Details

analyze121.0ms (8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample973.0ms (64.6%)

Results

960.0ms

8256×

body

128

valid

preprocess16.0ms (1.1%)

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 10 to 6 computations (40% saved)

simplify50.0ms (3.3%)

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

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)

prune3.0ms (0.2%)

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

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

Compiler

Compiled 23 to 13 computations (43.5% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.3%)

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)

rewrite35.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

360×	`pow1_binary64`
329×	`add-log-exp_binary64`
329×	`log1p-expm1-u_binary64`
329×	`expm1-log1p-u_binary64`
321×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	79	4
2	910	4

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

Inputs
(hypot.f64 x y)

Outputs
((#(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 (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 pow.f64 (hypot.f64 x y) 1)))) (#(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 (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 sqrt.f64 (pow.f64 (hypot.f64 x y) 2))))) (#(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)))))))

Outputs

((#(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 (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 pow.f64 (hypot.f64 x y) 1)))) (#(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 (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 sqrt.f64 (pow.f64 (hypot.f64 x y) 2))))) (#(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)))))))

simplify29.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

748×	`associate-*l/_binary64`
298×	`associate-/l/_binary64`
291×	`associate-/r/_binary64`
232×	`times-frac_binary64`
232×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	469
1	197	458
2	573	454
3	2333	454

Stop Event

1×	node limit

Counts

41 → 47

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

prune26.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	2	48

Error

0.0b

Counts

48 → 2

Alt Table

Status	Error	Program
▶	32.4b	(fma.f64 1/2 (*.f64 (/.f64 x y) x) y)
✓	0.0b	(hypot.f64 x y)

Compiler

Compiled 600 to 368 computations (38.7% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (*.f64 (/.f64 x y) x) y)
✓	0.1b	(*.f64 (/.f64 x y) x)

series8.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

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

rewrite40.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`pow1_binary64`
701×	`log1p-expm1-u_binary64`
701×	`expm1-log1p-u_binary64`
74×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	147	18
2	1859	18

Stop Event

1×	node limit

Counts

2 → 47

Calls

Call 1

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

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

Outputs

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

simplify81.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

514×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
289×	`associate-r_binary64`
288×	`associate-*r/_binary64`
281×	`sqr-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	435
1	18	399
2	34	399
3	65	399
4	168	399
5	609	399
6	2555	399
7	3692	399
8	3900	399
9	4119	399
10	4347	399
11	4680	399

Stop Event

1×	node limit

Counts

95 → 54

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

prune22.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	54	2	56

Error

0.0b

Counts

56 → 2

Alt Table

Status	Error	Program
✓	32.4b	(fma.f64 1/2 (*.f64 (/.f64 x y) x) y)
✓	0.0b	(hypot.f64 x y)

Compiler

Compiled 647 to 296 computations (54.3% saved)

regimes39.0ms (2.6%)

Accuracy

Total -47.7b remaining (-2122004.4%)

Threshold costs -47.7b (-2122004.4%)

Counts

6 → 1

Compiler

Compiled 78 to 45 computations (42.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x y)

Outputs
(hypot.f64 x y)

end51.0ms (3.4%)

Stop Event

1×

done

Remove

(sort x y)

Compiler

Compiled 31 to 16 computations (48.4% saved)

Details

analyze121.0ms (8%)

sample973.0ms (64.6%)

preprocess16.0ms (1.1%)

simplify50.0ms (3.3%)

prune3.0ms (0.2%)

localize2.0ms (0.1%)

series4.0ms (0.3%)

rewrite35.0ms (2.3%)

simplify29.0ms (1.9%)

prune26.0ms (1.7%)

localize5.0ms (0.3%)

series8.0ms (0.6%)

rewrite40.0ms (2.6%)

simplify81.0ms (5.4%)

prune22.0ms (1.5%)

regimes39.0ms (2.6%)

simplify2.0ms (0.1%)

end51.0ms (3.4%)

Profiling