 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 3)) (pow.f64 y 3))))) (.f64 5/72 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 2)) (pow.f64 y 2))))
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))
(-.f64 (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))

Outputs
(pow.f64 y 1/3)
(cbrt.f64 y)
(+.f64 (pow.f64 y 1/3) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/9) x)))
(+.f64 (cbrt.f64 y) (.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 y y)) 1/18) (pow.f64 (/.f64 1 (*.f64 y y)) 1/18)) x)))
(fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 y y)) 1/18) (pow.f64 (/.f64 1 (.f64 y y)) 1/18)) x) (cbrt.f64 y))
(-.f64 (+.f64 (pow.f64 y 1/3) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/9) x))) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/9) (pow.f64 x 2))))
(+.f64 (cbrt.f64 y) (-.f64 (.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 y y)) 1/18) (pow.f64 (/.f64 1 (.f64 y y)) 1/18)) x)) (.f64 1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18)) (*.f64 x x)))))
(+.f64 (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 y y)) 1/18) (pow.f64 (/.f64 1 (.f64 y y)) 1/18)) x) (cbrt.f64 y)) (.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18)) (.f64 x x)) -1/9))
(fma.f64 (.f64 x (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18) (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18)))) -1/9 (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 y y)) 1/18) (pow.f64 (/.f64 1 (*.f64 y y)) 1/18)) x) (cbrt.f64 y)))
(-.f64 (+.f64 (pow.f64 y 1/3) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/9) x)) (.f64 5/81 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 4)) 1/3) (pow.f64 x 3))))) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/9) (pow.f64 x 2))))
(+.f64 (cbrt.f64 y) (-.f64 (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 y y)) 1/18) (pow.f64 (/.f64 1 (.f64 y y)) 1/18)) x) (.f64 5/81 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 y 4))) (pow.f64 x 3)))) (.f64 1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18)) (.f64 x x)))))
(+.f64 (cbrt.f64 y) (+.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 y 4))) (.f64 (pow.f64 x 3) 5/81)) (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 y y)) 1/18) (pow.f64 (/.f64 1 (.f64 y y)) 1/18)) x) (.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18)) (.f64 x x)) -1/9))))
(fma.f64 (.f64 -1/9 (.f64 x x)) (.f64 (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 y 7)) 1/18)) (fma.f64 (.f64 (pow.f64 (/.f64 1 (.f64 y y)) 1/18) (pow.f64 (/.f64 1 (.f64 y y)) 1/18)) (.f64 x 1/3) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 y 4))) (.f64 (pow.f64 x 3) 5/81) (cbrt.f64 y))))
(pow.f64 x 1/3)
(cbrt.f64 x)
(+.f64 (pow.f64 x 1/3) (.f64 1/3 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9))))
(+.f64 (cbrt.f64 x) (.f64 1/3 (.f64 y (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (*.f64 x x)) 1/18)))))
(fma.f64 1/3 (.f64 y (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18))) (cbrt.f64 x))
(fma.f64 y (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) 1/3) (cbrt.f64 x))
(-.f64 (+.f64 (pow.f64 x 1/3) (.f64 1/3 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9)))) (.f64 1/9 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/9))))
(+.f64 (cbrt.f64 x) (-.f64 (.f64 1/3 (.f64 y (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)))) (.f64 1/9 (.f64 (.f64 y y) (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18))))))
(+.f64 (cbrt.f64 x) (fma.f64 (.f64 y 1/3) (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) (.f64 (.f64 -1/9 (.f64 y y)) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18)))))
(fma.f64 (.f64 (.f64 y y) -1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18)) (fma.f64 y (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (*.f64 x x)) 1/18)) 1/3) (cbrt.f64 x)))
(-.f64 (+.f64 (.f64 5/81 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 4)) 1/3))) (+.f64 (pow.f64 x 1/3) (.f64 1/3 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9))))) (.f64 1/9 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/9))))
(+.f64 (fma.f64 5/81 (.f64 (pow.f64 y 3) (cbrt.f64 (/.f64 1 (pow.f64 x 4)))) (+.f64 (cbrt.f64 x) (.f64 1/3 (.f64 y (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)))))) (.f64 -1/9 (.f64 (.f64 y y) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18)))))
(+.f64 (fma.f64 5/81 (.f64 (pow.f64 y 3) (cbrt.f64 (/.f64 1 (pow.f64 x 4)))) (cbrt.f64 x)) (fma.f64 (.f64 y 1/3) (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) (.f64 (.f64 -1/9 (.f64 y y)) (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18)))))
(fma.f64 5/81 (.f64 (pow.f64 y 3) (cbrt.f64 (/.f64 1 (pow.f64 x 4)))) (fma.f64 (.f64 (.f64 y y) -1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/18)) (fma.f64 y (.f64 (.f64 (pow.f64 (/.f64 1 (.f64 x x)) 1/18) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) 1/3) (cbrt.f64 x))))
(pow.f64 y 1/6)
(+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)))
(+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6))))
(fma.f64 1/6 (*.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6))
(fma.f64 x (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6))
(-.f64 (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x))) (.f64 5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))))
(+.f64 (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)))) (.f64 -5/72 (.f64 (*.f64 x x) (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))))
(+.f64 (pow.f64 y 1/6) (fma.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (.f64 (.f64 -5/72 (.f64 x x)) (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))))
(fma.f64 (.f64 x (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))) -5/72 (fma.f64 x (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6)))
(-.f64 (+.f64 (.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (pow.f64 x 3))) (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)))) (.f64 5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))))
(+.f64 (fma.f64 55/1296 (.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6)) (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6))))) (.f64 -5/72 (.f64 (.f64 x x) (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))))
(+.f64 (fma.f64 55/1296 (.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6)) (fma.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6))) (.f64 (.f64 -5/72 (*.f64 x x)) (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6)))
