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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 5 computations (50% saved)

sample1.0s (5.2%)

Memory

-18.8MiB live, 683.1MiB allocated

Samples

794.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 440.0ms

ival-hypot: 431.0ms (97.9% of total)

ival-true: 6.0ms (1.4% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain117.0ms (0.6%)

Memory

21.2MiB live, 112.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
120	-	2	(-3.022131280896856e-156 -4.734840245074485e-302)	`(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	98	0
↳	`(*.f64 y y)`	overflow	60
↳	`(*.f64 x x)`	overflow	55
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	98
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	20	0
↳	`(*.f64 y y)`	underflow	55
↳	`(*.f64 x x)`	underflow	78
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	20

Confusion

	Predicted +	Predicted -
+	118	2
-	0	136

Precision

1.0

Recall

0.9833333333333333

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	118	0	2
-	0	0	136

Precision?

1.0

Recall?

0.9833333333333333

Freqs

test

number	freq
0	138
1	118

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Total Time

10.27099609375

Average Time

0.04012107849121094

Samples

16.0ms

256×

valid

Compiler

Compiled 79 to 26 computations (67.1% saved)

Precisions

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

ival-hypot: 5.0ms (51.1% of total)

ival-mult: 3.0ms (30.6% of total)

ival-add: 1.0ms (10.2% of total)

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

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

preprocess24.0ms (0.1%)

Memory

-15.8MiB live, 20.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	35	42
2	77	42
3	145	42
4	204	42
5	217	42
6	219	42
0	6	8
0	10	8
1	11	8
0	11	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.8%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Memory

4.2MiB live, 4.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	-5120	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (.f64 x x) (.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	11	23
0	11	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

localize24.0ms (0.1%)

Memory

9.7MiB live, 46.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 y y))
accuracy	27.645848597938915	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

15.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

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

ival-hypot: 4.0ms (46% of total)

ival-mult: 3.0ms (34.5% of total)

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

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

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

series5.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

4 → 27

Calls

Call 1

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

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

Calls

6 calls:

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

simplify179.0ms (0.9%)

Memory

-28.1MiB live, 184.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	429
1	296	429
2	953	427
3	3667	393
4	6426	391
0	8051	354

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 25

Calls

Call 1

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

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

rewrite287.0ms (1.4%)

Memory

8.6MiB live, 240.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	29	21
2	196	21
3	1788	21
0	8624	15

Stop Event

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

Counts

4 → 245

Calls

Call 1

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

Outputs
(.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (exp.f64 (neg.f64 (log.f64 (.f64 (-.f64 x y) (+.f64 y x))))))
(.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (exp.f64 (neg.f64 (log.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.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)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))
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(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))) (.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (.f64 y x) #s(literal 6 binary64))) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64)))) (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64)))) (sqrt.f64 (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (sqrt.f64 (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 y x)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))
(hypot.f64 y x)
(hypot.f64 x y)
(exp.f64 (fma.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/4 binary64) (.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 y y (*.f64 x x))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64)))

eval68.0ms (0.3%)

Memory: 10.2MiB live, 47.8MiB allocated
Compiler: Compiled 7 430 to 986 computations (86.7% saved)

prune10.0ms (0%)

Memory

-24.8MiB live, 20.5MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	260	6	266
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	261	6	267

Accuracy

100.0%

Counts

267 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	56.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	56.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
	93.4%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
▶	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 134 to 92 computations (31.3% saved)

simplify55.0ms (0.3%)

Memory

13.2MiB live, 50.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 y x)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
cost-diff	-5120	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(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	20	94
0	30	82
1	42	82
2	54	82
3	60	82
4	65	82
5	72	82
6	87	82
7	136	82
8	204	82
9	388	82
10	728	82
11	1442	82
12	1588	82
13	1649	82
14	1667	82
15	1679	82
16	1751	82
17	2191	82
0	2191	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 y x) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
(*.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(/.f64 y x)
x

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

localize47.0ms (0.2%)

Memory

6.3MiB live, 80.6MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 y x)
accuracy	0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	0.140625	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
accuracy	59.93790539809661	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
accuracy	0	(fma.f64 y y (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	27.645848597938915	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0	(*.f64 y y)
accuracy	0.03163293782406456	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	27.645848597938915	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0	(neg.f64 x)
accuracy	62.730679723615694	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0	(hypot.f64 y x)

Samples

36.0ms

256×

valid

Compiler

Compiled 186 to 36 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-hypot: 9.0ms (38.2% of total)

ival-mult: 6.0ms (25.5% of total)

ival-add: 5.0ms (21.2% of total)

ival-div: 2.0ms (8.5% of total)

ival-neg: 1.0ms (4.2% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0%)

Memory

17.1MiB live, 17.1MiB allocated

Counts

13 → 33

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

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* -1 x)
(pow y 2)
(+ (pow x 2) (pow y 2))
(pow x 2)
(* 1/2 (/ (pow y 2) x))
(/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)
(/ y x)
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 (* 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 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))
(+ 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 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))))
(* (pow y 2) (+ (* 1/2 (/ 1 x)) (/ x (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
2.0ms	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) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))
2.0ms	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) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))
2.0ms	x	@	0	((sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (neg x) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (* y y) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))
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) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))
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) (+ (* y y) (* x x)) (* x x) (sqrt (+ (* y y) (* x x))) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ y x)) x) (* 1/2 y) (/ y x))

simplify264.0ms (1.3%)

