Details

analyze166.0ms (5.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	6
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	7
65.6%	65.6%	34.3%	0.1%	0%	0%	0%	8
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	9
82%	82%	18%	0.1%	0%	0%	0%	10
87.9%	87.8%	12.1%	0.1%	0%	0%	0%	11
90.8%	90.7%	9.2%	0.1%	0%	0%	0%	12

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.8s (64%)

Results

1.7s

8256×

body

256

valid

Bogosity

preprocess16.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`swap-x-y`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	8
1	13	8
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 (.f64 x x) (.f64 y y)))
(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

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

Symmetry

(sort x y)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify47.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4
2	12	4

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 3 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 7 to 3 computations (57.1% saved)

series5.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite53.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

360×	`pow1_binary64`
343×	`add-sqr-sqrt_binary64`
339×	`*-un-lft-identity_binary64`
329×	`add-log-exp_binary64`
329×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	79	4
2	911	4

Stop Event

1×	node limit

Counts

1 → 45

Calls

Call 1

Inputs
(hypot.f64 x y)

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

Outputs

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

simplify62.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

774×	`unswap-sqr_binary64`
754×	`associate-*l/_binary64`
619×	`associate-*r/_binary64`
441×	`fma-neg_binary64`
319×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	469
1	197	458
2	573	454
3	2335	454
4	6401	454

Stop Event

1×	node limit

Counts

69 → 75

Calls

Call 1

Inputs
y
(+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) y)) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))))))
x
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) x))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) x)))
(*.f64 -1 x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 -1 x) (.f64 -1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))))))
x
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) x))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) x)))
y
(+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) y)) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))))))
(*.f64 -1 y)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) y)) (.f64 -1 y))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) y)) (+.f64 (.f64 -1 y) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) y)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))) (+.f64 (.f64 -1 y) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))))

