Details

analyze50.0ms (1.4%)

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample757.0ms (20.5%)

Results

705.0ms	8256×	body	256	valid
35.0ms	503×	body	256	invalid

preprocess14.0ms (0.4%)

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 8 to 6 computations (25% saved)

simplify8.0ms (0.2%)

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))

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

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

Click to see full alt table

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 4 computations (63.6% saved)

series5.0ms (0.1%)

Counts

1 → 8

Calls

6 calls:

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

rewrite128.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`pow1_binary64`
553×	`add-log-exp_binary64`
553×	`log1p-expm1-u_binary64`
553×	`expm1-log1p-u_binary64`
539×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	109	6
2	1507	6

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

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

Outputs

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

simplify148.0ms (4%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-def_binary64`
577×	`associate-+l+_binary64`
544×	`associate-+r+_binary64`
457×	`associate-l_binary64`
388×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	210
1	130	204
2	339	204
3	959	198
4	2937	198
5	4374	198
6	4938	198
7	6701	198
8	7725	198

Stop Event

1×	node limit

Counts

32 → 38

Calls

Call 1

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

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

eval11.0ms (0.3%)

Compiler: Compiled 473 to 281 computations (40.6% saved)

prune8.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	4	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	5	39

Error

Counts

39 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.9b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (+.f64 x y))
▶	10.5b	(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)))
▶	0.6b	(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
▶	1.6b	(sqrt.f64 y)

Compiler

Compiled 61 to 45 computations (26.2% saved)

localize3.0ms (0.1%)

Compiler: Compiled 5 to 3 computations (40% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.3b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
✓	0.5b	(cbrt.f64 (+.f64 x y))
✓	0.6b	(cbrt.f64 (sqrt.f64 (+.f64 x y)))

Compiler

Compiled 30 to 7 computations (76.7% saved)

series17.0ms (0.5%)

Counts

3 → 40

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(cbrt.f64 (+.f64 x y))
2.0ms	y	@	0	(cbrt.f64 (+.f64 x y))
2.0ms	x	@	0	(cbrt.f64 (sqrt.f64 (+.f64 x y)))
1.0ms	x	@	-inf	(cbrt.f64 (sqrt.f64 (+.f64 x y)))
1.0ms	x	@	inf	(cbrt.f64 (sqrt.f64 (+.f64 x y)))

rewrite64.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

712×	`pow1_binary64`
666×	`add-log-exp_binary64`
666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
647×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	167	19
2	1907	19

Stop Event

1×	node limit

Counts

3 → 62

Calls

Call 1

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

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

Outputs

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

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

simplify119.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

732×	`distribute-rgt-in_binary64`
406×	`distribute-lft-out_binary64`
346×	`associate-+l+_binary64`
296×	`associate-+r+_binary64`
281×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	1648
1	723	1556
2	2591	1456
3	5854	1337