Memory

-14.7MiB live, 196.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	479
1	326	479
2	1025	477
3	3967	435
4	7531	435
0	8293	397

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

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

rewrite295.0ms (1.5%)

Memory

-26.5MiB live, 170.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	85
0	30	73
1	87	73
2	562	73
3	6972	73
0	8512	73

Stop Event

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

Counts

13 → 368

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

Outputs
(.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)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 y y)))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 x) x (.f64 y y)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (.f64 y y)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 y) y (.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x (*.f64 y y)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (*.f64 y y))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y y)))))
(sqrt.f64 (fma.f64 x x (*.f64 y y)))
(hypot.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 y)) x)
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 y)))
(hypot.f64 (exp.f64 (log.f64 x)) y)
(hypot.f64 x (exp.f64 (log.f64 y)))
(hypot.f64 x y)
(hypot.f64 y (exp.f64 (log.f64 x)))
(hypot.f64 y x)
(exp.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))
(.f64 (.f64 (neg.f64 x) x) (pow.f64 x #s(literal -1 binary64)))
(.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) x)) (neg.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (neg.f64 x))) x)
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 #s(literal 0 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64)))) (*.f64 (neg.f64 x) x))
(/.f64 (*.f64 (neg.f64 x) x) x)
(/.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (neg.f64 (pow.f64 x #s(literal 3 binary64)))))
(neg.f64 x)
(fma.f64 (*.f64 (neg.f64 x) x) (pow.f64 x #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x #s(literal 0 binary64))
(fma.f64 x #s(literal -1 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 x x) x))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x x)))
(-.f64 #s(literal 0 binary64) x)
(+.f64 #s(literal 0 binary64) (neg.f64 x))
(+.f64 (neg.f64 x) #s(literal 0 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)))
#s(approx (+ (* x x) (* y y)) (*.f64 y y))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(.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)))) (fma.f64 (.f64 x x) (fma.f64 x x (*.f64 y y)) (pow.f64 y #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 x x) (fma.f64 x x (*.f64 y y)) (pow.f64 y #s(literal 4 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 y #s(literal 12 binary64)))) (fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64))))
(.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)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 x y) #s(literal 2 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 x x (.f64 y y)))
(.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)))) (fma.f64 x x (.f64 y y)))
(.f64 (/.f64 (fma.f64 x x (.f64 y y)) (+.f64 x y)) (+.f64 x y))
(.f64 (pow.f64 (fma.f64 (neg.f64 x) x (.f64 y y)) #s(literal -1 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))
(.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 x y) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))
(.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (neg.f64 x) x (.f64 y y)))))
(.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x)))))
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(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 (.f64 (/.f64 y x) y) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x))) (neg.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 y x) y) x)
(fma.f64 (.f64 y y) (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) x)
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y))
(fma.f64 x #s(literal 1 binary64) (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y))
(fma.f64 y (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)))) (/.f64 (.f64 (pow.f64 (.f64 (/.f64 y x) y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (+.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y)))))
(-.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (.f64 (/.f64 y x) y) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)))) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))
(+.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (.f64 (/.f64 y x) y) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)))) (neg.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x))))
(+.f64 (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y) x)
(+.f64 x (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) y))
(.f64 (.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 y #s(literal 1/2 binary64))
(.f64 (/.f64 (neg.f64 y) (.f64 (neg.f64 x) x)) x)
(.f64 (/.f64 (neg.f64 y) (neg.f64 (pow.f64 x #s(literal 3 binary64)))) (.f64 x x))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 y)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 y #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 y #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 y) x))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) y)
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(*.f64 y (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(/.f64 (neg.f64 (/.f64 y #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 y #s(literal 1 binary64))) x)
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 y)) (neg.f64 x))
(/.f64 (*.f64 (neg.f64 y) #s(literal 1 binary64)) (neg.f64 x))
(/.f64 (/.f64 y #s(literal 1 binary64)) x)
(/.f64 (/.f64 (neg.f64 y) x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 x) y))
(/.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 y #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 y #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 y x)
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 x y)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 y) x)))
(neg.f64 (/.f64 (neg.f64 y) x))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 (neg.f64 y) x))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 y) x))
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) #s(literal -1 binary64)))

eval139.0ms (0.7%)

Memory: 18.7MiB live, 56.8MiB allocated
Compiler: Compiled 9 401 to 1 209 computations (87.1% saved)

prune10.0ms (0%)

Memory

15.8MiB live, 15.8MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	351	5	356
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	353	9	362

Accuracy

100.0%

Counts

362 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	56.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	93.4%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
▶	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x))
▶	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x))
▶	6.3%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x))
▶	3.6%	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) y) x) (.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))))
✓	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 255 to 164 computations (35.7% saved)

simplify171.0ms (0.9%)

Memory

-13.2MiB live, 65.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (/.f64 y x) (*.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) y) x) (.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))))
cost-diff	320	(.f64 (fma.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) y) x) (.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x))))
cost-diff	3968	(.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 x y))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x))
cost-diff	448	(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
cost-diff	0	(/.f64 y x)
cost-diff	0	(*.f64 (/.f64 y x) y)
cost-diff	0	(fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x))
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 (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	308
0	68	232
1	128	232
2	277	232
3	1029	232
4	3129	232
5	7741	232
0	8461	207

