Details

analyze60.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
15.8%	2.9%	81.3%	7
15.8%	2.9%	81.3%	8
17.4%	1.3%	81.3%	9
17.4%	1.3%	81.3%	10
18.1%	0.6%	81.3%	11
18.1%	0.6%	81.3%	12
18.4%	0.3%	81.3%	13
18.4%	0.3%	81.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample994.0ms (48.9%)

Results

981.0ms

8256×

body

128

valid

preprocess39.0ms (1.9%)

Algorithm

2×	egg-herbie

Rules

772×	`fma-def_binary64`
588×	`div-sub_binary64`
352×	`unsub-neg_binary64`
194×	`cancel-sign-sub-inv_binary64`
190×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	43	40
2	103	40
3	250	40
4	569	40
5	1563	40
6	3472	40
7	4656	40
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

Outputs
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 y y (.f64 x x)))
(.f64 (+.f64 x y) (/.f64 (-.f64 x y) (fma.f64 y y (.f64 x x))))
(.f64 (+.f64 x y) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y))))
(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (fma.f64 y y (.f64 x x))))
(/.f64 (.f64 (-.f64 y x) (+.f64 y x)) (+.f64 (.f64 y y) (*.f64 x x)))
(/.f64 (-.f64 y x) (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 x y)))
(.f64 (/.f64 (-.f64 y x) (fma.f64 y y (.f64 x x))) (+.f64 x y))
(.f64 (+.f64 x y) (/.f64 (-.f64 y x) (fma.f64 y y (.f64 x x))))
(.f64 (+.f64 x y) (/.f64 (-.f64 y x) (fma.f64 x x (.f64 y y))))
(.f64 (-.f64 y x) (/.f64 (+.f64 x y) (fma.f64 y y (.f64 x x))))

Compiler

Compiled 17 to 9 computations (47.1% saved)

simplify30.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
469×	`fma-neg_binary64`
365×	`sub-neg_binary64`
282×	`unsub-neg_binary64`
267×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	24	20
2	58	20
3	138	20
4	328	20
5	848	20
6	2017	20
7	4713	20

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

Outputs
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
(/.f64 (+.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (-.f64 x y)))
(.f64 (/.f64 (+.f64 x y) (fma.f64 x x (.f64 y y))) (-.f64 x y))
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (fma.f64 x x (.f64 y y))))
(.f64 (+.f64 x y) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y))))

prune4.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

21.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	21.7b	(.f64 (+.f64 x y) (/.f64 (-.f64 x y) (fma.f64 x x (.f64 y y))))
▶	21.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 97 to 46 computations (52.6% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	21.3b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series7.0ms (0.4%)

Counts

2 → 48

Calls

12 calls:

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

rewrite56.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

648×	`fma-def_binary64`
273×	`fma-neg_binary64`
211×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	237	26
2	3893	26

Stop Event

1×	node limit

Counts

2 → 93

Calls

Call 1

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

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

Outputs

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

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

simplify26.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

533×	`times-frac_binary64`
434×	`fma-def_binary64`
232×	`associate-+l+_binary64`
224×	`associate-/r*_binary64`
215×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	714
1	323	624
2	1203	542

Stop Event

1×	node limit

Counts

141 → 126

Calls

Call 1

Inputs
-1
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4)))) 1)
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 x 6) (pow.f64 y 6))) (+.f64 (.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (*.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4))))) 1)
1
(+.f64 (/.f64 y x) (+.f64 1 (*.f64 -1 (/.f64 y x))))
(-.f64 (+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 -1 (/.f64 y x))))) (/.f64 (pow.f64 y 2) (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) (+.f64 y (.f64 -1 y))) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 y x)))))) (/.f64 (pow.f64 y 2) (pow.f64 x 2)))
1
(+.f64 (/.f64 y x) (+.f64 1 (*.f64 -1 (/.f64 y x))))
(+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 y x)) (.f64 -1 (/.f64 (-.f64 (pow.f64 y 2) (*.f64 -1 (pow.f64 y 2))) (pow.f64 x 2))))))
(+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) (+.f64 y (.f64 -1 y))) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 y x)) (.f64 -1 (/.f64 (-.f64 (pow.f64 y 2) (.f64 -1 (pow.f64 y 2))) (pow.f64 x 2)))))))
1
(+.f64 1 (*.f64 -2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 (.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4))) (*.f64 -2 (/.f64 (pow.f64 y 6) (pow.f64 x 6))))))
-1
(-.f64 (+.f64 (/.f64 x y) (*.f64 -1 (/.f64 x y))) 1)
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (/.f64 x y) (.f64 -1 (/.f64 x y)))) (+.f64 (.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (/.f64 x y) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -1 x) x)) (pow.f64 y 3))) (.f64 -1 (/.f64 x y))))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
-1
(-.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y)) 1)
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y)) (/.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -1 x) x)) (pow.f64 y 3)))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))

