Metrics for Data.Octree.Internal:octantDistance from Octree-0.5.4.2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 10 to 5 computations (50% saved)

sample905.0ms (16.6%)

Memory

-24.3MiB live, 1 114.8MiB allocated

Samples

587.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 208.0ms

ival-hypot: 198.0ms (95.3% of total)

ival-true: 6.0ms (2.9% of total)

ival-assert: 3.0ms (1.4% of total)

Bogosity

explain92.0ms (1.7%)

Memory

42.2MiB live, 181.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
122	-	2	(1.0735889943679917e-256 8.131038929092841e-159)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`y`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	oflow-rescue	103	0
↳	`(*.f64 y y)`	overflow	65
↳	`(*.f64 x x)`	overflow	51
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	103
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	17	0
↳	`(*.f64 y y)`	underflow	61
↳	`(*.f64 x x)`	underflow	78
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	17

Confusion

	Predicted +	Predicted -
+	120	2
-	0	134

Precision

1.0

Recall

0.9836065573770492

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	0	2
-	0	0	134

Precision?

1.0

Recall?

0.9836065573770492

Freqs

test

number	freq
0	136
1	120

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

36.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-hypot: 9.0ms (46.4% of total)

ival-mult: 7.0ms (36.1% of total)

ival-add: 2.0ms (10.3% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess46.0ms (0.8%)

Memory

-27.7MiB live, 24.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	42	42
2	92	42
3	117	42
4	155	42
0	6	8
0	10	8
1	21	8
2	60	8
3	117	8
4	154	8
0	154	3

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

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 y x)

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.0%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify5.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	1	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	4	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	21	23
2	60	23
3	117	23
4	154	23
0	154	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.4%)

Memory

25.0MiB live, 25.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 (.f64 x x) (.f64 y y))
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	28.150328630326076	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

15.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-hypot: 4.0ms (45.9% of total)

ival-mult: 3.0ms (34.4% of total)

ival-add: 1.0ms (11.5% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series28.0ms (0.5%)

Memory

-29.5MiB live, 14.1MiB allocated

Counts

4 → 27

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
22.0ms	x	@	0	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
2.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
1.0ms	y	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
1.0ms	x	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
1.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))

simplify204.0ms (3.8%)

Memory

17.8MiB live, 250.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	441
1	323	441
2	1251	437
3	6235	435
0	8273	400

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 25

Calls

Call 1

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

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) (.f64 x x) #s(literal 1/2 binary64)) y) (.f64 x x) y)
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(pow x 2)
(*.f64 x x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) (/.f64 (/.f64 y x) x) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) (.f64 x x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 y y) x) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(.f64 (neg.f64 x) (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 y x) #s(literal 1 binary64)))))
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) x) (.f64 y y) #s(literal 1/2 binary64)) x) (.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64))) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)))) y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) y y) y)
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) y)
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(.f64 (neg.f64 y) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64) #s(literal 1 binary64)))))

rewrite344.0ms (6.3%)

Memory

-16.5MiB live, 346.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	39	21
2	346	21
3	5889	21
0	8197	15