Stop Event

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

Calls

Call 1

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

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

localize119.0ms (0.6%)

Memory

19.9MiB live, 93.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.14453125	(fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x))
accuracy	0.6937929633328805	(/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x))
accuracy	27.769828363489136	(.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))
accuracy	59.93790539809661	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) y) x) (.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x)))))
accuracy	0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	0.140625	(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x)
accuracy	0.22265625	(/.f64 #s(literal 1 binary64) (/.f64 x y))
accuracy	59.93790539809661	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1 binary64) (/.f64 x y)) x))
accuracy	0	(neg.f64 y)
accuracy	0.140625	(fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x)
accuracy	0.1953125	(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
accuracy	59.93790539809661	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y)) x))
accuracy	0	(/.f64 y x)
accuracy	0.01171875	(fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x)
accuracy	0.13671875	(*.f64 (/.f64 y x) y)
accuracy	59.93790539809661	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) x))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0	(*.f64 x x)
accuracy	0.05631870640774445	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
accuracy	4.193464676224613	(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)

Samples

93.0ms

256×

valid

Compiler

Compiled 560 to 78 computations (86.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-add: 34.0ms (45.6% of total)

ival-mult: 19.0ms (25.5% of total)

ival-div: 10.0ms (13.4% of total)

ival-hypot: 8.0ms (10.7% of total)

ival-neg: 2.0ms (2.7% of total)

exact: 1.0ms (1.3% of total)

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

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

series4.8s (24%)

Memory

-10.2MiB live, 28.3MiB allocated

Counts

22 → 64

Calls

Call 1

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

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow x 2)
(* 1/2 (/ (pow y 2) x))
(/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)
(/ (pow y 2) x)
(/ y x)
1
(/ (+ (* -1 (* (pow x 2) (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1))) (* 1/2 (pow y 2))) x)
(/ (+ (* 1/2 (pow y 2)) (* (pow x 2) (+ (* -1 (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (* -2 (/ (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1) (pow y 2)))))) (* -1 (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1))))) x)
(/ (+ (* 1/2 (pow y 2)) (* (pow x 2) (+ (* -1 (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1)) (* (pow x 2) (+ (* -2 (/ (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (* -2 (/ (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1) (pow y 2))))) (pow y 2))) (* -1 (- (* 2 (/ 1 (pow y 2))) (* -2 (/ (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1) (pow y 2)))))))))) x)
(* 2 (/ x (pow y 2)))
(* x (+ (* 4 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2)))))
(* x (+ (* (pow x 2) (+ (* 8 (/ (pow x 2) (pow y 6))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))
(* x (+ (* (pow x 2) (+ (* (pow x 2) (+ (* 16 (/ (pow x 2) (pow y 8))) (* 8 (/ 1 (pow y 6))))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))
(/ (+ (* -1 (pow x 2)) (* 1/2 (pow y 2))) x)
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)
(/ (- (* -1/2 (/ (pow y 2) (pow x 2))) 1) x)
(/ (- (* -1/4 (/ (pow y 4) (pow x 4))) (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) x)
(/ (- (* -1/8 (/ (pow y 6) (pow x 6))) (+ 1 (+ (* 1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) x)
(* -1 x)
(* x (- (* 1/2 (/ (pow y 2) (pow x 2))) 1))
(* -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 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))) (pow x 2))) 1)))
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))) (pow x 2))) (* -1 (/ (- (* -1/4 (pow y 4)) (* -1/2 (* (pow y 2) (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2)))))) (pow x 4)))) 1)))
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))) (pow x 2))) (+ (* -1 (/ (- (* -1/4 (pow y 4)) (* -1/2 (* (pow y 2) (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2)))))) (pow x 4))) (* -1/2 (/ (* (pow y 2) (- (* -1/4 (pow y 4)) (* -1/2 (* (pow y 2) (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))))))) (pow x 6))))) 1)))
(* -1 (/ (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))) x))
(* -1 (/ (- (+ 1 (* 1/4 (/ (pow y 4) (pow x 4)))) (* -1/2 (/ (pow y 2) (pow x 2)))) x))
(* -1 (/ (- (+ 1 (* 1/8 (/ (pow y 6) (pow x 6)))) (+ (* -1/2 (/ (pow y 2) (pow x 2))) (* -1/4 (/ (pow y 4) (pow x 4))))) x))
(* -1 (* x (+ 1 (* -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)
(* 1/2 y)
(* -1 y)
(- (* -1/2 (/ (pow y 2) (pow x 3))) (/ 1 x))
(- (* (pow y 2) (- (* -1/4 (/ (pow y 2) (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(- (* (pow y 2) (- (* (pow y 2) (- (* -1/8 (/ (pow y 2) (pow x 7))) (* 1/4 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(- (* 1/2 (/ (pow y 2) x)) 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) (+ (* 1/2 (/ 1 x)) (/ x (pow y 2))))
(/ (+ (* 2 x) (* 4 (/ (pow x 3) (pow y 2)))) (pow y 2))
(/ (- (+ (* 2 x) (* 8 (/ (pow x 5) (pow y 4)))) (* -4 (/ (pow x 3) (pow y 2)))) (pow y 2))
(/ (- (+ (* 2 x) (* 16 (/ (pow x 7) (pow y 6)))) (+ (* -8 (/ (pow x 5) (pow y 4))) (* -4 (/ (pow x 3) (pow y 2))))) (pow y 2))
(* (pow y 2) (+ (* -1 (/ x (pow y 2))) (* 1/2 (/ 1 x))))
(* -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
4.8s	y	@	0	((sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (/ 1 (/ x y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ 1 (/ x y))) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (neg y) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)))
5.0ms	x	@	0	((sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (/ 1 (/ x y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ 1 (/ x y))) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (neg y) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)))
4.0ms	x	@	-inf	((sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (/ 1 (/ x y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ 1 (/ x y))) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (neg y) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)))
4.0ms	y	@	inf	((sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (/ 1 (/ x y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ 1 (/ x y))) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (neg y) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)))
4.0ms	x	@	inf	((sqrt (+ (* y y) (* x x))) (+ (* (/ 1/2 y) (* x x)) y) (/ 1/2 y) (* x x) (sqrt (+ (* x x) (* y y))) (+ (* (* (/ y x) y) 1/2) x) (* (/ y x) y) (/ y x) (* (/ -1 x) (neg y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (* (/ -1 x) (neg y))) x) (* 1/2 y) (/ 1 (/ x y)) (sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 y) (/ 1 (/ x y))) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x))) (* (+ (* (/ y x) (* 1/2 y)) x) (* (+ (* (* (/ y x) 1/2) y) (neg x)) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)))) (sqrt (+ (* x x) (* y y))) (+ (* (/ y x) (* 1/2 y)) x) (neg y) (/ -1 (+ (* -1/2 (* (/ y x) y)) x)) (+ (* (* (/ y x) 1/2) y) (neg x)))