Outputs
-1
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 (/.f64 2 y) (/.f64 x (/.f64 y x)) -1)
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4)))) 1)
(+.f64 (fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) (*.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4)))) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) (fma.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4)) -1))
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 x 6) (pow.f64 y 6))) (+.f64 (.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (*.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4))))) 1)
(+.f64 (fma.f64 2 (/.f64 (pow.f64 x 6) (pow.f64 y 6)) (fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) (*.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4))))) -1)
(fma.f64 2 (/.f64 (pow.f64 x 6) (pow.f64 y 6)) (fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) (fma.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4)) -1)))
(fma.f64 2 (+.f64 (*.f64 (/.f64 x y) (/.f64 x y)) (/.f64 (pow.f64 x 6) (pow.f64 y 6))) (fma.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4)) -1))
1
(+.f64 (/.f64 y x) (+.f64 1 (*.f64 -1 (/.f64 y x))))
(+.f64 (/.f64 y x) (+.f64 1 (/.f64 (neg.f64 y) x)))
(+.f64 (/.f64 y x) (-.f64 1 (/.f64 y x)))
(+.f64 1 (*.f64 0 (/.f64 y x)))
(-.f64 (+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 -1 (/.f64 y x))))) (/.f64 (pow.f64 y 2) (pow.f64 x 2)))
(-.f64 (+.f64 (+.f64 (/.f64 y x) 1) (fma.f64 -1 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (neg.f64 y) x))) (/.f64 (.f64 y y) (.f64 x x)))
(+.f64 (/.f64 y x) (-.f64 (-.f64 (-.f64 1 (.f64 (/.f64 y x) (/.f64 y x))) (/.f64 y x)) (.f64 (/.f64 y x) (/.f64 y x))))
(+.f64 (fma.f64 -2 (.f64 (/.f64 y x) (/.f64 y x)) 1) (.f64 0 (/.f64 y x)))
(-.f64 (+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) (+.f64 y (.f64 -1 y))) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 y x)))))) (/.f64 (pow.f64 y 2) (pow.f64 x 2)))
(-.f64 (+.f64 (+.f64 (/.f64 y x) 1) (fma.f64 -1 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (neg.f64 y) x))) (/.f64 (.f64 y y) (.f64 x x)))
(+.f64 (/.f64 y x) (-.f64 (-.f64 (-.f64 1 (.f64 (/.f64 y x) (/.f64 y x))) (/.f64 y x)) (.f64 (/.f64 y x) (/.f64 y x))))
(+.f64 (fma.f64 -2 (.f64 (/.f64 y x) (/.f64 y x)) 1) (.f64 0 (/.f64 y x)))
1
(+.f64 (/.f64 y x) (+.f64 1 (*.f64 -1 (/.f64 y x))))
(+.f64 (/.f64 y x) (+.f64 1 (/.f64 (neg.f64 y) x)))
(+.f64 (/.f64 y x) (-.f64 1 (/.f64 y x)))
(+.f64 1 (*.f64 0 (/.f64 y x)))
(+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 y x)) (.f64 -1 (/.f64 (-.f64 (pow.f64 y 2) (*.f64 -1 (pow.f64 y 2))) (pow.f64 x 2))))))
(-.f64 (+.f64 (+.f64 (/.f64 y x) 1) (fma.f64 -1 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (neg.f64 y) x))) (/.f64 (.f64 y y) (.f64 x x)))
(+.f64 (/.f64 y x) (-.f64 (-.f64 (-.f64 1 (.f64 (/.f64 y x) (/.f64 y x))) (/.f64 y x)) (.f64 (/.f64 y x) (/.f64 y x))))
(+.f64 (fma.f64 -2 (.f64 (/.f64 y x) (/.f64 y x)) 1) (.f64 0 (/.f64 y x)))
(+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) (+.f64 y (.f64 -1 y))) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 y x)) (.f64 -1 (/.f64 (-.f64 (pow.f64 y 2) (.f64 -1 (pow.f64 y 2))) (pow.f64 x 2)))))))