(fma.f64 (pow.f64 x 3) (.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6)) (fma.f64 (.f64 x (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))) -5/72 (fma.f64 x (.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6))))
(pow.f64 x 1/6)
(+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6))
(fma.f64 1/6 (*.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))
(fma.f64 y (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) 1/6) (pow.f64 x 1/6))
(-.f64 (+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6)) (.f64 5/72 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(+.f64 (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)) (.f64 -5/72 (.f64 (.f64 y y) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(+.f64 (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)) (.f64 (.f64 -5/72 (.f64 y y)) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(fma.f64 (.f64 y (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))) -5/72 (fma.f64 y (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) 1/6) (pow.f64 x 1/6)))
(-.f64 (+.f64 (.f64 55/1296 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6))) (+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6))) (.f64 5/72 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(+.f64 (fma.f64 55/1296 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))) (.f64 -5/72 (.f64 (*.f64 y y) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(+.f64 (fma.f64 55/1296 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))) (.f64 (.f64 -5/72 (*.f64 y y)) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(fma.f64 (pow.f64 y 3) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) 55/1296) (fma.f64 (.f64 y (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))) -5/72 (fma.f64 y (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) 1/6) (pow.f64 x 1/6))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x)))
(+.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) y) x)))
(+.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 x y))))
(fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 x y)) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 1/6 (*.f64 (/.f64 y x) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x)))) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x))))
(-.f64 (+.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) y) x))) (.f64 5/72 (/.f64 (.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 y 2)) (pow.f64 x 2))))
(+.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (-.f64 (.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 x y))) (.f64 5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 (.f64 x x) (.f64 y y))))))
(-.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 x y)) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 (.f64 5/72 (.f64 (.f64 y y) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (.f64 x x)))
(fma.f64 (.f64 (.f64 (/.f64 y x) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x)))) (/.f64 y x)) -5/72 (fma.f64 1/6 (*.f64 (/.f64 y x) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x)))) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x)))))
(-.f64 (+.f64 (.f64 55/1296 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 y 3)) (pow.f64 x 3))) (+.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) y) x)))) (.f64 5/72 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 y 2)) (pow.f64 x 2))))
(+.f64 (fma.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 x y))))) (.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 (.f64 x x) (.f64 y y)))))
(+.f64 (fma.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 x y)) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (.f64 (.f64 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 x x)) (.f64 y y)) -5/72))
(fma.f64 (.f64 (.f64 (/.f64 y x) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x)))) (/.f64 y x)) -5/72 (fma.f64 1/6 (.f64 (/.f64 y x) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x)))) (fma.f64 55/1296 (.f64 (pow.f64 (/.f64 y x) 3) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x)))) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 x))))))
(pow.f64 x 1/6)
(+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6))
(fma.f64 1/6 (*.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))
(fma.f64 y (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) 1/6) (pow.f64 x 1/6))
(-.f64 (+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6)) (.f64 5/72 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(+.f64 (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)) (.f64 -5/72 (.f64 (.f64 y y) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(+.f64 (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)) (.f64 (.f64 -5/72 (.f64 y y)) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(fma.f64 (.f64 y (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))) -5/72 (fma.f64 y (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) 1/6) (pow.f64 x 1/6)))
(-.f64 (+.f64 (.f64 55/1296 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6))) (+.f64 (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (pow.f64 x 1/6))) (.f64 5/72 (.f64 (pow.f64 y 2) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(+.f64 (fma.f64 55/1296 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))) (.f64 -5/72 (.f64 (*.f64 y y) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(+.f64 (fma.f64 55/1296 (.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))) (.f64 (.f64 -5/72 (*.f64 y y)) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(fma.f64 (pow.f64 y 3) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) 55/1296) (fma.f64 (.f64 y (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))) -5/72 (fma.f64 y (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) 1/6) (pow.f64 x 1/6))))
(pow.f64 y 1/6)
(+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)))
(+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6))))
(fma.f64 1/6 (*.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6))
(fma.f64 x (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6))
(-.f64 (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x))) (.f64 5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))))