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 218

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (fma.f64 y y (.f64 x x)) (*.f64 y x)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 y x))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (.f64 y x) #s(literal 4 binary64))))) #s(literal 1/2 binary64)) (hypot.f64 (fma.f64 y y (.f64 x x)) (.f64 y x)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (pow.f64 (neg.f64 (neg.f64 (+.f64 y x))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (neg.f64 x) (neg.f64 y))))
(*.f64 (pow.f64 (neg.f64 (+.f64 (neg.f64 y) x)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (neg.f64 x) y)))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 y x))) (pow.f64 (neg.f64 (-.f64 (neg.f64 x) (neg.f64 y))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 y x))) (pow.f64 (-.f64 (neg.f64 y) (neg.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 y x))) (sqrt.f64 (-.f64 (neg.f64 x) (neg.f64 y))))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 y x))) (sqrt.f64 (-.f64 x y)))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 y) x)) (pow.f64 (neg.f64 (-.f64 (neg.f64 x) y)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 y) x)) (pow.f64 (-.f64 (neg.f64 y) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 y) x)) (pow.f64 (-.f64 y (neg.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 y) x)) (sqrt.f64 (-.f64 (neg.f64 x) y)))
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(fma.f64 (/.f64 (neg.f64 x) (+.f64 y x)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x y)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))))
(fma.f64 (/.f64 (.f64 x x) (neg.f64 (+.f64 y x))) (/.f64 (.f64 x x) (-.f64 (neg.f64 x) (neg.f64 y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 (neg.f64 y) x)) (/.f64 (.f64 x x) (-.f64 (neg.f64 x) y)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))))
(fma.f64 (/.f64 x (neg.f64 (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (neg.f64 x) (neg.f64 y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))))
(fma.f64 (/.f64 x (+.f64 (neg.f64 y) x)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (neg.f64 x) y)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))))
(fma.f64 (/.f64 x (+.f64 y x)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x y)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (*.f64 (neg.f64 x) x))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (*.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 (neg.f64 y) y))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 y y))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (neg.f64 x) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (.f64 (neg.f64 x) x) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (.f64 y y) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (.f64 x x) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (neg.f64 y) (neg.f64 y) (*.f64 (neg.f64 x) x))
(fma.f64 (neg.f64 y) (neg.f64 y) (*.f64 x x))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(fma.f64 (neg.f64 x) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 (neg.f64 y) y))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 y y))
(fma.f64 (neg.f64 x) x (*.f64 y y))
(fma.f64 (.f64 y y) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 y (neg.f64 y) (*.f64 x x))
(fma.f64 y y (*.f64 (neg.f64 x) x))
(fma.f64 y y (*.f64 x x))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 (.f64 x x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 x (neg.f64 x) (*.f64 y y))
(fma.f64 x x (*.f64 (neg.f64 y) y))
(fma.f64 x x (*.f64 y y))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(-.f64 (.f64 y y) (.f64 (neg.f64 x) x))
(-.f64 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 (neg.f64 y) y))
(-.f64 (.f64 x x) (.f64 y y))
(+.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(+.f64 (.f64 (neg.f64 x) x) (.f64 y y))
(+.f64 (.f64 (neg.f64 y) y) (.f64 x x))
(+.f64 (.f64 y y) (.f64 (neg.f64 x) x))
(+.f64 (.f64 y y) (.f64 x x))
(+.f64 (.f64 x x) (.f64 (neg.f64 y) y))
(+.f64 (.f64 x x) (.f64 y y))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 (neg.f64 y) (neg.f64 y))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 y) y))
(sqrt.f64 (pow.f64 y #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 y) y))
(fabs.f64 (*.f64 y y))
(exp.f64 (.f64 (.f64 (log.f64 (neg.f64 y)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (/.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 y))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 y)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (neg.f64 y)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (neg.f64 y)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))))

eval105.0ms (1.9%)

Memory: 12.9MiB live, 103.3MiB allocated
Compiler: Compiled 4 457 to 759 computations (83% saved)

prune18.0ms (0.3%)

Memory

-28.8MiB live, 23.8MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	238	5	243
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	239	5	244

Accuracy

100.0%

Counts

244 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	55.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	95.2%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 100 to 70 computations (30% saved)

simplify28.0ms (0.5%)

Memory

-4.2MiB live, 40.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 y y (*.f64 x x))
cost-diff	4	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
cost-diff	0	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
cost-diff	0	(hypot.f64 y x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	94
0	28	82
1	46	82
2	117	82
3	270	82
4	487	82
5	653	82
6	666	82
0	666	82

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(hypot.f64 y x)
y
x
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(neg.f64 x)
x
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 y y)
y
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
y
(*.f64 x x)
x
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(*.f64 x x)
x

Outputs
(hypot.f64 y x)
(hypot.f64 x y)
y
x
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(neg.f64 x)
x
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 y y)
y
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(hypot.f64 x y)
(fma.f64 y y (*.f64 x x))
(fma.f64 x x (*.f64 y y))
y
(*.f64 x x)
x
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(*.f64 x x)
x

localize45.0ms (0.8%)

Memory

28.1MiB live, 117.6MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.0	(*.f64 x x)
accuracy	0.14259019912837573	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
accuracy	2.974031932753256	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
accuracy	0.0	(fma.f64 y y (*.f64 x x))
accuracy	0.0	(*.f64 x x)
accuracy	28.150328630326076	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0.0	(*.f64 y y)
accuracy	0.14974932086191012	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	28.150328630326076	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0.0	(neg.f64 x)
accuracy	62.740428516076626	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0.0	(hypot.f64 y x)

Samples

32.0ms

256×

valid

Compiler

Compiled 88 to 15 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-hypot: 8.0ms (38.2% of total)

ival-mult: 6.0ms (28.6% of total)

ival-add: 3.0ms (14.3% of total)

ival-div: 2.0ms (9.5% of total)

ival-neg: 1.0ms (4.8% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

18.8MiB live, 18.8MiB allocated

Counts

12 → 32

Calls

Call 1

Inputs
(hypot.f64 y x)
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(neg.f64 x)
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 y y)
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(/.f64 #s(literal 1/2 binary64) y)

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))
1.0ms	y	@	-inf	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))
1.0ms	y	@	inf	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))
1.0ms	y	@	0	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))
1.0ms	x	@	-inf	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (sqrt (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y))

simplify386.0ms (7.1%)