(-.f64 (+.f64 (+.f64 (/.f64 y x) 1) (fma.f64 -1 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (neg.f64 y) x))) (/.f64 (.f64 y y) (.f64 x x)))
(+.f64 (/.f64 y x) (-.f64 (-.f64 (-.f64 1 (.f64 (/.f64 y x) (/.f64 y x))) (/.f64 y x)) (.f64 (/.f64 y x) (/.f64 y x))))
(+.f64 (fma.f64 -2 (.f64 (/.f64 y x) (/.f64 y x)) 1) (.f64 0 (/.f64 y x)))
1
(+.f64 1 (*.f64 -2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))))
(+.f64 1 (/.f64 (.f64 -2 (.f64 y y)) (*.f64 x x)))
(fma.f64 -2 (*.f64 (/.f64 y x) (/.f64 y x)) 1)
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -2 (/.f64 (.f64 y y) (.f64 x x)) (*.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(+.f64 (fma.f64 -2 (.f64 (/.f64 y x) (/.f64 y x)) 1) (.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4))))
(fma.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4)) (fma.f64 -2 (*.f64 (/.f64 y x) (/.f64 y x)) 1))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 (.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4))) (*.f64 -2 (/.f64 (pow.f64 y 6) (pow.f64 x 6))))))
(+.f64 1 (fma.f64 -2 (/.f64 (.f64 y y) (.f64 x x)) (fma.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4)) (*.f64 -2 (/.f64 (pow.f64 y 6) (pow.f64 x 6))))))
(+.f64 1 (fma.f64 -2 (.f64 (/.f64 y x) (/.f64 y x)) (fma.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4)) (.f64 -2 (/.f64 (pow.f64 y 6) (pow.f64 x 6))))))
(+.f64 (fma.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4)) 1) (.f64 -2 (+.f64 (.f64 (/.f64 y x) (/.f64 y x)) (/.f64 (pow.f64 y 6) (pow.f64 x 6)))))
-1
(-.f64 (+.f64 (/.f64 x y) (*.f64 -1 (/.f64 x y))) 1)
-1
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (/.f64 x y) (.f64 -1 (/.f64 x y)))) (+.f64 (.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 0 (/.f64 x y)) (fma.f64 -1 (/.f64 (.f64 x x) (*.f64 y y)) 1)))
(+.f64 (.f64 (/.f64 x y) (/.f64 x y)) (-.f64 -1 (/.f64 (.f64 (neg.f64 x) x) (*.f64 y y))))
(+.f64 -1 (fma.f64 (/.f64 x y) (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))))
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (/.f64 x y) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -1 x) x)) (pow.f64 y 3))) (.f64 -1 (/.f64 x y))))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 0 (/.f64 x y)) (fma.f64 -1 (/.f64 (.f64 x x) (*.f64 y y)) 1)))
(+.f64 (.f64 (/.f64 x y) (/.f64 x y)) (-.f64 -1 (/.f64 (.f64 (neg.f64 x) x) (*.f64 y y))))
(+.f64 -1 (fma.f64 (/.f64 x y) (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))))
-1
(-.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y)) 1)
-1
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 0 (/.f64 x y)) (fma.f64 -1 (/.f64 (.f64 x x) (*.f64 y y)) 1)))
(+.f64 (.f64 (/.f64 x y) (/.f64 x y)) (-.f64 -1 (/.f64 (.f64 (neg.f64 x) x) (*.f64 y y))))
(+.f64 -1 (fma.f64 (/.f64 x y) (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))))
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y)) (/.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -1 x) x)) (pow.f64 y 3)))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 0 (/.f64 x y)) (fma.f64 -1 (/.f64 (.f64 x x) (*.f64 y y)) 1)))
(+.f64 (.f64 (/.f64 x y) (/.f64 x y)) (-.f64 -1 (/.f64 (.f64 (neg.f64 x) x) (*.f64 y y))))
(+.f64 -1 (fma.f64 (/.f64 x y) (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))