(+.f64 (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)))) (.f64 -5/72 (.f64 (*.f64 x x) (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))))
(+.f64 (pow.f64 y 1/6) (fma.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (.f64 (.f64 -5/72 (.f64 x x)) (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))))
(fma.f64 (.f64 x (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))) -5/72 (fma.f64 x (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6)))
(-.f64 (+.f64 (.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (pow.f64 x 3))) (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)))) (.f64 5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))))
(+.f64 (fma.f64 55/1296 (.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6)) (+.f64 (pow.f64 y 1/6) (.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6))))) (.f64 -5/72 (.f64 (.f64 x x) (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))))
(+.f64 (fma.f64 55/1296 (.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6)) (fma.f64 1/6 (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6))) (.f64 (.f64 -5/72 (*.f64 x x)) (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6)))
(fma.f64 (pow.f64 x 3) (.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6)) (fma.f64 (.f64 x (.f64 x (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6))) -5/72 (fma.f64 x (.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6)) (pow.f64 y 1/6))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))
(pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y)))
(+.f64 (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y)) (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))))
(fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 y x)) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))))
(fma.f64 1/6 (*.f64 (/.f64 x y) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y)))) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y)) (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))))) (.f64 5/72 (/.f64 (.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 2)) (pow.f64 y 2))))
(+.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 y x)) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 (.f64 y y) (*.f64 x x)))))
(-.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 y x)) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 (/.f64 5/72 y) (/.f64 (.f64 (*.f64 x x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) y)))
(fma.f64 (.f64 (.f64 (/.f64 x y) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y)))) (/.f64 x y)) -5/72 (fma.f64 1/6 (*.f64 (/.f64 x y) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y)))) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y)))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) x) y)) (+.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 55/1296 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 3)) (pow.f64 y 3))))) (.f64 5/72 (/.f64 (.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (pow.f64 x 2)) (pow.f64 y 2))))
(+.f64 (+.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 y x)) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))) (.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 (pow.f64 y 3) (pow.f64 x 3))))) (.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 (.f64 y y) (.f64 x x)))))
(+.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) (/.f64 y x)) (fma.f64 55/1296 (/.f64 (pow.f64 x 3) (/.f64 (pow.f64 y 3) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))))) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))))) (.f64 (.f64 (/.f64 (*.f64 x x) y) (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y)))) y)) -5/72))
(fma.f64 (.f64 (.f64 (/.f64 x y) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y)))) (/.f64 x y)) -5/72 (fma.f64 1/6 (.f64 (/.f64 x y) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y)))) (fma.f64 55/1296 (.f64 (pow.f64 (/.f64 x y) 3) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y)))) (pow.f64 (exp.f64 1/6) (+.f64 0 (log.f64 y))))))
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(fma.f64 1/2 (*.f64 x (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y))
(fma.f64 x (*.f64 1/2 (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 (.f64 x (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y)) (.f64 -1/8 (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))))
(+.f64 (fma.f64 1/2 (.f64 x (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y)) (.f64 (.f64 -1/8 (.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))
(fma.f64 (.f64 -1/8 (.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (fma.f64 x (*.f64 1/2 (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y)))
(-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3))) (sqrt.f64 y))) (.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 (.f64 x (sqrt.f64 (/.f64 1 y))) (fma.f64 1/16 (.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (sqrt.f64 y))) (.f64 -1/8 (.f64 (*.f64 x x) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))))
(+.f64 (fma.f64 1/2 (.f64 x (sqrt.f64 (/.f64 1 y))) (fma.f64 1/16 (.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (sqrt.f64 y))) (.f64 (.f64 -1/8 (*.f64 x x)) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))
(fma.f64 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) -1/8 (fma.f64 x (.f64 1/2 (sqrt.f64 (/.f64 1 y))) (fma.f64 (pow.f64 x 3) (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 y 5)))) (sqrt.f64 y))))
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2) (sqrt.f64 x))
(-.f64 (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x)) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (.f64 -1/8 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (.f64 (.f64 y (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) -1/8))
(fma.f64 (.f64 y (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) -1/8 (fma.f64 y (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2) (sqrt.f64 x)))
(-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 x))) (.f64 1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (.f64 -1/8 (.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))) (.f64 (.f64 y (*.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) -1/8))
(fma.f64 (pow.f64 y 3) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16) (fma.f64 (.f64 y (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) -1/8 (fma.f64 y (.f64 (sqrt.f64 (/.f64 1 x)) 1/2) (sqrt.f64 x))))