Memory

-3.0MiB live, 240.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	483
1	349	483
2	1327	466
3	6699	466
0	8417	428

Stop Event

1×	iter limit
1×	node limit

Counts

32 → 30

Calls

Call 1

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

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) y) y) (.f64 x x) #s(literal 1/2 binary64)) y) (.f64 x x) y)
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(* -1 x)
(neg.f64 x)
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
(pow x 2)
(*.f64 x x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) (/.f64 y (*.f64 x x)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64)))) x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) (.f64 x x))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (-.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) y)) x) x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 y y) x) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64))) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64)))) (neg.f64 x))
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) x) (.f64 y y) #s(literal 1/2 binary64)) x) (.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(/ 1/2 y)
(/.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 (/.f64 (.f64 x x) y) y (.f64 y y))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y) (neg.f64 y))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(neg.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y)))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 y) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 x x) y) y)) #s(literal 1 binary64)) (neg.f64 y))

rewrite178.0ms (3.3%)

Memory

-9.2MiB live, 78.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	82
0	28	70
1	87	70
2	720	70
0	9851	70

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

12 → 309

Calls

Call 1

Inputs
(hypot.f64 y x)
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(neg.f64 x)
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 y y)
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(/.f64 #s(literal 1/2 binary64) y)

Outputs
(.f64 (neg.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64))))
(.f64 (fabs.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 x y))) (sqrt.f64 (-.f64 (neg.f64 x) (neg.f64 y))))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 x) y)) (sqrt.f64 (-.f64 (neg.f64 x) y)))
(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 x y)))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 y x))) (sqrt.f64 (-.f64 (neg.f64 y) (neg.f64 x))))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 y) x)) (sqrt.f64 (-.f64 (neg.f64 y) x)))
(*.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (-.f64 y x)))
(.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (*.f64 y y)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
(pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (*.f64 (hypot.f64 x y) (hypot.f64 x y))) (neg.f64 (hypot.f64 x y)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (hypot.f64 (fma.f64 x x (.f64 y y)) (.f64 x y))))
(/.f64 (*.f64 (hypot.f64 x y) (hypot.f64 x y)) (hypot.f64 x y))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (hypot.f64 (fma.f64 x x (.f64 y y)) (.f64 x y)))
(sqrt.f64 (fma.f64 x x (*.f64 y y)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 y)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 y))
(hypot.f64 (exp.f64 (log.f64 x)) y)
(hypot.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 y)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 y)) x)
(hypot.f64 (neg.f64 y) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 y) (neg.f64 x))
(hypot.f64 (neg.f64 y) x)
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 y)))
(hypot.f64 (neg.f64 x) (neg.f64 y))
(hypot.f64 (neg.f64 x) y)
(hypot.f64 x (exp.f64 (log.f64 y)))
(hypot.f64 x (neg.f64 y))
(hypot.f64 x y)
(hypot.f64 y (exp.f64 (log.f64 x)))
(hypot.f64 y (neg.f64 x))
(hypot.f64 y x)
(exp.f64 (.f64 (log.f64 (fma.f64 x x (.f64 y y))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (fma.f64 x x (.f64 y y))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (fma.f64 x x (.f64 y y))) #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(neg.f64 x)
(.f64 (neg.f64 (pow.f64 #s(approx (+ ( x x) (* y y)) (.f64 y y)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #s(literal 1/4 binary64))))
(.f64 (fabs.f64 (pow.f64 #s(approx (+ ( x x) (* y y)) (.f64 y y)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(approx (+ ( x x) (* y y)) (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(approx (+ ( x x) (* y y)) (.f64 y y)) #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
(exp.f64 (.f64 (log.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 #s(approx (+ ( x x) (* y y)) (.f64 y y))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y))) #s(literal 1/2 binary64))))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 (neg.f64 y) (neg.f64 y))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 y) y))
(sqrt.f64 (pow.f64 y #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 y) y))
(fabs.f64 (*.f64 y y))
(exp.f64 (*.f64 (log.f64 (neg.f64 y)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))))
(.f64 (neg.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64))))
(.f64 (fabs.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 x y))) (sqrt.f64 (-.f64 (neg.f64 x) (neg.f64 y))))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 x) y)) (sqrt.f64 (-.f64 (neg.f64 x) y)))
(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (-.f64 x y)))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 y x))) (sqrt.f64 (-.f64 (neg.f64 y) (neg.f64 x))))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 y) x)) (sqrt.f64 (-.f64 (neg.f64 y) x)))
(*.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (-.f64 y x)))
(.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (*.f64 y y)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
(pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (*.f64 (hypot.f64 x y) (hypot.f64 x y))) (neg.f64 (hypot.f64 x y)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (hypot.f64 (fma.f64 x x (.f64 y y)) (.f64 x y))))
(/.f64 (*.f64 (hypot.f64 x y) (hypot.f64 x y)) (hypot.f64 x y))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (hypot.f64 (fma.f64 x x (.f64 y y)) (.f64 x y)))
(sqrt.f64 (fma.f64 x x (*.f64 y y)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 y)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 y))
(hypot.f64 (exp.f64 (log.f64 x)) y)
(hypot.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 y)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 y)) x)
(hypot.f64 (neg.f64 y) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 y) (neg.f64 x))
(hypot.f64 (neg.f64 y) x)
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 y)))
(hypot.f64 (neg.f64 x) (neg.f64 y))
(hypot.f64 (neg.f64 x) y)
(hypot.f64 x (exp.f64 (log.f64 y)))
(hypot.f64 x (neg.f64 y))
(hypot.f64 x y)
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(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)) (.f64 (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y) (.f64 y y))) (.f64 (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y) (-.f64 (.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)))
(/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))) (.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))) (pow.f64 y #s(literal 3 binary64)))) (.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))))
(/.f64 (fma.f64 y y (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 y (.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 y) y))) (neg.f64 (-.f64 (.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x y))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))))
(/.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 y) y)) (-.f64 (.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 x y)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 y) y))) (-.f64 (.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 y) y)) (neg.f64 (-.f64 (.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))))))
(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(fma.f64 (sqrt.f64 (neg.f64 y)) (sqrt.f64 (neg.f64 y)) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) y) x) (neg.f64 x) y)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x x) y) y)
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) y) y)
(fma.f64 (neg.f64 x) (*.f64 (/.f64 #s(literal -1/2 binary64) y) x) y)
(fma.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) y)
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))) (/.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))
(-.f64 (/.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)))
(-.f64 y (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) x) x))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x y))))) (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64))) (fma.f64 y y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x y))))))
(+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64))) (fma.f64 y y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x y))))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x y))))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))) (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))))
(+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))))
(+.f64 (/.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)))
(+.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)
(+.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 #s(literal 1/2 binary64) y)
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))