Stop Event

1×	node limit

Counts

102 → 126

Calls

Call 1

Inputs
(pow.f64 y 1/6)
(+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (pow.f64 y 1/6))
(+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (+.f64 (.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))) (pow.f64 y 1/6)))
(+.f64 (.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (pow.f64 x 3))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (+.f64 (.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))) (pow.f64 y 1/6))))
(pow.f64 x 1/6)
(+.f64 (pow.f64 x 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)))
(+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (+.f64 (.f64 -1/12 (pow.f64 y 2)) (.f64 1/72 (pow.f64 y 2)))) (+.f64 (pow.f64 x 1/6) (.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y))))
(+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (+.f64 (.f64 -1/12 (pow.f64 y 2)) (.f64 1/72 (pow.f64 y 2)))) (+.f64 (pow.f64 x 1/6) (+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (+.f64 (.f64 1/18 (pow.f64 y 3)) (+.f64 (.f64 1/1296 (pow.f64 y 3)) (*.f64 -1/72 (pow.f64 y 3))))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (.f64 1/6 (/.f64 (.f64 y (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) x)) (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(+.f64 (.f64 1/6 (/.f64 (.f64 y (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) x)) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 -1/12 (pow.f64 y 2)) (.f64 1/72 (pow.f64 y 2)))) (pow.f64 x 2)) (exp.f64 (.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(+.f64 (.f64 1/6 (/.f64 (.f64 y (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) x)) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 -1/12 (pow.f64 y 2)) (.f64 1/72 (pow.f64 y 2)))) (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 -1/1296 (pow.f64 y 3)) (+.f64 (.f64 -1/18 (pow.f64 y 3)) (.f64 1/72 (pow.f64 y 3))))) (pow.f64 x 3))) (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(pow.f64 x 1/6)
(+.f64 (pow.f64 x 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)))
(+.f64 (pow.f64 x 1/6) (+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)) (.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 y 2)))))
(+.f64 (pow.f64 x 1/6) (+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)) (+.f64 (.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 y 2))) (.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 y 3))))))
(pow.f64 y 1/6)
(+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (pow.f64 y 1/6))
(+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (+.f64 (.f64 -1/12 (pow.f64 x 2)) (.f64 1/72 (pow.f64 x 2)))) (+.f64 (.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (pow.f64 y 1/6)))
(+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (+.f64 (.f64 -1/12 (pow.f64 x 2)) (.f64 1/72 (pow.f64 x 2)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (+.f64 (.f64 1/18 (pow.f64 x 3)) (+.f64 (.f64 1/1296 (pow.f64 x 3)) (*.f64 -1/72 (pow.f64 x 3))))) (pow.f64 y 1/6))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))
(+.f64 (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) x) y)) (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))))
(+.f64 (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) x) y)) (+.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (+.f64 (.f64 -1/12 (pow.f64 x 2)) (*.f64 1/72 (pow.f64 x 2)))) (pow.f64 y 2))))
(+.f64 (.f64 1/6 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) x) y)) (+.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (+.f64 (.f64 -1/1296 (pow.f64 x 3)) (+.f64 (.f64 1/72 (pow.f64 x 3)) (.f64 -1/18 (pow.f64 x 3))))) (pow.f64 y 3))) (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1)))) (+.f64 (.f64 -1/12 (pow.f64 x 2)) (.f64 1/72 (pow.f64 x 2)))) (pow.f64 y 2)))))
(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 (pow.f64 y 1/3) (+.f64 (.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 (pow.f64 y 1/3) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/9) x)) (+.f64 (.f64 -1/3 (.f64 (.f64 (+.f64 (.f64 1/27 (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/3)) (.f64 -2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/3)))) (pow.f64 x 3)) (pow.f64 (/.f64 1 (pow.f64 y 2)) 1/3))) (.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 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9) y)))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9) y)) (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/9) (pow.f64 y 2)))))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9) y)) (+.f64 (.f64 -1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3) (.f64 (pow.f64 y 3) (+.f64 (.f64 1/27 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3)) (.f64 -2/9 (.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/3))))))) (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/9) (pow.f64 y 2))))))
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))) (+.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))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))))))