prune83.0ms (6.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	170	3	173

Error

Counts

173 → 3

Alt Table

Status	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (+.f64 x y) 1/4) 2)
✓	0.8b	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x y))) (cbrt.f64 (+.f64 x y)))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 3451 to 1915 computations (44.5% saved)

regimes34.0ms (2.5%)

Accuracy

Total 0.0b remaining (65%)

Threshold costs 0.0b (65%)

Counts

12 → 1

Compiler

Compiled 108 to 55 computations (49.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

Calls

Call 1

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

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

end53.0ms (3.9%)

Stop Event

1×

done

Remove

(sort x y)

Compiler

Compiled 51 to 34 computations (33.3% saved)

Details

analyze102.0ms (7.5%)

sample691.0ms (50.8%)

preprocess15.0ms (1.1%)

simplify5.0ms (0.4%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series6.0ms (0.4%)

rewrite29.0ms (2.2%)

simplify29.0ms (2.1%)

prune29.0ms (2.1%)

localize6.0ms (0.4%)

series14.0ms (1%)

rewrite38.0ms (2.8%)

simplify51.0ms (3.7%)

prune63.0ms (4.6%)

localize6.0ms (0.4%)

series12.0ms (0.9%)

rewrite50.0ms (3.7%)

simplify38.0ms (2.8%)

prune83.0ms (6.1%)

regimes34.0ms (2.5%)

simplify2.0ms (0.1%)

end53.0ms (3.9%)

Profiling