eval70.0ms (1.3%)

Memory: -2.2MiB live, 42.4MiB allocated
Compiler: Compiled 7 646 to 1 010 computations (86.8% saved)

prune7.0ms (0.1%)

Memory

18.7MiB live, 18.7MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	312	2	314
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	313	6	319

Accuracy

100.0%

Counts

319 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	55.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
▶	3.7%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))

Compiler

Compiled 76 to 51 computations (32.9% saved)

simplify82.0ms (1.5%)

Memory

-41.7MiB live, 25.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
cost-diff	0	(/.f64 (*.f64 x x) y)
cost-diff	0	(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	97
0	26	95
1	51	95
2	133	95
3	304	95
4	528	95
5	664	95
6	667	95
0	667	85

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(/.f64 (*.f64 x x) y)
(*.f64 x x)
x
y
#s(literal 1/2 binary64)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
x

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 x x) y)
(*.f64 x x)
x
y
#s(literal 1/2 binary64)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
(fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y)
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
x

localize103.0ms (1.9%)

Memory

18.4MiB live, 64.0MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.14259019912837573	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
accuracy	0.203125	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	0.00390625	(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
accuracy	0.14259019912837573	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
accuracy	6.4196981540828855	(/.f64 (*.f64 x x) y)
accuracy	61.64058232925564	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))

Samples

94.0ms

256×

valid

Compiler

Compiled 65 to 15 computations (76.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 7.0ms (40.5% of total)

ival-hypot: 4.0ms (23.2% of total)

ival-div: 3.0ms (17.4% of total)

ival-add: 2.0ms (11.6% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series84.0ms (1.5%)

Memory

-23.3MiB live, 24.1MiB allocated

Counts

8 → 29

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(/.f64 (*.f64 x x) y)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)

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

Calls

6 calls:

Time	Variable		Point	Expression
76.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
3.0ms	y	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	y	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	x	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (/ (* x x) y) 1/2) (/ (* x x) y) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))

simplify362.0ms (6.7%)

Memory

15.8MiB live, 345.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	454
1	332	454
2	1265	439
3	6069	436
0	8290	404

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 27

Calls

Call 1

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

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal -1/8 binary64) #s(literal 1/2 binary64)) y) (.f64 x x) y)
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(/ (pow x 2) y)
(/.f64 (*.f64 x x) y)
(* 1/2 (/ x y))
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) (/.f64 y (*.f64 x x)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64)))) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (-.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) y)) x) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 y y) x) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(.f64 (neg.f64 x) (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64)))))
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) x) (.f64 y y) #s(literal 1/2 binary64)) x) (.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(/ 1/2 y)
(/.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y) (neg.f64 y))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(neg.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y)))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 y) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 x x) y) y)) #s(literal 1 binary64)) (neg.f64 y))

rewrite164.0ms (3%)