Outputs
(pow.f64 y 1/6)
(+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (pow.f64 y 1/6))
(fma.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x) (pow.f64 y 1/6))
(+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (+.f64 (.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))) (pow.f64 y 1/6)))
(fma.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x) (fma.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (*.f64 x x)) (pow.f64 y 1/6)))
(fma.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x) (fma.f64 (.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6)) (*.f64 x x) (pow.f64 y 1/6)))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (.f64 x (.f64 x -5/72)) (fma.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x) (pow.f64 y 1/6)))
(+.f64 (.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (pow.f64 x 3))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (+.f64 (.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (pow.f64 x 2))) (pow.f64 y 1/6))))
(fma.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (pow.f64 x 3)) (fma.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x) (fma.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (.f64 x x)) (pow.f64 y 1/6))))
(fma.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (pow.f64 x 3)) (fma.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x) (fma.f64 (.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6)) (.f64 x x) (pow.f64 y 1/6))))
(fma.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 17)) 1/6) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 y 11)) 1/6) (.f64 x (.f64 x -5/72)) (fma.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x) (pow.f64 y 1/6))))
(pow.f64 x 1/6)
(+.f64 (pow.f64 x 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)))
(+.f64 (pow.f64 x 1/6) (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 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 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (+.f64 (.f64 -1/12 (pow.f64 y 2)) (.f64 1/72 (pow.f64 y 2)))) (+.f64 (pow.f64 x 1/6) (.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 (.f64 y y) -5/72) (+.f64 (pow.f64 x 1/6) (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 -5/72 (.f64 y y)) (fma.f64 1/6 (*.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 y (.f64 y -5/72)) (fma.f64 1/6 (*.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)))
(+.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (+.f64 (.f64 -1/12 (pow.f64 y 2)) (.f64 1/72 (pow.f64 y 2)))) (+.f64 (pow.f64 x 1/6) (+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (+.f64 (.f64 1/18 (pow.f64 y 3)) (+.f64 (.f64 1/1296 (pow.f64 y 3)) (*.f64 -1/72 (pow.f64 y 3))))))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 (.f64 y y) -5/72) (+.f64 (pow.f64 x 1/6) (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (fma.f64 1/18 (pow.f64 y 3) (*.f64 (pow.f64 y 3) -17/1296))))))
(+.f64 (fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 -5/72 (.f64 y y)) (pow.f64 x 1/6)) (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (.f64 55/1296 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 y 3)))))
(+.f64 (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)) (.f64 (.f64 y y) (+.f64 (.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (.f64 (.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) y))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6))
(pow.f64 (exp.f64 1/6) (log.f64 x))
(+.f64 (.f64 1/6 (/.f64 (.f64 y (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) x)) (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(fma.f64 1/6 (/.f64 y (/.f64 x (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(fma.f64 1/6 (*.f64 (/.f64 y x) (pow.f64 (exp.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)))))
(fma.f64 1/6 (.f64 (/.f64 y x) (.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6))) (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)))
(.f64 (+.f64 (/.f64 (.f64 1/6 y) x) 1) (pow.f64 (exp.f64 1/6) (log.f64 x)))
(+.f64 (.f64 1/6 (/.f64 (.f64 y (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) x)) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 -1/12 (pow.f64 y 2)) (.f64 1/72 (pow.f64 y 2)))) (pow.f64 x 2)) (exp.f64 (.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(fma.f64 1/6 (/.f64 y (/.f64 x (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (.f64 x x) (.f64 (*.f64 y y) -5/72)))))
(+.f64 (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 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (/.f64 (.f64 -5/72 (.f64 y y)) x))))
(+.f64 (.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)) (fma.f64 1/6 (.f64 (/.f64 y x) (.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6))) (/.f64 (pow.f64 (/.f64 -1 x) -1/6) (/.f64 (.f64 (/.f64 x (.f64 y (.f64 y -5/72))) x) (pow.f64 -1 1/6)))))
(+.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) (.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) (+.f64 (/.f64 (.f64 1/6 y) x) (/.f64 (.f64 y (.f64 y -5/72)) (*.f64 x x)))))