prune99.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	125	3	128

Error

Counts

128 → 3

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	21.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
	17.8b	(fma.f64 (/.f64 2 y) (/.f64 x (/.f64 y x)) -1)

Compiler

Compiled 2557 to 1104 computations (56.8% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	0.0b	(/.f64 (-.f64 x y) (hypot.f64 x y))
✓	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))

series11.0ms (0.5%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
1.0ms	x	@	0	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
1.0ms	x	@	0	(/.f64 (+.f64 x y) (hypot.f64 x y))
1.0ms	y	@	0	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
0.0ms	x	@	inf	(/.f64 (+.f64 x y) (hypot.f64 x y))

rewrite122.0ms (6%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
179×	`egg-rr`
114×	`add-sqr-sqrt_binary64`
113×	`pow1_binary64`
112×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	42
1	214	39
2	3523	39

Stop Event

1×	node limit

Counts

3 → 260

Calls

Call 1

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

Outputs
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Outputs

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

simplify42.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

783×	`times-frac_binary64`
745×	`fma-def_binary64`
381×	`associate-/r*_binary64`
349×	`associate-/l*_binary64`
149×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	1292
1	494	1206
2	1753	1068

Stop Event

1×	node limit

Counts

332 → 335

Calls

Call 1

Inputs
1
(+.f64 1 (/.f64 x y))
(+.f64 1 (+.f64 (/.f64 x y) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2)))))
(+.f64 1 (+.f64 (/.f64 x y) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))))))
1
(+.f64 (/.f64 y x) 1)
(+.f64 (/.f64 y x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) 1))
(+.f64 (/.f64 y x) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 1 (.f64 -1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3))))))
-1
(-.f64 (*.f64 -1 (/.f64 y x)) 1)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 -1 (/.f64 y x))) 1)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 y x)))) 1)
1
(+.f64 (/.f64 y x) 1)
(+.f64 (/.f64 y x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) 1))
(+.f64 (/.f64 y x) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 1 (.f64 -1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3))))))
1
(+.f64 1 (/.f64 x y))
(+.f64 1 (+.f64 (/.f64 x y) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2)))))
(+.f64 1 (+.f64 (/.f64 x y) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))))))
-1
(-.f64 (*.f64 -1 (/.f64 x y)) 1)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -1 (/.f64 x y))) 1)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (*.f64 -1 (/.f64 x y)))) 1)
-1
(-.f64 (/.f64 x y) 1)
(-.f64 (+.f64 (/.f64 x y) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2)))) 1)
(-.f64 (+.f64 (/.f64 x y) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))))) 1)
1
(+.f64 1 (*.f64 -1 (/.f64 y x)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 1 (.f64 -1 (/.f64 y x))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 1 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3))) (*.f64 -1 (/.f64 y x)))))
-1
(-.f64 (/.f64 y x) 1)
(-.f64 (+.f64 (/.f64 y x) (*.f64 1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2)))) 1)
(-.f64 (+.f64 (/.f64 y x) (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3))))) 1)
1
(+.f64 1 (*.f64 -1 (/.f64 y x)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 1 (.f64 -1 (/.f64 y x))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 1 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3))) (*.f64 -1 (/.f64 y x)))))
-1
(-.f64 (/.f64 x y) 1)
(-.f64 (+.f64 (/.f64 x y) (*.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2)))) 1)
(-.f64 (+.f64 (/.f64 x y) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))))) 1)
1
(+.f64 1 (*.f64 -1 (/.f64 x y)))
(+.f64 1 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -1 (/.f64 x y))))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (*.f64 -1 (/.f64 x y)))))
-1
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4)))) 1)
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 x 6) (pow.f64 y 6))) (+.f64 (.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (*.f64 -2 (/.f64 (pow.f64 x 4) (pow.f64 y 4))))) 1)
1
(+.f64 (/.f64 y x) (+.f64 1 (*.f64 -1 (/.f64 y x))))
(-.f64 (+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 -1 (/.f64 y x))))) (/.f64 (pow.f64 y 2) (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) (+.f64 y (.f64 -1 y))) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 y x)))))) (/.f64 (pow.f64 y 2) (pow.f64 x 2)))
1
(+.f64 (/.f64 y x) (+.f64 1 (*.f64 -1 (/.f64 y x))))
(+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 y x)) (.f64 -1 (/.f64 (-.f64 (pow.f64 y 2) (*.f64 -1 (pow.f64 y 2))) (pow.f64 x 2))))))
(+.f64 (/.f64 y x) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 y 2) (+.f64 y (.f64 -1 y))) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 y x)) (.f64 -1 (/.f64 (-.f64 (pow.f64 y 2) (.f64 -1 (pow.f64 y 2))) (pow.f64 x 2)))))))
1
(+.f64 1 (*.f64 -2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4)))))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 (.f64 2 (/.f64 (pow.f64 y 4) (pow.f64 x 4))) (*.f64 -2 (/.f64 (pow.f64 y 6) (pow.f64 x 6))))))
-1
(-.f64 (+.f64 (/.f64 x y) (*.f64 -1 (/.f64 x y))) 1)
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (/.f64 x y) (.f64 -1 (/.f64 x y)))) (+.f64 (.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (/.f64 x y) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -1 x) x)) (pow.f64 y 3))) (.f64 -1 (/.f64 x y))))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
-1
(-.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y)) 1)
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y)) (/.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -1 x) x)) (pow.f64 y 3)))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))