simplify9.8s (49.2%)

Memory

-0.1MiB live, 150.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	280	1263
1	828	1182
2	2758	1120
0	8387	1036

Stop Event

1×	iter limit
1×	node limit

Counts

64 → 62

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 x 2)
(* 1/2 (/ (pow y 2) x))
(/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)
(/ (pow y 2) x)
(/ y x)
1
(/ (+ (* -1 (* (pow x 2) (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1))) (* 1/2 (pow y 2))) x)
(/ (+ (* 1/2 (pow y 2)) (* (pow x 2) (+ (* -1 (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (* -2 (/ (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1) (pow y 2)))))) (* -1 (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1))))) x)
(/ (+ (* 1/2 (pow y 2)) (* (pow x 2) (+ (* -1 (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1)) (* (pow x 2) (+ (* -2 (/ (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (* -2 (/ (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1) (pow y 2))))) (pow y 2))) (* -1 (- (* 2 (/ 1 (pow y 2))) (* -2 (/ (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1) (pow y 2)))))))))) x)
(* 2 (/ x (pow y 2)))
(* x (+ (* 4 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2)))))
(* x (+ (* (pow x 2) (+ (* 8 (/ (pow x 2) (pow y 6))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))
(* x (+ (* (pow x 2) (+ (* (pow x 2) (+ (* 16 (/ (pow x 2) (pow y 8))) (* 8 (/ 1 (pow y 6))))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))
(/ (+ (* -1 (pow x 2)) (* 1/2 (pow y 2))) x)
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)
(/ (- (* -1/2 (/ (pow y 2) (pow x 2))) 1) x)
(/ (- (* -1/4 (/ (pow y 4) (pow x 4))) (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) x)
(/ (- (* -1/8 (/ (pow y 6) (pow x 6))) (+ 1 (+ (* 1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) x)
(* -1 x)
(* x (- (* 1/2 (/ (pow y 2) (pow x 2))) 1))
(* -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 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))) (pow x 2))) 1)))
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))) (pow x 2))) (* -1 (/ (- (* -1/4 (pow y 4)) (* -1/2 (* (pow y 2) (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2)))))) (pow x 4)))) 1)))
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))) (pow x 2))) (+ (* -1 (/ (- (* -1/4 (pow y 4)) (* -1/2 (* (pow y 2) (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2)))))) (pow x 4))) (* -1/2 (/ (* (pow y 2) (- (* -1/4 (pow y 4)) (* -1/2 (* (pow y 2) (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))))))) (pow x 6))))) 1)))
(* -1 (/ (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))) x))
(* -1 (/ (- (+ 1 (* 1/4 (/ (pow y 4) (pow x 4)))) (* -1/2 (/ (pow y 2) (pow x 2)))) x))
(* -1 (/ (- (+ 1 (* 1/8 (/ (pow y 6) (pow x 6)))) (+ (* -1/2 (/ (pow y 2) (pow x 2))) (* -1/4 (/ (pow y 4) (pow x 4))))) x))
(* -1 (* x (+ 1 (* -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)
(* 1/2 y)
(* -1 y)
(- (* -1/2 (/ (pow y 2) (pow x 3))) (/ 1 x))
(- (* (pow y 2) (- (* -1/4 (/ (pow y 2) (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(- (* (pow y 2) (- (* (pow y 2) (- (* -1/8 (/ (pow y 2) (pow x 7))) (* 1/4 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(- (* 1/2 (/ (pow y 2) x)) 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) (+ (* 1/2 (/ 1 x)) (/ x (pow y 2))))
(/ (+ (* 2 x) (* 4 (/ (pow x 3) (pow y 2)))) (pow y 2))
(/ (- (+ (* 2 x) (* 8 (/ (pow x 5) (pow y 4)))) (* -4 (/ (pow x 3) (pow y 2)))) (pow y 2))
(/ (- (+ (* 2 x) (* 16 (/ (pow x 7) (pow y 6)))) (+ (* -8 (/ (pow x 5) (pow y 4))) (* -4 (/ (pow x 3) (pow y 2))))) (pow y 2))
(* (pow y 2) (+ (* -1 (/ x (pow y 2))) (* 1/2 (/ 1 x))))
(* -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 (fma.f64 (.f64 #s(literal -1/8 binary64) x) (/.f64 x (pow.f64 y #s(literal 3 binary64))) (/.f64 #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 x 2)
(*.f64 x x)
(* 1/2 (/ (pow y 2) x))
(.f64 (/.f64 (.f64 y y) x) #s(literal 1/2 binary64))
(/ (+ (* 1/2 (pow y 2)) (pow x 2)) x)
(/.f64 (fma.f64 (.f64 y y) #s(literal 1/2 binary64) (.f64 x x)) x)
(/ (pow y 2) x)
(/.f64 (*.f64 y y) x)
(/ y x)
(/.f64 y x)
1
#s(literal 1 binary64)
(/ (+ (* -1 (* (pow x 2) (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1))) (* 1/2 (pow y 2))) x)
(/.f64 (fma.f64 (.f64 y y) #s(literal 1/2 binary64) (.f64 x x)) x)