Memory

10.0MiB live, 151.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	88
0	26	86
1	97	86
2	618	86
0	8946	76

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

8 → 123

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(/.f64 (*.f64 x x) y)
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)))
(.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) x) (neg.f64 x))
(.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (neg.f64 x) y))
(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))
(.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal -1/2 binary64) y))
(.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (neg.f64 x) x) y))
(.f64 (neg.f64 x) (.f64 (/.f64 (neg.f64 x) y) #s(literal 1/2 binary64)))
(.f64 (neg.f64 x) (.f64 (/.f64 #s(literal -1/2 binary64) y) x))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
(.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) y))
(.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) y))
(.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) y) x))
(/.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) (neg.f64 y))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) y)
(neg.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))
(*.f64 (/.f64 (neg.f64 x) y) (neg.f64 x))
(*.f64 (/.f64 x y) x)
(*.f64 (neg.f64 x) (/.f64 (neg.f64 x) y))
(*.f64 x (/.f64 x y))
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 y))
(/.f64 (*.f64 x x) y)
(neg.f64 (/.f64 (*.f64 (neg.f64 x) x) y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y))
(.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y))))))
(.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y)) (pow.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y))) (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y))
(.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y))))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))
(.f64 (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y)) (/.f64 (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))))
(.f64 (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))) (.f64 (/.f64 (.f64 y y) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 y y) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 y y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y)))) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))))) (.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))))) (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y))) y)))))
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(fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)) (/.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y)))
(fma.f64 (fabs.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) (/.f64 (fabs.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y)))
(fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))))
(fma.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y))) y))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y))) y))))
(fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y)
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
(fma.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (/.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y)))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))))
(fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal -1/2 binary64) y) y)
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (neg.f64 x) x) y) y)
(fma.f64 (neg.f64 x) (*.f64 (/.f64 (neg.f64 x) y) #s(literal 1/2 binary64)) y)
(fma.f64 (neg.f64 x) (*.f64 (/.f64 #s(literal -1/2 binary64) y) x) y)
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) y)
(fma.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (/.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y)))
(fma.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x x) y) y)
(fma.f64 (.f64 y y) (/.f64 y (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y)))))
(fma.f64 y (/.f64 (.f64 y y) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y)))))
(fma.f64 (.f64 x x) (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y)))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) y) y)
(fma.f64 x (/.f64 (.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) #s(literal 2 binary64)) x) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) y)
(-.f64 (/.f64 (.f64 y y) (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))) (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y)))))
(-.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 y y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y)))
(-.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y))) (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y))) y)))))
(+.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y))) y))))
(+.f64 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x)) y)))
(+.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)
(+.f64 y (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)))
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (/.f64 (neg.f64 x) y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
(*.f64 x (/.f64 #s(literal 1/2 binary64) y))
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) x)) y)
(/.f64 (*.f64 #s(literal -1/2 binary64) x) (neg.f64 y))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(neg.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) y) x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 #s(literal 1/2 binary64) y)
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))

eval37.0ms (0.7%)

Memory: -8.3MiB live, 37.0MiB allocated
Compiler: Compiled 5 966 to 563 computations (90.6% saved)

prune8.0ms (0.1%)

Memory

21.5MiB live, 21.5MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	148	7	155

Accuracy

100.0%

Counts

155 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	55.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
▶	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
✓	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
▶	3.7%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))

Compiler

Compiled 115 to 70 computations (39.1% saved)

simplify276.0ms (5.1%)

Memory

-23.9MiB live, 127.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
cost-diff	20	(.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
cost-diff	0	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	204
0	37	204
1	68	204
2	169	202
3	513	198
4	1649	198
5	4636	166
0	8035	152

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
x
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
x
(neg.f64 y)
(/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))
(-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y))
(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))
(/.f64 x y)
(*.f64 #s(literal 1/2 binary64) x)
(-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
x
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64) y) #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))
(.f64 (fma.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64) y) #s(literal 1 binary64))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
x
(neg.f64 y)
(/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) (neg.f64 y)) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y))
(-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y))
(-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) (neg.f64 y))
(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
(/.f64 x y)
(*.f64 #s(literal 1/2 binary64) x)
(-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)
(-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)

localize63.0ms (1.2%)

Memory

23.5MiB live, 67.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))
accuracy	0.1015625	(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))
accuracy	0.14259019912837573	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
accuracy	0.203125	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	0.1015625	(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
accuracy	0.14259019912837573	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
accuracy	0.203125	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	61.64058232925564	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))