(+.f64 (.f64 1/6 (/.f64 (.f64 y (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) x)) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 -1/12 (pow.f64 y 2)) (.f64 1/72 (pow.f64 y 2)))) (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 -1/1296 (pow.f64 y 3)) (+.f64 (.f64 -1/18 (pow.f64 y 3)) (.f64 1/72 (pow.f64 y 3))))) (pow.f64 x 3))) (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(fma.f64 1/6 (/.f64 y (/.f64 x (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (+.f64 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (.f64 x x) (.f64 (.f64 y y) -5/72))) (fma.f64 -1 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (pow.f64 x 3) (fma.f64 -1/1296 (pow.f64 y 3) (.f64 (pow.f64 y 3) -1/24)))) (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(+.f64 (-.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 3) -55/1296)))) (fma.f64 1/6 (.f64 (/.f64 y x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (.f64 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (/.f64 (.f64 -5/72 (*.f64 y y)) x))))
(+.f64 (fma.f64 1/6 (.f64 (/.f64 y x) (.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6))) (.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6))) (.f64 (.f64 (/.f64 (pow.f64 (/.f64 -1 x) -1/6) x) (/.f64 (pow.f64 -1 1/6) x)) (-.f64 (.f64 y (*.f64 y -5/72)) (/.f64 (pow.f64 y 3) (/.f64 x -55/1296)))))
(+.f64 (.f64 (+.f64 (/.f64 (.f64 1/6 y) x) 1) (pow.f64 (exp.f64 1/6) (log.f64 x))) (.f64 (/.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) (.f64 x x)) (fma.f64 y (.f64 y -5/72) (/.f64 (.f64 (pow.f64 y 3) 55/1296) x))))
(pow.f64 x 1/6)
(+.f64 (pow.f64 x 1/6) (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)))
(+.f64 (pow.f64 x 1/6) (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))
(fma.f64 1/6 (*.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))
(+.f64 (pow.f64 x 1/6) (+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)) (.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 y 2)))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 (.f64 y y) -5/72) (+.f64 (pow.f64 x 1/6) (.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 -5/72 (.f64 y y)) (fma.f64 1/6 (*.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 y (.f64 y -5/72)) (fma.f64 1/6 (*.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)))
(+.f64 (pow.f64 x 1/6) (+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) y)) (+.f64 (.f64 -5/72 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 y 2))) (.f64 55/1296 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 y 3))))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 (.f64 y y) -5/72) (+.f64 (pow.f64 x 1/6) (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (fma.f64 1/18 (pow.f64 y 3) (*.f64 (pow.f64 y 3) -17/1296))))))
(+.f64 (fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (.f64 -5/72 (.f64 y y)) (pow.f64 x 1/6)) (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (.f64 55/1296 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 y 3)))))
(+.f64 (fma.f64 1/6 (.f64 y (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)) (.f64 (.f64 y y) (+.f64 (.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (.f64 (.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) y))))
(pow.f64 y 1/6)
(+.f64 (.f64 1/6 (.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x)) (pow.f64 y 1/6))
(fma.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 y 5)) 1/6) x) (pow.f64 y 1/6))
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(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (log.f64 -1))))
(pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (log.f64 -1)))
(pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 y))))
(*.f64 (pow.f64 (/.f64 -1 y) -1/6) (pow.f64 -1 1/6))
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(pow.f64 y 1/3)
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(fma.f64 1/3 (.f64 x (.f64 (pow.f64 (/.f64 1 (.f64 y y)) 1/18) (pow.f64 (/.f64 1 (.f64 y y)) 1/18))) (cbrt.f64 y))
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(pow.f64 x 1/3)
(cbrt.f64 x)
(+.f64 (pow.f64 x 1/3) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 x 2)) 1/9) y)))
(+.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 1/3 (.f64 (.f64 y (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) (pow.f64 (/.f64 1 (.f64 x x)) 1/18)) (cbrt.f64 x))
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(sqrt.f64 y)
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(fma.f64 1/2 (*.f64 x (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y))
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(fma.f64 -1/8 (.f64 x (.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (fma.f64 1/2 (*.f64 x (sqrt.f64 (/.f64 1 y))) (sqrt.f64 y)))
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(sqrt.f64 x)
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(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
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(fma.f64 -1/8 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))))))
(fma.f64 -1/8 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)))
(fma.f64 -1/8 (.f64 y (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 y 2) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))))))
(fma.f64 -1/8 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 x) (.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 1 x)))))))
(fma.f64 -1/8 (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (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))))
(fma.f64 -1/8 (.f64 y (.f64 y (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (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))))