(/ (+ (* 1/2 (pow y 2)) (* (pow x 2) (+ (* -1 (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (* -2 (/ (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1) (pow y 2)))))) (* -1 (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1))))) x)
(/.f64 (fma.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal -2 binary64) y) y) (/.f64 (/.f64 #s(literal -2 binary64) y) y)) (fma.f64 (.f64 y y) #s(literal 1/2 binary64) (.f64 x x))) x)
(/ (+ (* 1/2 (pow y 2)) (* (pow x 2) (+ (* -1 (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1)) (* (pow x 2) (+ (* -2 (/ (* (pow x 2) (- (* 2 (/ 1 (pow y 2))) (* -2 (/ (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1) (pow y 2))))) (pow y 2))) (* -1 (- (* 2 (/ 1 (pow y 2))) (* -2 (/ (- (* -2 (/ (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2))) (pow y 2))) 1) (pow y 2)))))))))) x)
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) y (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -2 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 4 binary64)))) (-.f64 (/.f64 (/.f64 #s(literal -2 binary64) y) y) (/.f64 (/.f64 #s(literal -2 binary64) y) y))) (.f64 x x))) x)
(* 2 (/ x (pow y 2)))
(.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64))
(* x (+ (* 4 (/ (pow x 2) (pow y 4))) (* 2 (/ 1 (pow y 2)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 4 binary64) (pow.f64 y #s(literal 4 binary64))) (.f64 (/.f64 x (.f64 y y)) #s(literal 2 binary64)))
(* x (+ (* (pow x 2) (+ (* 8 (/ (pow x 2) (pow y 6))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 x y) (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 (/.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 6 binary64))) x) x (/.f64 #s(literal 4 binary64) (pow.f64 y #s(literal 4 binary64))))))
(* x (+ (* (pow x 2) (+ (* (pow x 2) (+ (* 16 (/ (pow x 2) (pow y 8))) (* 8 (/ 1 (pow y 6))))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))
(fma.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 x y) (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal 16 binary64) x) (/.f64 x (pow.f64 y #s(literal 8 binary64))) (/.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 6 binary64)))) (*.f64 x x) (/.f64 #s(literal 4 binary64) (pow.f64 y #s(literal 4 binary64))))))
(/ (+ (* -1 (pow x 2)) (* 1/2 (pow y 2))) x)
(/.f64 (neg.f64 (fma.f64 x x (.f64 #s(literal -1/2 binary64) (.f64 y y)))) x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #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 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #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 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) 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 (/.f64 y x) x) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ (- (* -1/2 (/ (pow y 2) (pow x 2))) 1) x)
(/.f64 (fma.f64 (/.f64 (/.f64 (*.f64 y y) x) x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(/ (- (* -1/4 (/ (pow y 4) (pow x 4))) (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 (*.f64 y y) x) x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)
(/ (- (* -1/8 (/ (pow y 6) (pow x 6))) (+ 1 (+ (* 1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) x)
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 (*.f64 y y) x) x) #s(literal -1/2 binary64) #s(literal -1 binary64)))) x)
(* -1 x)
(neg.f64 x)
(* x (- (* 1/2 (/ (pow y 2) (pow x 2))) 1))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal -1/2 binary64) #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 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #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 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(* -1 (* x (- (* -1/2 (/ (pow y 2) (pow x 2))) 1)))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (/ (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))) (pow x 2))) 1)))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))) (pow x 2))) (* -1 (/ (- (* -1/4 (pow y 4)) (* -1/2 (* (pow y 2) (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2)))))) (pow x 4)))) 1)))
(.f64 (+.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) (/.f64 y x) (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64)) (*.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)) x)