Outputs
1
(+.f64 1 (/.f64 x y))
(+.f64 1 (+.f64 (/.f64 x y) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2)))))
(+.f64 1 (+.f64 (/.f64 x y) (.f64 -1/2 (/.f64 (.f64 x x) (*.f64 y y)))))
(+.f64 1 (fma.f64 -1/2 (*.f64 (/.f64 x y) (/.f64 x y)) (/.f64 x y)))
(fma.f64 -1/2 (*.f64 (/.f64 x y) (/.f64 x y)) (+.f64 1 (/.f64 x y)))
(+.f64 1 (+.f64 (/.f64 x y) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (.f64 -1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))))))
(+.f64 1 (+.f64 (/.f64 x y) (.f64 -1/2 (+.f64 (/.f64 (.f64 x x) (*.f64 y y)) (/.f64 (pow.f64 x 3) (pow.f64 y 3))))))
(+.f64 1 (fma.f64 -1/2 (+.f64 (*.f64 (/.f64 x y) (/.f64 x y)) (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (/.f64 x y)))
(+.f64 1 (fma.f64 -1/2 (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (/.f64 x y)))
1
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
(+.f64 (/.f64 y x) (+.f64 (*.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) 1))
(+.f64 (/.f64 y x) (fma.f64 -1/2 (/.f64 (.f64 y y) (.f64 x x)) 1))
(+.f64 (/.f64 y x) (fma.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 y x)) 1))
(+.f64 1 (fma.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 y x)) (/.f64 y x)))
(+.f64 (/.f64 y x) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (+.f64 1 (.f64 -1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3))))))
(+.f64 (/.f64 y x) (+.f64 (fma.f64 -1/2 (/.f64 (.f64 y y) (.f64 x x)) 1) (*.f64 -1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3)))))
(+.f64 (/.f64 y x) (fma.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 y x)) (fma.f64 -1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) 1)))
(+.f64 (fma.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 y x)) 1) (fma.f64 -1/2 (pow.f64 (/.f64 y x) 3) (/.f64 y x)))
-1
(-.f64 (*.f64 -1 (/.f64 y x)) 1)
(fma.f64 -1 (/.f64 y x) -1)
(fma.f64 (/.f64 y x) -1 -1)
(-.f64 -1 (/.f64 y x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 -1 (/.f64 y x))) 1)
(+.f64 (fma.f64 1/2 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (neg.f64 y) x)) -1)
(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) 1/2 (fma.f64 (/.f64 y x) -1 -1))
(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) 1/2 (-.f64 -1 (/.f64 y x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) (pow.f64 x 2))) (*.f64 -1 (/.f64 y x)))) 1)
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 (.f64 y y) (.f64 x x)) (/.f64 (neg.f64 y) x))) -1)
(+.f64 -1 (-.f64 (.f64 1/2 (+.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (.f64 (/.f64 y x) (/.f64 y x)))) (/.f64 y x)))
(fma.f64 1/2 (+.f64 (pow.f64 (/.f64 y x) 3) (*.f64 (/.f64 y x) (/.f64 y x))) (-.f64 -1 (/.f64 y x)))
1
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(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 x) x) y)) (/.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -1 x) x)) (pow.f64 y 3)))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1))
(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 0 (/.f64 x y)) (fma.f64 -1 (/.f64 (.f64 x x) (*.f64 y y)) 1)))
(+.f64 (.f64 (/.f64 x y) (/.f64 x y)) (-.f64 -1 (/.f64 (.f64 (neg.f64 x) x) (*.f64 y y))))
(+.f64 (fma.f64 (/.f64 x y) (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))) -1)

prune283.0ms (13.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	335	0	335
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	335	3	338