Samples

51.0ms

256×

valid

Compiler

Compiled 151 to 21 computations (86.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 10.0ms (39.1% of total)

ival-div: 5.0ms (19.6% of total)

ival-hypot: 5.0ms (19.6% of total)

ival-add: 2.0ms (7.8% of total)

ival-sub: 2.0ms (7.8% of total)

ival-neg: 1.0ms (3.9% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series21.0ms (0.4%)

Memory

-30.2MiB live, 14.5MiB allocated

Counts

8 → 32

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))
(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))

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

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	x	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ 1/2 y) x) x) (* (/ 1/2 y) x) (* (+ (* (* (/ 1/2 y) x) x) (neg y)) (/ (- (* (/ x y) (* 1/2 x)) (neg y)) (- (* (/ x y) (* 1/2 x)) y))) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) (neg y)) (* (/ x y) (* 1/2 x)))
1.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ 1/2 y) x) x) (* (/ 1/2 y) x) (* (+ (* (* (/ 1/2 y) x) x) (neg y)) (/ (- (* (/ x y) (* 1/2 x)) (neg y)) (- (* (/ x y) (* 1/2 x)) y))) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) (neg y)) (* (/ x y) (* 1/2 x)))
1.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ 1/2 y) x) x) (* (/ 1/2 y) x) (* (+ (* (* (/ 1/2 y) x) x) (neg y)) (/ (- (* (/ x y) (* 1/2 x)) (neg y)) (- (* (/ x y) (* 1/2 x)) y))) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) (neg y)) (* (/ x y) (* 1/2 x)))
1.0ms	y	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ 1/2 y) x) x) (* (/ 1/2 y) x) (* (+ (* (* (/ 1/2 y) x) x) (neg y)) (/ (- (* (/ x y) (* 1/2 x)) (neg y)) (- (* (/ x y) (* 1/2 x)) y))) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) (neg y)) (* (/ x y) (* 1/2 x)))
1.0ms	y	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (/ 1/2 y) (* x x)) y) (* (* (/ 1/2 y) x) x) (* (/ 1/2 y) x) (* (+ (* (* (/ 1/2 y) x) x) (neg y)) (/ (- (* (/ x y) (* 1/2 x)) (neg y)) (- (* (/ x y) (* 1/2 x)) y))) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) (neg y)) (* (/ x y) (* 1/2 x)))

simplify183.0ms (3.4%)

Memory

22.2MiB live, 250.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	500
1	374	500
2	1422	484
3	6753	484
0	8385	449

Stop Event

1×	iter limit
1×	node limit

Counts

32 → 30

Calls

Call 1

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

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal -1/8 binary64) #s(literal 1/2 binary64)) y) (.f64 x x) y)
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ x y))
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(* -1 y)
(neg.f64 y)
(- (* 1/2 (/ (pow x 2) y)) y)
(fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) (neg.f64 y))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) y) (/.f64 y (*.f64 x x)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64)))) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (-.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) y)) x) x)
(* (pow x 2) (+ (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 y))))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 y (*.f64 x x))) x) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 y y) x) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(.f64 (neg.f64 x) (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) y #s(literal 1 binary64)))))
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) x) (.f64 y y) #s(literal 1/2 binary64)) x) (.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) y)
(fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) (neg.f64 y))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
(* y (- (* 1/2 (/ (pow x 2) (pow y 2))) 1))
(.f64 (-.f64 (.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64)) #s(literal 1 binary64)) y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y) (neg.f64 y))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(neg.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y)))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 y) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 x x) y) y)) #s(literal 1 binary64)) (neg.f64 y))
(* -1 (* y (+ 1 (* -1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) (neg.f64 y))

rewrite212.0ms (3.9%)

Memory

28.4MiB live, 361.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	140
0	37	140
1	136	98
2	1135	98
0	9108	84