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))) (pow x 2))) (+ (* -1 (/ (- (* -1/4 (pow y 4)) (* -1/2 (* (pow y 2) (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2)))))) (pow x 4))) (* -1/2 (/ (* (pow y 2) (- (* -1/4 (pow y 4)) (* -1/2 (* (pow y 2) (- (* -1 (+ (* -1/2 (pow y 2)) (* 1/2 (pow y 2)))) (* -1/2 (pow y 2))))))) (pow x 6))))) 1)))
(fma.f64 (neg.f64 x) (fma.f64 (.f64 y y) (fma.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64)) (.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64)) (.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))))) (pow.f64 x #s(literal 4 binary64)))) x)
(* -1 (/ (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))) x))
(/.f64 (fma.f64 (/.f64 (/.f64 (*.f64 y y) x) x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(* -1 (/ (- (+ 1 (* 1/4 (/ (pow y 4) (pow x 4)))) (* -1/2 (/ (pow y 2) (pow x 2)))) x))
(/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 (*.f64 y y) x) x) #s(literal -1/2 binary64) #s(literal -1 binary64))) x)
(* -1 (/ (- (+ 1 (* 1/8 (/ (pow y 6) (pow x 6)))) (+ (* -1/2 (/ (pow y 2) (pow x 2))) (* -1/4 (/ (pow y 4) (pow x 4))))) x))
(/.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 (*.f64 y y) x) x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (neg.f64 x))
(* -1 (* x (+ 1 (* -1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x) #s(literal -1 binary64)) x)
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 y (pow.f64 x #s(literal 3 binary64))) (/.f64 #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)
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 y y)) y)
(/ 1/2 y)
(/.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* -1 y)
(neg.f64 y)
(- (* -1/2 (/ (pow y 2) (pow x 3))) (/ 1 x))
(/.f64 (fma.f64 (/.f64 (/.f64 (*.f64 y y) x) x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(- (* (pow y 2) (- (* -1/4 (/ (pow y 2) (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal -1 binary64) x))
(- (* (pow y 2) (- (* (pow y 2) (- (* -1/8 (/ (pow y 2) (pow x 7))) (* 1/4 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 y (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 y y) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 y y) (/.f64 #s(literal -1 binary64) x))
(- (* 1/2 (/ (pow y 2) x)) x)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) y (neg.f64 x))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(.f64 (fma.f64 (.f64 x (/.f64 x (*.f64 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 x (/.f64 x (*.f64 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 x (/.f64 x (*.f64 y y))) #s(literal 1/2 binary64) #s(literal 1 binary64)))) y)
(* (pow y 2) (+ (* 1/2 (/ 1 x)) (/ x (pow y 2))))
(.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 x (*.f64 y y))) y) y)
(/ (+ (* 2 x) (* 4 (/ (pow x 3) (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) y) (/.f64 #s(literal 4 binary64) y) (.f64 #s(literal 2 binary64) x)) (.f64 y y))
(/ (- (+ (* 2 x) (* 8 (/ (pow x 5) (pow y 4)))) (* -4 (/ (pow x 3) (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) y) (/.f64 #s(literal 4 binary64) y) (fma.f64 (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 8 binary64) (.f64 #s(literal 2 binary64) x))) (.f64 y y))
(/ (- (+ (* 2 x) (* 16 (/ (pow x 7) (pow y 6)))) (+ (* -8 (/ (pow x 5) (pow y 4))) (* -4 (/ (pow x 3) (pow y 2))))) (pow y 2))
(/.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) y) (/.f64 #s(literal 4 binary64) y) (fma.f64 (pow.f64 x #s(literal 7 binary64)) (/.f64 #s(literal 16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 8 binary64) (.f64 #s(literal 2 binary64) x)))) (.f64 y y))
(* (pow y 2) (+ (* -1 (/ x (pow y 2))) (* 1/2 (/ 1 x))))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 x (*.f64 y y))) y) y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(.f64 (fma.f64 (.f64 x (/.f64 x (*.f64 y y))) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 y))
(* -1 (* 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 x (/.f64 x (*.f64 y y))) #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 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))))))))
(.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 x (/.f64 x (*.f64 y y))) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (neg.f64 y))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(.f64 (fma.f64 (.f64 x (/.f64 x (*.f64 y y))) #s(literal -1/2 binary64) #s(literal -1 binary64)) (neg.f64 y))