Error

Counts

338 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	21.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
▶	17.8b	(fma.f64 (/.f64 2 y) (/.f64 x (/.f64 y x)) -1)

Compiler

Compiled 13123 to 3513 computations (73.2% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 2 y) (/.f64 x (/.f64 y x)) -1)
✓	0.2b	(/.f64 x (/.f64 y x))

series7.0ms (0.4%)

Counts

2 → 48

Calls

12 calls:

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

rewrite46.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

477×	`log-prod_binary64`
247×	`pow2_binary64`
174×	`pow1/3_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	193	21
2	2541	21

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

Inputs
(/.f64 x (/.f64 y x))
(fma.f64 (/.f64 2 y) (/.f64 x (/.f64 y x)) -1)

Outputs

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

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

simplify35.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

708×	`associate-/l*_binary64`
424×	`associate-/l/_binary64`
421×	`associate-/r*_binary64`
399×	`unswap-sqr_binary64`
327×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	462
1	27	462
2	53	462
3	148	462
4	769	462
5	4777	462

Stop Event

1×	node limit

Counts

120 → 78

Calls

Call 1

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

Outputs
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 x (/.f64 x y))
(*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2)))
(.f64 2 (/.f64 (.f64 x x) (*.f64 y y)))
(.f64 2 (.f64 (/.f64 x y) (/.f64 x y)))
(.f64 x (.f64 2 (/.f64 x (*.f64 y y))))
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
-1
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
-1
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
-1
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2)))
(.f64 2 (/.f64 (.f64 x x) (*.f64 y y)))
(.f64 2 (.f64 (/.f64 x y) (/.f64 x y)))
(.f64 x (.f64 2 (/.f64 x (*.f64 y y))))
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2)))
(.f64 2 (/.f64 (.f64 x x) (*.f64 y y)))
(.f64 2 (.f64 (/.f64 x y) (/.f64 x y)))
(.f64 x (.f64 2 (/.f64 x (*.f64 y y))))
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)
(-.f64 (*.f64 2 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) 1)
(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
(fma.f64 2 (.f64 x (/.f64 x (.f64 y y))) -1)
(fma.f64 (.f64 x 2) (/.f64 x (.f64 y y)) -1)

prune48.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	78	3	81

Error

Counts

81 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	21.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
✓	17.8b	(fma.f64 (/.f64 2 y) (/.f64 x (/.f64 y x)) -1)

Compiler

Compiled 1223 to 639 computations (47.8% saved)

regimes44.0ms (2.1%)

Accuracy

Total -36.3b remaining (-94045.2%)

Threshold costs -36.3b (-94045.2%)

Counts

23 → 1

Compiler

Compiled 324 to 148 computations (54.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	13	22
2	18	22
3	20	22
4	21	22

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

end56.0ms (2.7%)

Stop Event

1×

done

Compiler

Compiled 74 to 27 computations (63.5% saved)

Details

analyze60.0ms (2.9%)

sample994.0ms (48.9%)

preprocess39.0ms (1.9%)

simplify30.0ms (1.5%)

prune4.0ms (0.2%)

localize8.0ms (0.4%)

series7.0ms (0.4%)

rewrite56.0ms (2.7%)

simplify26.0ms (1.3%)

prune99.0ms (4.9%)

localize8.0ms (0.4%)

series11.0ms (0.5%)

rewrite122.0ms (6%)

simplify42.0ms (2.1%)

prune283.0ms (13.9%)

localize6.0ms (0.3%)

series7.0ms (0.4%)

rewrite46.0ms (2.3%)

simplify35.0ms (1.7%)

prune48.0ms (2.4%)

regimes44.0ms (2.1%)

simplify2.0ms (0.1%)

end56.0ms (2.7%)

Profiling