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

8 → 497

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y)))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))
(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) y)))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))
(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
(.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) y))
(.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x y)))
(.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) y))
(.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) y) x))
(/.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (.f64 (neg.f64 x) (.f64 #s(literal 1/2 binary64) x))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (neg.f64 x))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x))) (neg.f64 (neg.f64 y)))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (neg.f64 y))
(/.f64 (.f64 (neg.f64 x) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y))
(/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (neg.f64 y))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (neg.f64 x)) (neg.f64 y))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x)) (neg.f64 y))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) y)
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
(*.f64 x (/.f64 #s(literal 1/2 binary64) y))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) #s(literal 1/2 binary64))) (neg.f64 (neg.f64 y)))
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(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 x y))))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) x))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x)))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (neg.f64 (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (neg.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)))
(fma.f64 (/.f64 x (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (/.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(fma.f64 (/.f64 x (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (/.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (neg.f64 y) y) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(fma.f64 (/.f64 (/.f64 x y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(fma.f64 (/.f64 (/.f64 x y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (neg.f64 y) y) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (/.f64 (.f64 (/.f64 x y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) x) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (/.f64 (.f64 (/.f64 x y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (neg.f64 y) y) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) (neg.f64 x)) (neg.f64 x) (neg.f64 y))
(fma.f64 (*.f64 (/.f64 x y) x) #s(literal 1/2 binary64) (neg.f64 y))
(fma.f64 (.f64 (/.f64 (.f64 x x) y) (/.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(fma.f64 (.f64 (/.f64 (.f64 x x) y) (/.f64 #s(literal 1/2 binary64) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))) (/.f64 (.f64 (neg.f64 y) y) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) y)) (neg.f64 y))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) (neg.f64 y))
(fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) (neg.f64 y))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) (neg.f64 y))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x x) y) (neg.f64 y))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 x y)) (neg.f64 y))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) y) (neg.f64 y))
(fma.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) (neg.f64 y))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))))
(-.f64 (/.f64 (.f64 y y) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (/.f64 (.f64 y y) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(-.f64 (neg.f64 y) (.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) (neg.f64 x))) (neg.f64 x)))
(-.f64 (neg.f64 y) (.f64 (neg.f64 (.f64 (/.f64 x y) x)) #s(literal 1/2 binary64)))
(-.f64 (neg.f64 y) (.f64 (neg.f64 (neg.f64 x)) (.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) y))))
(-.f64 (neg.f64 y) (.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) x)) (/.f64 x y)))
(-.f64 (neg.f64 y) (.f64 (neg.f64 (/.f64 x y)) (.f64 #s(literal 1/2 binary64) x)))
(-.f64 (neg.f64 y) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))
(-.f64 (neg.f64 y) (.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 x y))))
(-.f64 (neg.f64 y) (.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) x))
(-.f64 (neg.f64 y) (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x)))
(-.f64 (neg.f64 y) (.f64 (neg.f64 (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)))
(-.f64 (neg.f64 y) (.f64 (neg.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)))
(-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) y)
(-.f64 y (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 2 binary64)) (.f64 (neg.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))) (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 3 binary64)) (fma.f64 y y (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 2 binary64)) (.f64 (neg.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 3 binary64)) (fma.f64 y y (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 2 binary64)) (.f64 (neg.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 2 binary64)) (.f64 (neg.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (/.f64 (.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (/.f64 (.f64 (neg.f64 y) y) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))) (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)))))
(+.f64 (neg.f64 y) (.f64 (neg.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x))) x))
(+.f64 (neg.f64 y) (.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) y))) (.f64 x x)))
(+.f64 (neg.f64 y) (.f64 (neg.f64 (neg.f64 (.f64 x x))) (/.f64 #s(literal 1/2 binary64) y)))
(+.f64 (neg.f64 y) (.f64 (neg.f64 (neg.f64 x)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)))
(+.f64 (neg.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))
(+.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x) (neg.f64 y))
(+.f64 y (.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) (neg.f64 x))) (neg.f64 x)))
(+.f64 y (.f64 (neg.f64 (.f64 (/.f64 x y) x)) #s(literal 1/2 binary64)))
(+.f64 y (.f64 (neg.f64 (neg.f64 x)) (.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) y))))
(+.f64 y (.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) x)) (/.f64 x y)))
(+.f64 y (.f64 (neg.f64 (/.f64 x y)) (.f64 #s(literal 1/2 binary64) x)))
(+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))
(+.f64 y (.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 x y))))
(+.f64 y (.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) x))
(+.f64 y (.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x)))
(+.f64 y (.f64 (neg.f64 (.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)))
(+.f64 y (.f64 (neg.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (/.f64 x y) x) #s(literal 1/2 binary64))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) y)))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))
(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
(.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) y))
(.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x y)))
(.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) y))
(.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) y) x))
(/.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (.f64 (neg.f64 x) (.f64 #s(literal 1/2 binary64) x))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (neg.f64 x))) (neg.f64 (neg.f64 y)))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x))) (neg.f64 (neg.f64 y)))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (neg.f64 y))
(/.f64 (.f64 (neg.f64 x) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y))
(/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (neg.f64 y))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (neg.f64 x)) (neg.f64 y))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x)) (neg.f64 y))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) y)

eval188.0ms (3.5%)

Memory: -32.3MiB live, 253.6MiB allocated
Compiler: Compiled 32 537 to 1 924 computations (94.1% saved)

prune16.0ms (0.3%)

Memory

2.3MiB live, 49.2MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	515	1	516
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	516	7	523

Accuracy

100.0%

Counts

523 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	55.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))))
✓	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
✓	3.7%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))