rewrite522.0ms (2.6%)

Memory

-14.8MiB live, 247.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	254
0	68	197
1	268	196
2	1829	193
0	8610	168

Stop Event

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

Counts

22 → 2 373

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(.f64 (fma.f64 (pow.f64 (.f64 y #s(literal 2 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 y) y)) (pow.f64 (fma.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64) (neg.f64 y)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 (.f64 y #s(literal 2 binary64)) #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 y (-.f64 y (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))) (.f64 (pow.f64 (.f64 y #s(literal 2 binary64)) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)))
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(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) (neg.f64 x))
(fma.f64 (neg.f64 y) (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) (neg.f64 x))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (neg.f64 (pow.f64 y #s(literal -1 binary64)))) (neg.f64 x))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1 binary64) y)) (neg.f64 x))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (.f64 (neg.f64 y) (.f64 #s(literal 1/2 binary64) y)) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 (neg.f64 x) y)) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) x (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y))
(fma.f64 (*.f64 (/.f64 y x) y) #s(literal -1/2 binary64) x)
(fma.f64 (*.f64 (/.f64 y x) y) #s(literal 1/2 binary64) (neg.f64 x))
(fma.f64 (/.f64 y x) (/.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1 binary64))) (neg.f64 x))
(fma.f64 (/.f64 y x) (/.f64 (*.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 (/.f64 y x) (*.f64 y #s(literal -1/2 binary64)) x)
(fma.f64 (/.f64 y x) (/.f64 #s(literal 1/2 binary64) (pow.f64 y #s(literal -1 binary64))) (neg.f64 x))
(fma.f64 (/.f64 y x) (*.f64 #s(literal 1/2 binary64) y) (neg.f64 x))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 y x) (pow.f64 y #s(literal -1 binary64))) (neg.f64 x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 y x) y) (neg.f64 x))
(fma.f64 x #s(literal -1 binary64) (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y))
(fma.f64 y (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) x)
(fma.f64 y (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) (neg.f64 x))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 2 binary64)) (.f64 #s(literal -1 binary64) (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x))))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)) #s(literal -1 binary64)) (/.f64 (/.f64 (.f64 x x) (fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 x x) (fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 2 binary64)) (neg.f64 (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x))) (/.f64 (.f64 x x) (neg.f64 (fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 2 binary64)) (-.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y)))))
(-.f64 (/.f64 (.f64 x x) (-.f64 (neg.f64 x) (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 2 binary64)) (-.f64 (neg.f64 x) (.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y))) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y))) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 2 binary64)))))
(-.f64 (fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y #s(literal 0 binary64)) x)
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)) (/.f64 (.f64 x x) (fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)))
(-.f64 #s(literal 0 binary64) (-.f64 x (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y)))
(-.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 y x) y) x))
(-.f64 (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y) x)
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)) x)
(+.f64 (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y) (neg.f64 x))
(+.f64 (neg.f64 x) (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) y))
(+.f64 x (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 y x) y)))

eval389.0ms (2%)

Memory: -8.3MiB live, 143.4MiB allocated
Compiler: Compiled 46 883 to 4 792 computations (89.8% saved)

prune27.0ms (0.1%)

Memory

18.4MiB live, 57.6MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1 174	2	1 176
Fresh	0	0	0
Picked	5	0	5
Done	0	4	4
Total	1 179	6	1 185

Accuracy

100.0%

Counts

1 185 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	56.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	99.9%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
▶	3.9%	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
✓	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 76 to 51 computations (32.9% saved)

simplify5.0ms (0%)

Memory

7.3MiB live, 7.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	97
0	26	95
1	41	95
2	53	95
3	54	95
0	54	85

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize45.0ms (0.2%)

Memory

-16.6MiB live, 64.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.05631870640774445	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
accuracy	0.2109375	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	0.0078125	(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
accuracy	0.05631870640774445	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
accuracy	8.821104772339819	(/.f64 (*.f64 x x) y)
accuracy	61.47253991724836	#s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))

Samples

33.0ms

256×

valid

Compiler

Compiled 162 to 35 computations (78.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-hypot: 10.0ms (41.3% of total)

ival-mult: 7.0ms (28.9% of total)

ival-div: 4.0ms (16.5% of total)

ival-add: 2.0ms (8.3% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

8 → 29

Calls

Call 1

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

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

Calls

6 calls:

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

simplify191.0ms (1%)

Memory

-9.3MiB live, 231.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	451
1	306	451
2	983	449
3	3635	413
4	7500	413
0	8236	378

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 27

Calls

Call 1

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

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

rewrite153.0ms (0.8%)

Memory

29.3MiB live, 220.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	88
0	26	86
1	96	86
2	516	86
3	5948	86
0	8006	76

