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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

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)

sample1.1s (25.5%)

Memory

-14.7MiB live, 944.0MiB allocated; 343ms collecting garbage

Samples

765.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 383.0ms

ival-hypot: 373.0ms (97.4% of total)

ival-true: 6.0ms (1.6% of total)

ival-assert: 3.0ms (0.8% of total)

adjust: 2.0ms (0.5% of total)

Bogosity

explain155.0ms (3.7%)

Memory

7.3MiB live, 242.9MiB allocated; 26ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
107	-	1	(-3.7247556894227474e-262 -6.53145912754228e-162)	`(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	97	0
↳	`(*.f64 y y)`	overflow	55
↳	`(*.f64 x x)`	overflow	59
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	97
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	9	0
↳	`(*.f64 y y)`	underflow	65
↳	`(*.f64 x x)`	underflow	53
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	9

Confusion

	Predicted +	Predicted -
+	106	1
-	0	149

Precision

1.0

Recall

0.9906542056074766

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	106	0	1
-	0	0	149

Precision?

1.0

Recall?

0.9906542056074766

Freqs

test

number	freq
0	150
1	106

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

44.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

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

ival-mult: 9.0ms (42.9% of total)

ival-hypot: 9.0ms (42.9% of total)

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

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

adjust: 0.0ms (0% of total)

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

preprocess19.0ms (0.4%)

Memory

4.5MiB live, 50.7MiB allocated; 4ms collecting garbage

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; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.2%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify7.0ms (0.2%)

Memory

-32.2MiB live, 12.9MiB allocated; 4ms collecting garbage

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

localize38.0ms (0.9%)

Memory

-9.0MiB live, 52.5MiB allocated; 23ms collecting garbage

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	24.84085811873642	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

33.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-hypot: 5.0ms (49.8% of total)

ival-mult: 3.0ms (29.9% of total)

ival-add: 1.0ms (10% of total)

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

adjust: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated; 0ms collecting garbage

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
1.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* x x) (* y y))
1.0ms	x	@	0	((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))

simplify175.0ms (4.1%)

Memory

40.6MiB live, 176.2MiB allocated; 19ms collecting garbage

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)))))

rewrite213.0ms (5.1%)

Memory

-16.3MiB live, 226.7MiB allocated; 35ms collecting garbage

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))))

eval48.0ms (1.1%)

Memory: -4.8MiB live, 87.4MiB allocated; 6ms collecting garbage
Compiler: Compiled 4 457 to 759 computations (83% saved)

prune25.0ms (0.6%)

Memory

-21.0MiB live, 25.5MiB allocated; 2ms collecting garbage

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)
▶	61.2%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	60.9%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	93.5%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 100 to 70 computations (30% saved)

simplify14.0ms (0.3%)

Memory

44.9MiB live, 44.9MiB allocated; 0ms collecting garbage

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

localize61.0ms (1.5%)

Memory

-1.0MiB live, 138.3MiB allocated; 14ms collecting garbage

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	0.16196877620355396	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
accuracy	4.029907076085048	(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	24.84085811873642	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0.0	(*.f64 y y)
accuracy	0.17537347402019118	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	24.84085811873642	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0.0	(neg.f64 x)
accuracy	62.8411748880354	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0.0	(hypot.f64 y x)

Samples

52.0ms

256×

valid

Compiler

Compiled 88 to 15 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 19.0ms (50.4% of total)

ival-hypot: 12.0ms (31.8% of total)

ival-add: 3.0ms (8% of total)

ival-div: 2.0ms (5.3% of total)

ival-neg: 1.0ms (2.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.3%)

Memory

-19.2MiB live, 24.9MiB allocated; 8ms collecting garbage

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
6.0ms	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	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))

simplify265.0ms (6.3%)

Memory

9.8MiB live, 258.5MiB allocated; 43ms collecting garbage

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))

rewrite163.0ms (3.9%)

Memory

-27.5MiB live, 110.7MiB allocated; 12ms collecting garbage

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))

eval50.0ms (1.2%)

Memory: 30.8MiB live, 79.1MiB allocated; 14ms collecting garbage
Compiler: Compiled 7 646 to 1 010 computations (86.8% saved)

prune40.0ms (0.9%)