Outputs
y
(+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))
(+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y)))
(fma.f64 1/2 (/.f64 x (/.f64 y x)) y)
(fma.f64 1/2 (*.f64 (/.f64 x y) x) y)
(fma.f64 1/2 (*.f64 x (/.f64 x y)) y)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (/.f64 x (/.f64 y x)) y))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (*.f64 (/.f64 x y) x) y))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (*.f64 x (/.f64 x y)) y))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) y)) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (+.f64 y (fma.f64 1/2 (/.f64 (.f64 x x) y) (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (+.f64 y (fma.f64 1/2 (/.f64 x (/.f64 y x)) (/.f64 1/16 (/.f64 (pow.f64 y 5) (pow.f64 x 6))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (*.f64 (/.f64 x y) x) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) y)))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (*.f64 x (/.f64 x y)) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) y)))
x
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)
(fma.f64 1/2 (/.f64 (*.f64 y y) x) x)
(fma.f64 1/2 (*.f64 (/.f64 y x) y) x)
(fma.f64 1/2 (*.f64 y (/.f64 y x)) x)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 (*.f64 y y) x) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) x))
(fma.f64 1/2 (*.f64 (/.f64 y x) y) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) x))
(fma.f64 1/2 (*.f64 y (/.f64 y x)) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) x))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) x)))
(fma.f64 1/2 (/.f64 (*.f64 y y) x) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) x)))
(fma.f64 1/2 (*.f64 (/.f64 y x) y) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) x)))
(fma.f64 1/2 (*.f64 y (/.f64 y x)) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 (*.f64 y y) x) (neg.f64 x))
(-.f64 (.f64 (/.f64 (.f64 y y) x) -1/2) x)
(-.f64 (.f64 (/.f64 -1/2 x) (.f64 y y)) x)
(-.f64 (.f64 (.f64 y y) (/.f64 -1/2 x)) x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (*.f64 -1 x)))
(fma.f64 -1/2 (/.f64 (*.f64 y y) x) (fma.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) (neg.f64 x)))
(fma.f64 (/.f64 (.f64 y y) x) -1/2 (-.f64 (.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) 1/8) x))
(-.f64 (fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) 1/8 (.f64 (/.f64 -1/2 x) (.f64 y y))) x)
(-.f64 (.f64 (.f64 y y) (/.f64 -1/2 x)) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) (+.f64 (.f64 -1 x) (.f64 -1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))))))
(fma.f64 -1/2 (/.f64 (.f64 y y) x) (fma.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) (fma.f64 -1 x (.f64 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) -1/16))))
(fma.f64 (/.f64 (.f64 y y) x) -1/2 (fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) 1/8 (-.f64 (.f64 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) -1/16) x)))
(fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) 1/8 (-.f64 (fma.f64 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) -1/16 (.f64 (/.f64 -1/2 x) (.f64 y y))) x))
(-.f64 (fma.f64 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) 1/8 (.f64 (.f64 y y) (/.f64 -1/2 x))) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) x))
x
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 y 2) x)) x)
(fma.f64 1/2 (/.f64 (*.f64 y y) x) x)
(fma.f64 1/2 (*.f64 (/.f64 y x) y) x)
(fma.f64 1/2 (*.f64 y (/.f64 y x)) x)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 (*.f64 y y) x) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) x))
(fma.f64 1/2 (*.f64 (/.f64 y x) y) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) x))
(fma.f64 1/2 (*.f64 y (/.f64 y x)) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) x))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 y 2) x)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3))) x)))
(fma.f64 1/2 (/.f64 (*.f64 y y) x) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) x)))
(fma.f64 1/2 (*.f64 (/.f64 y x) y) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) x)))
(fma.f64 1/2 (*.f64 y (/.f64 y x)) (fma.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 x 3)) (fma.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 x 5)) x)))
y
(+.f64 y (*.f64 1/2 (/.f64 (pow.f64 x 2) y)))
(+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y)))
(fma.f64 1/2 (/.f64 x (/.f64 y x)) y)
(fma.f64 1/2 (*.f64 (/.f64 x y) x) y)
(fma.f64 1/2 (*.f64 x (/.f64 x y)) y)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (.f64 1/2 (/.f64 (pow.f64 x 2) y))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (+.f64 y (.f64 1/2 (/.f64 (.f64 x x) y))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (/.f64 x (/.f64 y x)) y))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (*.f64 (/.f64 x y) x) y))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (*.f64 x (/.f64 x y)) y))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))) (+.f64 y (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) y)) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (+.f64 y (fma.f64 1/2 (/.f64 (.f64 x x) y) (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (+.f64 y (fma.f64 1/2 (/.f64 x (/.f64 y x)) (/.f64 1/16 (/.f64 (pow.f64 y 5) (pow.f64 x 6))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (*.f64 (/.f64 x y) x) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) y)))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) (fma.f64 1/2 (*.f64 x (/.f64 x y)) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) y)))
(*.f64 -1 y)
(neg.f64 y)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) y)) (.f64 -1 y))
(fma.f64 -1/2 (/.f64 (*.f64 x x) y) (neg.f64 y))
(-.f64 (*.f64 (/.f64 x (/.f64 y x)) -1/2) y)
(-.f64 (.f64 (/.f64 -1/2 y) (.f64 x x)) y)
(-.f64 (.f64 (.f64 x x) (/.f64 -1/2 y)) y)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) y)) (+.f64 (.f64 -1 y) (*.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3)))))
(fma.f64 -1/2 (/.f64 (.f64 x x) y) (fma.f64 -1 y (.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) 1/8)))
(fma.f64 (/.f64 x (/.f64 y x)) -1/2 (-.f64 (*.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) 1/8) y))
(-.f64 (fma.f64 (.f64 (/.f64 x y) x) -1/2 (/.f64 (.f64 (pow.f64 x 4) 1/8) (pow.f64 y 3))) y)
(fma.f64 (/.f64 -1/2 y) (.f64 x x) (-.f64 (/.f64 (.f64 (pow.f64 x 4) 1/8) (pow.f64 y 3)) y))
(fma.f64 (.f64 x x) (/.f64 -1/2 y) (-.f64 (/.f64 (.f64 (pow.f64 x 4) 1/8) (pow.f64 y 3)) y))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) y)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5))) (+.f64 (.f64 -1 y) (.f64 1/8 (/.f64 (pow.f64 x 4) (pow.f64 y 3))))))
(fma.f64 -1/2 (/.f64 (.f64 x x) y) (fma.f64 -1/16 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) (fma.f64 -1 y (.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) 1/8))))
(fma.f64 (/.f64 x (/.f64 y x)) -1/2 (fma.f64 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) -1/16 (-.f64 (*.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) 1/8) y)))
(fma.f64 (.f64 (/.f64 x y) x) -1/2 (-.f64 (fma.f64 (/.f64 (pow.f64 x 4) (pow.f64 y 3)) 1/8 (.f64 (/.f64 (pow.f64 x 6) (pow.f64 y 5)) -1/16)) y))
(fma.f64 (/.f64 -1/16 (pow.f64 y 5)) (pow.f64 x 6) (fma.f64 (/.f64 -1/2 y) (.f64 x x) (-.f64 (/.f64 (.f64 (pow.f64 x 4) 1/8) (pow.f64 y 3)) y)))
(fma.f64 (pow.f64 x 6) (/.f64 -1/16 (pow.f64 y 5)) (fma.f64 (.f64 x x) (/.f64 -1/2 y) (-.f64 (/.f64 (.f64 (pow.f64 x 4) 1/8) (pow.f64 y 3)) y)))