localize54.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 y)) x)
✓	0.4b	(/.f64 1 (pow.f64 y 3))
✓	12.0b	(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
✓	20.2b	(sqrt.f64 (/.f64 1 (pow.f64 y 3)))

Compiler

Compiled 106 to 79 computations (25.5% saved)

series14.0ms (0.4%)

Counts

4 → 0

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
1.0ms	x	@	0	(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
1.0ms	y	@	-inf	(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
1.0ms	x	@	0	(*.f64 (sqrt.f64 (/.f64 1 y)) x)
1.0ms	y	@	-inf	(*.f64 (sqrt.f64 (/.f64 1 y)) x)

rewrite72.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

545×	`log-prod_binary64`
400×	`pow-prod-down_binary64`
295×	`pow2_binary64`
222×	`pow-unpow_binary64`
218×	`pow-to-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	297	24
2	3281	24

Stop Event

1×	node limit

Counts

4 → 171

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 1 (pow.f64 y 3)))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(/.f64 1 (pow.f64 y 3))
(*.f64 (sqrt.f64 (/.f64 1 y)) x)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 y -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 y -3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 y -3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 y -3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 y -3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 y -3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 y -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 y -3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 y -1/2) (/.f64 1 y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 y -2)) (pow.f64 (/.f64 1 y) 5/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 y) (pow.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 y -3/4) (pow.f64 y -3/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 1 (cbrt.f64 y)) 4) (pow.f64 y -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 y -1/2) 5/2) (pow.f64 y -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 y 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 y 3/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 y -1/2) y)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 y) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (pow.f64 y 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (.f64 (neg.f64 y) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (pow.f64 y -1/2)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 y -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y 3) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -3) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -1/2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y 9) -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -2) 3/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -6) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -9) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 y y) -3/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -9/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 y)) 9/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 y) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 y) -9/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -1/6) 9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y 3/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 y) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -1/4) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -3/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 y 3/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 y -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 y -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 y -3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 y -9/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 y -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 y -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -3/2 (log.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -3 (log.f64 y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -3/2 (log.f64 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 y) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 y)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -1/2 (log.f64 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 y -9/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 y)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3/2 (log.f64 y)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 y -3/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 y)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 y) 1) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 3 (log.f64 y)) 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 y) -3) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 3 (log.f64 y)) -1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 -3 (log.f64 y)) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 -3 (log.f64 y)) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 -3/2 (log.f64 y)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (neg.f64 (log.f64 y)) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 -1/2 (log.f64 y)) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 y) -1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (neg.f64 (log.f64 y)) 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 (log.f64 y) 3/2) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 y -3/2) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (.f64 x x)) (pow.f64 y -3/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (.f64 x x)) (pow.f64 y -3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 x x)) (pow.f64 y -3/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 x x)) (pow.f64 y -3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 y -3/2) (.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x x) (pow.f64 y 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 y -3/2) (.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 y -3) (pow.f64 x 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 6) (pow.f64 y -9/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 y -1/2) (cbrt.f64 (.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (pow.f64 y -3/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 x (sqrt.f64 y)) (pow.f64 y -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 y -3) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (.f64 x x)) (pow.f64 y -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 y -3/2) (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 6) (pow.f64 y -9/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 y -3/2) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 y -3/2) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 y -3/2) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 y -3/2) (.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) (pow.f64 y -9/2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 y -1/2) (cbrt.f64 (.f64 x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (pow.f64 y -3/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 (pow.f64 y -3/2) (.f64 x x))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 y -3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 y -3))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 y -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 y -3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 y -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 y -3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 y -3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 y -3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 y -3/2) (pow.f64 y -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 y -2) (/.f64 1 y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 y) (pow.f64 y -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 y -3/4) (sqrt.f64 (pow.f64 y -9/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 y -2) 1) (/.f64 1 y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 y -9/2)) (pow.f64 y -3/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 y -5/2) (pow.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 y -2) (cbrt.f64 (pow.f64 y -2))) (/.f64 1 (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 y -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y 3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -3/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -1/2) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y 6) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y 9) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -2) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -6) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -9) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 y y) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -9/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 y)) 9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 y) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 y) -9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y 3/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 y) -6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y -3/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (pow.f64 y 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 y -6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 y -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 y -3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 y -9))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 y -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 y -3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -3 (log.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 y) -3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 y)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -3 (log.f64 y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -3/2 (log.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -6 (log.f64 y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 y -9)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 y) 1) -3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 3 (log.f64 y)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 y) -3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 3 (log.f64 y)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 -3 (log.f64 y)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 -3 (log.f64 y)) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 -3/2 (log.f64 y)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 y) -1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 (neg.f64 (log.f64 y)) 1) 3))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (sqrt.f64 y)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (sqrt.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (sqrt.f64 y))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (sqrt.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (sqrt.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (sqrt.f64 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (sqrt.f64 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 x (sqrt.f64 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 x (sqrt.f64 y)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 x (sqrt.f64 y)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 x (sqrt.f64 y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 (log.f64 (/.f64 x (sqrt.f64 y))) 1) 1))))))

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

171 → 171

Calls

Call 1

Inputs

Outputs

localize23.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
✓	0.2b	(sqrt.f64 (/.f64 1 y))
	0.3b	(*.f64 (sqrt.f64 (/.f64 1 y)) x)