Memory

-23.8MiB live, 19.4MiB allocated; 8ms collecting garbage

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)
✓	61.2%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	60.9%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	99.7%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
✓	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 71 to 48 computations (32.4% saved)

simplify22.0ms (0.5%)

Memory

24.1MiB live, 24.1MiB allocated; 0ms collecting garbage

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	89
0	22	81
1	46	81
2	152	81
3	471	81
4	942	81
5	1256	81
6	1322	81
0	1322	71

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize66.0ms (1.6%)

Memory

-5.6MiB live, 38.0MiB allocated; 8ms collecting garbage

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	0.16196877620355396	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
accuracy	0.1796875	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	0.11328125	(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
accuracy	0.16196877620355396	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
accuracy	0.1796875	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	0.43359375	(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x))

Samples

58.0ms

256×

valid

Compiler

Compiled 71 to 13 computations (81.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-hypot: 37.0ms (79.4% of total)

ival-mult: 4.0ms (8.6% of total)

ival-div: 2.0ms (4.3% of total)

ival-add: 2.0ms (4.3% of total)

ival-sqrt: 2.0ms (4.3% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Counts

8 → 32

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	0	((+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ 1/2 y) x) x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
2.0ms	y	@	-inf	((+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ 1/2 y) x) x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	y	@	inf	((+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ 1/2 y) x) x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	x	@	inf	((+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ 1/2 y) x) x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))
1.0ms	x	@	-inf	((+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ 1/2 y) x) x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ 1/2 y) x) x) y) (* (/ 1/2 y) x) (/ 1/2 y))

simplify197.0ms (4.7%)

Memory

27.2MiB live, 257.0MiB allocated; 52ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	123	453
1	362	453
2	1390	443
3	7478	443
0	8768	405

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))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (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)))))))
(* -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))))))))
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(+ 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)))))
(sqrt 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 (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (pow x 2) (pow y 2))) (pow (sqrt -1) 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 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))

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

rewrite166.0ms (3.9%)

Memory

-17.6MiB live, 183.2MiB allocated; 42ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	75
0	22	67
1	88	67
2	698	67
0	9031	57

Stop Event

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

Counts

8 → 271

Calls

Call 1

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

eval93.0ms (2.2%)

Memory: -16.1MiB live, 81.1MiB allocated; 19ms collecting garbage
Compiler: Compiled 8 717 to 837 computations (90.4% saved)

prune8.0ms (0.2%)

Memory

-16.6MiB live, 29.1MiB allocated; 2ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	0	0	0
Picked	0	2	2
Done	2	2	4
Total	250	5	255

Accuracy

100.0%

Counts

255 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	61.2%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	99.7%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	99.1%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
▶	99.4%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))

Compiler

Compiled 72 to 47 computations (34.7% saved)

simplify41.0ms (1%)

Memory

23.6MiB live, 66.4MiB allocated; 7ms collecting garbage

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
0	15	32
1	40	32
2	146	32
3	463	32
4	935	32
5	1254	32
6	1320	32
0	1320	25

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))
#s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y)
y

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))
#s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y)
y

localize40.0ms (0.9%)

Memory

-12.2MiB live, 85.4MiB allocated; 14ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.16196877620355396	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))
accuracy	0.41472317271541925	#s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y)

Samples

32.0ms

256×

valid

Compiler

Compiled 24 to 12 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 4.0ms (29.7% of total)

ival-hypot: 4.0ms (29.7% of total)

ival-div: 2.0ms (14.9% of total)

ival-sqrt: 2.0ms (14.9% of total)

ival-add: 1.0ms (7.4% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

14.0MiB live, 14.0MiB allocated; 0ms collecting garbage

Counts

2 → 27

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))
#s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) 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)))))
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)))))))
(* 1/2 (/ (pow x 2) y))
(* (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)
(* 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 (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (pow x 2) (pow y 2))) (pow (sqrt -1) 2))))

Calls

6 calls:

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

simplify192.0ms (4.6%)

Memory

22.5MiB live, 251.4MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	432
1	342	432
2	1340	422
3	7357	422
0	8637	385

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)))))
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)))))))
(* 1/2 (/ (pow x 2) y))
(* (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)
(* 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 (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (pow x 2) (pow y 2))) (pow (sqrt -1) 2))))