Compiler

Compiled 316 to 117 computations (63% saved)

regimes24.0ms (0.4%)

Memory

7.9MiB live, 51.0MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))
(hypot.f64 y x)

Outputs
(hypot.f64 y x)

Calls

6 calls:

7.0ms	(*.f64 x x)
4.0ms	y
3.0ms	x
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 y y)`
100.0%	1	`(*.f64 x x)`
100.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes23.0ms (0.4%)

Memory

6.1MiB live, 51.8MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))))
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) (neg.f64 y)) (-.f64 (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x)) y))))

Outputs

#s(approx (sqrt (+ (* x x) (* y y))) (*.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))))

Calls

6 calls:

7.0ms	(+.f64 (.f64 x x) (.f64 y y))
3.0ms	y
3.0ms	x
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
99.8%	1	`(*.f64 y y)`
99.8%	1	`(*.f64 x x)`
99.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.8%	1	`x`
99.8%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes22.0ms (0.4%)

Memory

-15.7MiB live, 39.6MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))

Calls

6 calls:

8.0ms	(*.f64 x x)
3.0ms	x
3.0ms	y
3.0ms	(*.f64 y y)
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.8%	1	`(*.f64 y y)`
99.8%	1	`(*.f64 x x)`
99.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.8%	1	`x`
99.8%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes12.0ms (0.2%)

Memory

34.3MiB live, 34.3MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))

Outputs
(sqrt.f64 (fma.f64 y y (*.f64 x x)))

Calls

6 calls:

2.0ms	x
2.0ms	y
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(*.f64 y y)
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
56.0%	1	`(*.f64 y y)`
56.0%	1	`(*.f64 x x)`
56.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
56.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
56.0%	1	`x`
56.0%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes15.0ms (0.3%)

Memory

-14.9MiB live, 29.4MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))

Outputs
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))

Calls

6 calls:

6.0ms	x
2.0ms	y
2.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
55.8%	1	`(*.f64 y y)`
55.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
55.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
55.8%	1	`y`
55.8%	1	`(*.f64 x x)`
55.8%	1	`x`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes7.0ms (0.1%)

Memory

19.4MiB live, 19.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Calls

6 calls:

1.0ms	x
1.0ms	y
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	(+.f64 (.f64 x x) (.f64 y y))
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
2.0%	1	`(*.f64 y y)`
2.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
2.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
2.0%	1	`y`
2.0%	1	`(*.f64 x x)`
2.0%	1	`x`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify15.0ms (0.3%)

Memory

-19.3MiB live, 26.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	87
1	45	87
2	86	87
3	143	87
4	180	87

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 y x)
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Outputs
(hypot.f64 y x)
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

soundness894.0ms (16.4%)

Memory

3.0MiB live, 726.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	140
0	37	140
1	136	98
2	1135	98
0	9108	84
0	19	82
0	28	70
1	87	70
2	720	70
0	9851	70
0	19	88
0	26	86
1	97	86
2	618	86
0	8946	76
0	6	21
0	10	21
1	39	21
2	346	21
3	5889	21
0	8197	15
0	104	441
1	323	441
2	1251	437
3	6235	435
0	8273	400

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 186 to 95 computations (48.9% saved)

preprocess134.0ms (2.5%)

Memory

-19.7MiB live, 129.0MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 246 to 112 computations (54.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample905.0ms (16.6%)

explain92.0ms (1.7%)

preprocess46.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize20.0ms (0.4%)

series28.0ms (0.5%)

simplify204.0ms (3.8%)

rewrite344.0ms (6.3%)

eval105.0ms (1.9%)

prune18.0ms (0.3%)

simplify28.0ms (0.5%)

localize45.0ms (0.8%)

series8.0ms (0.1%)

simplify386.0ms (7.1%)

rewrite178.0ms (3.3%)

eval70.0ms (1.3%)

prune7.0ms (0.1%)

simplify82.0ms (1.5%)

localize103.0ms (1.9%)

series84.0ms (1.5%)

simplify362.0ms (6.7%)

rewrite164.0ms (3%)

eval37.0ms (0.7%)

prune8.0ms (0.1%)

simplify276.0ms (5.1%)

localize63.0ms (1.2%)

series21.0ms (0.4%)

simplify183.0ms (3.4%)

rewrite212.0ms (3.9%)

eval188.0ms (3.5%)

prune16.0ms (0.3%)

regimes24.0ms (0.4%)

regimes23.0ms (0.4%)

regimes22.0ms (0.4%)

regimes12.0ms (0.2%)

regimes15.0ms (0.3%)

regimes7.0ms (0.1%)

simplify15.0ms (0.3%)

soundness894.0ms (16.4%)

preprocess134.0ms (2.5%)

end0.0ms (0%)

Profiling