eval21.0ms (0.7%)

Compiler: Compiled 902 to 511 computations (43.3% saved)

prune12.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	5	76

Error

Counts

76 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.6b	(fma.f64 1/2 (*.f64 x (/.f64 x y)) y)
▶	35.3b	(-.f64 (.f64 (.f64 y y) (/.f64 -1/2 x)) x)
	29.5b	y
▶	32.9b	(neg.f64 x)
✓	0.0b	(hypot.f64 x y)

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize2.0ms (0.1%)

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

localize30.0ms (1.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 y y) (/.f64 -1/2 x)) x)
✓	8.0b	(.f64 (.f64 y y) (/.f64 -1/2 x))

Compiler

Compiled 27 to 13 computations (51.9% saved)

series7.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

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

rewrite70.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

957×	`pow1_binary64`
895×	`add-log-exp_binary64`
894×	`log1p-expm1-u_binary64`
894×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	182	23
2	2476	23

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

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

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

Outputs

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

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

simplify122.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

853×	`distribute-rgt-neg-in_binary64`
760×	`distribute-lft-neg-in_binary64`
566×	`fma-neg_binary64`
541×	`div-sub_binary64`
530×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	513
1	23	513
2	43	513
3	79	513
4	206	513
5	788	513
6	3361	513
7	6921	513

Stop Event

1×	node limit

Counts

108 → 66

Calls

Call 1

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

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

localize32.0ms (1.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x (/.f64 x y))

Compiler

Compiled 21 to 7 computations (66.7% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite51.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

568×	`pow1_binary64`
525×	`add-log-exp_binary64`
525×	`log1p-expm1-u_binary64`
525×	`expm1-log1p-u_binary64`
513×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	105	7
2	1410	7

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify116.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

759×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
423×	`*-commutative_binary64`
423×	`associate-*r/_binary64`
393×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	11	168
2	20	168
3	37	168
4	83	168
5	266	168
6	1091	168
7	3478	168
8	4280	168
9	4465	168
10	4681	168
11	5028	168
12	5456	168
13	5935	168
14	6584	168
15	7273	168

Stop Event

1×	node limit

Counts

44 → 22

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)

Outputs
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))
(/.f64 (pow.f64 x 2) y)
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(*.f64 (/.f64 x y) x)
(*.f64 x (/.f64 x y))

eval24.0ms (0.9%)

Compiler: Compiled 1205 to 612 computations (49.2% saved)

prune17.0ms (0.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	88	5	93

Error

Counts

93 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.6b	(fma.f64 1/2 (*.f64 x (/.f64 x y)) y)
✓	35.3b	(-.f64 (.f64 (.f64 y y) (/.f64 -1/2 x)) x)
	29.5b	y
✓	32.9b	(neg.f64 x)
✓	0.0b	(hypot.f64 x y)