Compiler

Compiled 40 to 27 computations (32.5% saved)

series8.0ms (0.2%)

Counts

2 → 3

Calls

9 calls:

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

rewrite90.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`log-prod_binary64`
383×	`exp-prod_binary64`
348×	`pow-prod-down_binary64`
300×	`fma-def_binary64`
275×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	231	16
2	2899	16

Stop Event

1×	node limit

Counts

2 → 125

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 1 y))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))

Outputs

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

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

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	16	27
2	23	27
3	25	27

Stop Event

1×

saturated

Counts

128 → 127

Calls

Call 1

Inputs
(sqrt.f64 y)
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x))
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x))

Outputs
(sqrt.f64 y)
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x))
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x))

eval325.0ms (8.8%)

Compiler: Compiled 10031 to 6278 computations (37.4% saved)

prune86.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	482	2	484
Fresh	0	0	0
Picked	1	0	1
Done	1	3	4
Total	484	5	489

Error

Counts

489 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.6b	(sqrt.f64 y)
▶	4.3b	(+.f64 (.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 y 3/2))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y)))
✓	0.9b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (+.f64 x y))
▶	0.6b	(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))

Compiler

Compiled 56 to 38 computations (32.1% saved)

localize51.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
	0.2b	(sqrt.f64 (/.f64 1 y))
	0.3b	(*.f64 (sqrt.f64 (/.f64 1 y)) x)
✓	12.4b	(/.f64 (*.f64 x x) (pow.f64 y 3/2))

Compiler

Compiled 85 to 53 computations (37.6% saved)

series28.0ms (0.8%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
23.0ms	y	@	-inf	(/.f64 (*.f64 x x) (pow.f64 y 3/2))
3.0ms	x	@	0	(/.f64 (*.f64 x x) (pow.f64 y 3/2))
0.0ms	y	@	inf	(/.f64 (*.f64 x x) (pow.f64 y 3/2))
0.0ms	x	@	inf	(/.f64 (*.f64 x x) (pow.f64 y 3/2))
0.0ms	y	@	0	(/.f64 (*.f64 x x) (pow.f64 y 3/2))

rewrite242.0ms (6.6%)

Algorithm

1×	batch-egg-rewrite

Rules

729×	`pow1_binary64`
684×	`add-log-exp_binary64`
684×	`log1p-expm1-u_binary64`
684×	`expm1-log1p-u_binary64`
666×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	152	10
2	1946	10

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

Inputs
(/.f64 (*.f64 x x) (pow.f64 y 3/2))

Outputs

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

simplify119.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

796×	`unswap-sqr_binary64`
681×	`sqr-pow_binary64`
600×	`associate-l_binary64`
456×	`associate-/r*_binary64`
441×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	180
1	25	180
2	45	180
3	81	180
4	177	180
5	525	180
6	1996	180
7	4338	180
8	4572	180
9	4910	180
10	5273	180
11	5803	180
12	6489	180
13	7348	180
14	7886	180

Stop Event

1×	node limit

Counts

45 → 35

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))

Outputs
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))
(*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x x))

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))
✓	0.2b	(/.f64 x (sqrt.f64 y))

Compiler

Compiled 26 to 10 computations (61.5% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(/.f64 x (sqrt.f64 y))
1.0ms	y	@	-inf	(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))
0.0ms	x	@	0	(/.f64 x (sqrt.f64 y))
0.0ms	y	@	0	(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))
0.0ms	y	@	inf	(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))

rewrite248.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

971×	`pow1_binary64`
905×	`add-log-exp_binary64`
905×	`log1p-expm1-u_binary64`
905×	`expm1-log1p-u_binary64`
91×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	178	18
2	2483	18

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

Inputs
(/.f64 x (sqrt.f64 y))
(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))

Outputs

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

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

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	270
1	19	270
2	28	270
3	34	270

Stop Event

1×

saturated

Counts

92 → 74

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x)) (sqrt.f64 y))