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

rewrite191.0ms (4.5%)

Memory

-57.7MiB live, 162.3MiB allocated; 73ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	39
0	15	31
1	74	31
2	607	31
3	7464	31
0	8248	24

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))
#s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y)

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))
#s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y)

eval3.0ms (0.1%)

Memory: 5.9MiB live, 5.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 637 to 122 computations (80.8% saved)

prune3.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	23	5	28

Accuracy

100.0%

Counts

28 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	61.2%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	99.7%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
✓	99.1%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))

Compiler

Compiled 192 to 84 computations (56.3% saved)

regimes41.0ms (1%)

Memory

-9.4MiB live, 35.1MiB allocated; 7ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

Outputs
(hypot.f64 y x)

Calls

6 calls:

27.0ms	(*.f64 y y)
3.0ms	y
3.0ms	x
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(+.f64 (.f64 x x) (.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)

regimes15.0ms (0.4%)

Memory

40.3MiB live, 40.3MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

3.0ms	x
3.0ms	y
2.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
99.7%	1	`(*.f64 y y)`
99.7%	1	`(*.f64 x x)`
99.7%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.7%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.7%	1	`x`
99.7%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes22.0ms (0.5%)

Memory

-3.6MiB live, 46.4MiB allocated; 13ms collecting garbage

Accuracy

Total -62.4b remaining (-15052.9%)

Threshold costs -62.4b (-15052.9%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))

Calls

6 calls:

14.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
99.4%	1	`(*.f64 y y)`
99.4%	1	`(*.f64 x x)`
99.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.4%	1	`x`
99.4%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify73.0ms (1.7%)

Memory

-19.1MiB live, 69.3MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	45	40
2	151	40
3	470	40
4	946	40
5	1298	40
6	1367	40
7	1379	40
8	1408	40
9	1604	40
10	3826	40
11	7798	40

Stop Event

1×	node limit

Calls

Call 1

Inputs

(hypot.f64 y 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))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))

Outputs

(hypot.f64 y 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))) #s(approx (+ (* (sqrt y) (sqrt y)) (* (* (/ 1/2 y) x) x)) y))

derivations635.0ms (15.1%)

Memory

5.9MiB live, 591.7MiB allocated; 95ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	441
1	323	441
2	1251	437
3	6235	435
0	8273	400
0	19	82
0	28	70
1	87	70
2	720	70
0	9851	70
0	123	453
1	362	453
2	1390	443
3	7478	443
0	8768	405
0	6	21
0	10	21
1	39	21
2	346	21
3	5889	21
0	8197	15

Stop Event

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

Compiler

Compiled 44 to 21 computations (52.3% saved)

preprocess31.0ms (0.7%)

Memory

5.3MiB live, 52.2MiB allocated; 3ms collecting garbage

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 160 to 98 computations (38.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample1.1s (25.5%)

explain155.0ms (3.7%)

preprocess19.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify7.0ms (0.2%)

localize38.0ms (0.9%)

series5.0ms (0.1%)

simplify175.0ms (4.1%)

rewrite213.0ms (5.1%)

eval48.0ms (1.1%)

prune25.0ms (0.6%)

simplify14.0ms (0.3%)

localize61.0ms (1.5%)

series12.0ms (0.3%)

simplify265.0ms (6.3%)

rewrite163.0ms (3.9%)

eval50.0ms (1.2%)

prune40.0ms (0.9%)

simplify22.0ms (0.5%)

localize66.0ms (1.6%)

series10.0ms (0.2%)

simplify197.0ms (4.7%)

rewrite166.0ms (3.9%)

eval93.0ms (2.2%)

prune8.0ms (0.2%)

simplify41.0ms (1%)

localize40.0ms (0.9%)

series3.0ms (0.1%)

simplify192.0ms (4.6%)

rewrite191.0ms (4.5%)

eval3.0ms (0.1%)

prune3.0ms (0.1%)

regimes41.0ms (1%)

regimes15.0ms (0.4%)

regimes22.0ms (0.5%)

simplify73.0ms (1.7%)

derivations635.0ms (15.1%)

preprocess31.0ms (0.7%)

end0.0ms (0%)

Profiling