Compiler

Compiled 33 to 21 computations (36.4% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.6b	(fma.f64 1/2 (*.f64 x (/.f64 x y)) y)
✓	35.3b	(-.f64 (.f64 (.f64 y y) (/.f64 -1/2 x)) x)
	29.5b	y
✓	32.9b	(neg.f64 x)
✓	0.0b	(hypot.f64 x y)

Compiler

Compiled 33 to 21 computations (36.4% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.6b	(fma.f64 1/2 (*.f64 x (/.f64 x y)) y)
✓	35.3b	(-.f64 (.f64 (.f64 y y) (/.f64 -1/2 x)) x)
	29.5b	y
✓	32.9b	(neg.f64 x)
✓	0.0b	(hypot.f64 x y)

Compiler

Compiled 33 to 21 computations (36.4% saved)

regimes49.0ms (1.7%)

Counts

6 → 1

Calls

Call 1

Inputs
y
(neg.f64 x)
(-.f64 (.f64 (.f64 y y) (/.f64 -1/2 x)) x)
(hypot.f64 x y)
(fma.f64 1/2 (*.f64 x (/.f64 x y)) y)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Outputs
(hypot.f64 x y)

Calls

8 calls:

14.0ms	(*.f64 y y)
7.0ms	x
6.0ms	(+.f64 (.f64 x x) (.f64 y y))
5.0ms	y
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Results

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

Compiler

Compiled 78 to 43 computations (44.9% saved)

regimes42.0ms (1.5%)

Accuracy

Total -56.1b remaining (-854.8%)

Threshold costs -56.1b (-854.8%)

Counts

3 → 2

Calls

Call 1

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

Outputs
(neg.f64 x)
y

Calls

4 calls:

20.0ms	x
10.0ms	y
6.0ms	(*.f64 y y)
5.0ms	(*.f64 y y)

Results

Error	Segments	Branch
8.2b	4	`x`
6.6b	2	`y`
12.7b	2	`(*.f64 y y)`
12.7b	2	`(*.f64 y y)`

Compiler

Compiled 30 to 18 computations (40% saved)

bsearch19.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
19.0ms	9.316965023834248e-160	3.141762226889575e-158

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	13	15
2	15	15
3	16	15

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs

(hypot.f64 x y)

(if (<=.f64 y 921747479942319/989321605892418136242010084078588760140525396404847359656252224371588900426127468681265604244972179958390685704064557357405460137227004839870184620407572671666427088594796544) (neg.f64 x) y)

Outputs

(hypot.f64 x y)

(if (<=.f64 y 921747479942319/989321605892418136242010084078588760140525396404847359656252224371588900426127468681265604244972179958390685704064557357405460137227004839870184620407572671666427088594796544) (neg.f64 x) y)

Compiler

Compiled 17 to 11 computations (35.3% saved)

soundness9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4
2	12	4

Stop Event

1×

saturated

Compiler

Compiled 15 to 9 computations (40% saved)

end24.0ms (0.9%)

Remove: (sort x y)
Compiler: Compiled 23 to 13 computations (43.5% saved)

Details

analyze166.0ms (5.9%)

sample1.8s (64%)

preprocess16.0ms (0.6%)

simplify47.0ms (1.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite53.0ms (1.9%)

simplify62.0ms (2.2%)

eval21.0ms (0.7%)

prune12.0ms (0.4%)

localize2.0ms (0.1%)

localize30.0ms (1.1%)

series7.0ms (0.3%)

rewrite70.0ms (2.5%)

simplify122.0ms (4.3%)

localize32.0ms (1.1%)

series4.0ms (0.1%)

rewrite51.0ms (1.8%)

simplify116.0ms (4.1%)

eval24.0ms (0.9%)

prune17.0ms (0.6%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes49.0ms (1.7%)

regimes42.0ms (1.5%)

bsearch19.0ms (0.7%)

simplify5.0ms (0.2%)

soundness9.0ms (0.3%)

end24.0ms (0.9%)

Profiling