Outputs
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) x)
(*.f64 (sqrt.f64 (/.f64 1 y)) 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 (*.f64 (sqrt.f64 (/.f64 1 y)) x) 1/2 (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x 1/2) (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 (*.f64 (sqrt.f64 (/.f64 1 y)) x) 1/2 (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x 1/2) (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 (*.f64 (sqrt.f64 (/.f64 1 y)) x) 1/2 (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x 1/2) (sqrt.f64 y))
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x))
(.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 y))) x)
(.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x 1/2))
(+.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 (*.f64 (sqrt.f64 (/.f64 1 y)) x) 1/2 (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x 1/2) (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 (*.f64 (sqrt.f64 (/.f64 1 y)) x) 1/2 (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x 1/2) (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 (*.f64 (sqrt.f64 (/.f64 1 y)) x) 1/2 (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x 1/2) (sqrt.f64 y))
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) x))
(.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 y))) x)
(.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x 1/2))
(+.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 (*.f64 (sqrt.f64 (/.f64 1 y)) x) 1/2 (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x 1/2) (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 (*.f64 (sqrt.f64 (/.f64 1 y)) x) 1/2 (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x 1/2) (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 (*.f64 (sqrt.f64 (/.f64 1 y)) x) 1/2 (sqrt.f64 y))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x 1/2) (sqrt.f64 y))

eval315.0ms (8.5%)

Compiler: Compiled 5555 to 3072 computations (44.7% saved)

prune63.0ms (1.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	0	0
Picked	0	1	1
Done	1	3	4
Total	258	5	263

Error

Counts

263 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.9b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.6b	(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))
▶	4.3b	(+.f64 (.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 y 3/2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))
✓	1.6b	(sqrt.f64 y)

Compiler

Compiled 54 to 35 computations (35.2% saved)

localize43.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 y 3/2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))
	0.0b	(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))
	0.2b	(/.f64 x (sqrt.f64 y))
	12.4b	(/.f64 (*.f64 x x) (pow.f64 y 3/2))

Compiler

Compiled 69 to 32 computations (53.6% saved)

series4.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(+.f64 (.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 y 3/2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))
1.0ms	y	@	0	(+.f64 (.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 y 3/2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))
1.0ms	y	@	inf	(+.f64 (.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 y 3/2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))
1.0ms	x	@	0	(+.f64 (.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 y 3/2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))
0.0ms	x	@	inf	(+.f64 (.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 y 3/2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))

rewrite82.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

623×	`fma-def_binary64`
379×	`fma-neg_binary64`
289×	`expm1-udef_binary64`
289×	`log1p-udef_binary64`
238×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	348	25
2	5000	25

Stop Event

1×	node limit

Counts

1 → 97

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) 1/64) (-.f64 (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2)))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))) (/.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) 2) (-.f64 (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2)))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))) 2) (cbrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))) (sqrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 (*.f64 x (*.f64 x (pow.f64 y -3/2))) 3) -1/512 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) 3)) (/.f64 1 (fma.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) (-.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))))) (*.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) 1/64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) 1/64) (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) 2)) (/.f64 1 (-.f64 (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2)))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) (-.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))))) (*.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) 1/64)) (fma.f64 (pow.f64 (*.f64 x (*.f64 x (pow.f64 y -3/2))) 3) -1/512 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2)))) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) (-.f64 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x 1/2) (sqrt.f64 y)) (sqrt.f64 y))) (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 (*.f64 x x)) (pow.f64 y -3/2) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/2) (pow.f64 y -1/2) (+.f64 (sqrt.f64 y) (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (/.f64 (*.f64 x 1/2) (sqrt.f64 y))) 1 (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (/.f64 (*.f64 x 1/2) (sqrt.f64 y)))) (cbrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (/.f64 (*.f64 x 1/2) (sqrt.f64 y))))) (cbrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (/.f64 (*.f64 x 1/2) (sqrt.f64 y)))) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 y) 2)) (sqrt.f64 (cbrt.f64 y)) (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (/.f64 (*.f64 x 1/2) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (/.f64 (*.f64 x 1/2) (sqrt.f64 y)))) (sqrt.f64 (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (/.f64 (*.f64 x 1/2) (sqrt.f64 y)))) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 y) (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (/.f64 (*.f64 x 1/2) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 y) 2) 1/2) (pow.f64 (cbrt.f64 y) 1/2) (fma.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))) (/.f64 (*.f64 x 1/2) (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/8 y) (/.f64 (*.f64 x x) (sqrt.f64 y)) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/8 (pow.f64 y 3/4)) (/.f64 (*.f64 x x) (pow.f64 y 3/4)) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (cbrt.f64 y)) (/.f64 x (cbrt.f64 (sqrt.f64 y))) (+.f64 (sqrt.f64 y) (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (pow.f64 y 1/4)) (/.f64 x (pow.f64 y 1/4)) (+.f64 (sqrt.f64 y) (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 (cbrt.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)))) (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 y)) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 (/.f64 x (pow.f64 y 3/4))) (/.f64 x (pow.f64 y 3/4)) (fma.f64 1/2 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (cbrt.f64 (/.f64 (*.f64 x x) y))) (cbrt.f64 (/.f64 x (sqrt.f64 y))) (+.f64 (sqrt.f64 y) (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 (/.f64 x (sqrt.f64 y)))) (sqrt.f64 (/.f64 x (sqrt.f64 y))) (+.f64 (sqrt.f64 y) (*.f64 -1/8 (*.f64 x (*.f64 x (pow.f64 y -3/2))))))))))

simplify220.0ms (6%)

Algorithm

1×	egg-herbie

Rules

690×	`sqr-pow_binary64`
548×	`associate-/l/_binary64`
481×	`fma-def_binary64`
450×	`unswap-sqr_binary64`
437×	`cube-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	312
1	50	312
2	99	310
3	213	288
4	471	288
5	1402	288
6	2325	288
7	4069	288
8	4222	288
9	4453	288
10	4742	288
11	5190	288
12	5776	288
13	6543	288
14	7429	288
15	7949	288

Stop Event

1×	node limit

Counts

109 → 106

Calls

Call 1

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

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

eval109.0ms (3%)

Compiler: Compiled 5508 to 2987 computations (45.8% saved)

prune51.0ms (1.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	215	5	220

Error

Counts

220 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.9b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (sqrt.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.6b	(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y))
✓	4.3b	(+.f64 (.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 y 3/2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 y))) (sqrt.f64 y)))
✓	1.6b	(sqrt.f64 y)

Compiler

Compiled 54 to 35 computations (35.2% saved)

regimes25.0ms (0.7%)

Accuracy

Total -11.7b remaining (-99700.6%)

Threshold costs -11.7b (-99700.6%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 x y))
5.0ms	(+.f64 x y)
5.0ms	y
5.0ms	x

Results

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

Compiler

Compiled 119 to 71 computations (40.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	7	9

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 10 to 7 computations (30% saved)

soundness0.0ms (0%)

end16.0ms (0.4%)

Remove: (sort x y)
Compiler: Compiled 20 to 13 computations (35% saved)

Details

analyze50.0ms (1.4%)

sample757.0ms (20.5%)

preprocess14.0ms (0.4%)

simplify8.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite128.0ms (3.5%)

simplify148.0ms (4%)

eval11.0ms (0.3%)

prune8.0ms (0.2%)

localize3.0ms (0.1%)

localize11.0ms (0.3%)

series17.0ms (0.5%)

rewrite64.0ms (1.7%)

simplify119.0ms (3.2%)

localize54.0ms (1.5%)

series14.0ms (0.4%)

rewrite72.0ms (2%)

simplify10.0ms (0.3%)

localize23.0ms (0.6%)

series8.0ms (0.2%)

rewrite90.0ms (2.4%)

simplify14.0ms (0.4%)

eval325.0ms (8.8%)

prune86.0ms (2.3%)

localize51.0ms (1.4%)

series28.0ms (0.8%)

rewrite242.0ms (6.6%)

simplify119.0ms (3.2%)

localize10.0ms (0.3%)

series5.0ms (0.1%)

rewrite248.0ms (6.7%)

simplify12.0ms (0.3%)

eval315.0ms (8.5%)

prune63.0ms (1.7%)

localize43.0ms (1.2%)

series4.0ms (0.1%)

rewrite82.0ms (2.2%)

simplify220.0ms (6%)

eval109.0ms (3%)

prune51.0ms (1.4%)

regimes25.0ms (0.7%)

simplify3.0ms (0.1%)

soundness0.0ms (0%)

end16.0ms (0.4%)

Profiling