Stop Event

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

Counts

8 → 241

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (*.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)))))
#s(approx (+ (* (/ 1/2 y) (* x x)) y) (*.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) y))
(.f64 (/.f64 (.f64 (neg.f64 x) x) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) y))
(.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) y))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 y #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1/2 binary64) y) (.f64 (neg.f64 x) x))
(.f64 (.f64 (neg.f64 x) (/.f64 x y)) #s(literal -1/2 binary64))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) x) x) (/.f64 #s(literal -1 binary64) y))
(*.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)))
(.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y))
(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (pow.f64 y #s(literal -1 binary64)))
(.f64 (pow.f64 y #s(literal -1 binary64)) (/.f64 (.f64 x x) #s(literal 2 binary64)))
(.f64 (pow.f64 y #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1/2 binary64)))
(.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal -1/2 binary64) y))
(.f64 #s(literal -1/2 binary64) (.f64 (/.f64 #s(literal -1 binary64) y) (*.f64 x x)))
(.f64 #s(literal -1/2 binary64) (.f64 (neg.f64 x) (/.f64 x y)))
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)
(.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) y))
(.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) y))
(.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) y) x))
(pow.f64 (/.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) x) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) #s(literal -1 binary64)) y)
(/.f64 (neg.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x)) y)
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) (neg.f64 y))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.f64 y x))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)) y)
(/.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) (neg.f64 y))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) x)))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 y x))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) y)
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) x))
(/.f64 (.f64 (neg.f64 x) x) (.f64 y #s(literal -2 binary64)))
(/.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 y) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (/.f64 #s(literal 1/2 binary64) y) (pow.f64 x #s(literal -2 binary64)))
(/.f64 (/.f64 (*.f64 x x) y) #s(literal 2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 y (*.f64 x x)))
(/.f64 (.f64 x x) (.f64 #s(literal 2 binary64) y))
(/.f64 x (/.f64 (*.f64 #s(literal 2 binary64) y) x))
(neg.f64 (.f64 (.f64 x x) (/.f64 #s(literal -1/2 binary64) y)))
(neg.f64 (.f64 (/.f64 #s(literal -1/2 binary64) y) (.f64 x x)))
(neg.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) y) x) x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 (/.f64 #s(literal 1/2 binary64) y))) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x)) (/.f64 #s(literal -1 binary64) y))
(.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 y (*.f64 x x)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 x y))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (neg.f64 x) y))
(.f64 (/.f64 #s(literal -1 binary64) y) (.f64 (neg.f64 x) x))
(.f64 (neg.f64 x) (.f64 x (/.f64 #s(literal -1 binary64) y)))
(*.f64 (neg.f64 x) (/.f64 x (neg.f64 y)))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) (/.f64 x y)))
(*.f64 (/.f64 x y) x)
(.f64 (pow.f64 y #s(literal -1 binary64)) (.f64 x x))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) y))
(.f64 (.f64 (neg.f64 x) x) (/.f64 #s(literal -1 binary64) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1 binary64))
(.f64 (.f64 x x) (pow.f64 y #s(literal -1 binary64)))
(*.f64 x (/.f64 x y))
(pow.f64 (/.f64 y (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 x x) y) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 (neg.f64 x) x) #s(literal 1 binary64)) (neg.f64 y))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) x)) (neg.f64 y))
(/.f64 (/.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64)) y)
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 y) (pow.f64 x #s(literal -2 binary64))))
(/.f64 (pow.f64 y #s(literal -1 binary64)) (pow.f64 x #s(literal -2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 y (*.f64 x x)))
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 y))
(/.f64 (*.f64 x x) y)
(/.f64 x (/.f64 y x))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 y (*.f64 x x))))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) (/.f64 x y))))
(neg.f64 (*.f64 (neg.f64 x) (/.f64 x y)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 y)) (*.f64 (neg.f64 x) (/.f64 x y)))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (/.f64 x y)))
(exp.f64 (.f64 (log.f64 (/.f64 y (.f64 x x))) #s(literal -1 binary64)))
#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y))
(.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (-.f64 (.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -3 binary64)) #s(literal 1/8 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 y (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y))))
(.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) y) x) x) #s(literal -4 binary64)) (pow.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))))))
(.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (pow.f64 (.f64 #s(literal 2 binary64) y) #s(literal -6 binary64)) (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y) #s(literal 3 binary64)))) (fma.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y) (-.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) y) (.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) x) #s(literal -4 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 y) y))) (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y))
(.f64 (-.f64 (.f64 y y) (.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 x y) y)) (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)))
(.f64 (pow.f64 (fma.f64 (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (.f64 y y)) #s(literal -1 binary64)) (fma.f64 (pow.f64 (/.f64 y (*.f64 x x)) #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y))) (pow.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 x y) y) #s(literal -1 binary64)))
(.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (*.f64 y y))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 x y) y)))
(*.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y))
(.f64 (fma.f64 (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (.f64 y y)) (/.f64 (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y) (fma.f64 (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (*.f64 y y))))
(.f64 (fma.f64 (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (.f64 y y)) (.f64 (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y) (pow.f64 (fma.f64 (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (.f64 y y)) #s(literal -1 binary64))))
(.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (*.f64 y y)) #s(literal -1 binary64)))
(.f64 (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y) (/.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))))
(.f64 (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 x y) y))))
(pow.f64 (/.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y))) (-.f64 (.f64 y y) (.f64 (pow.f64 (/.f64 y (*.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
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(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (neg.f64 (.f64 y (/.f64 y (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y)
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/2 binary64) y)) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (neg.f64 (.f64 y (/.f64 y (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(fma.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64) y)
(fma.f64 (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) (/.f64 (.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (neg.f64 (.f64 y (/.f64 y (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x x) y) y)
(fma.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal -2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (neg.f64 (.f64 y (/.f64 y (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1/2 binary64) y) y)
(fma.f64 x (/.f64 (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) y) x) #s(literal -2 binary64)) x) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))) (neg.f64 (.f64 y (/.f64 y (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))))))
(fma.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) y)
(fma.f64 y #s(literal 1 binary64) (*.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 y y) (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x x) y)))) (/.f64 (.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal -2 binary64)) #s(literal 1/4 binary64)) (+.f64 y (.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) y)))))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) y) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) y)) (.f64 y (/.f64 y (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64)) y) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) y) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y)) y)) (neg.f64 (.f64 y (/.f64 y (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x (neg.f64 y))))))
(+.f64 (*.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))) y)
(+.f64 y (*.f64 (/.f64 x y) (/.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) y))
(*.f64 (/.f64 x (neg.f64 y)) #s(literal -1/2 binary64))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) y))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (pow.f64 y #s(literal -1 binary64)))
(.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1 binary64) y))
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 y #s(literal -1 binary64)))
(*.f64 (pow.f64 y #s(literal -1 binary64)) (/.f64 x #s(literal 2 binary64)))
(.f64 (pow.f64 y #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1/2 binary64) y) x))
(.f64 #s(literal -1/2 binary64) (.f64 (/.f64 #s(literal -1 binary64) y) x))
(*.f64 #s(literal -1/2 binary64) (/.f64 x (neg.f64 y)))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
(*.f64 x (/.f64 #s(literal 1/2 binary64) y))
(pow.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) #s(literal -1 binary64))
(/.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64)) y)
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) (neg.f64 y))
(/.f64 (.f64 x #s(literal -1 binary64)) (.f64 y #s(literal -2 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) x)) y)
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) y)
(/.f64 (neg.f64 x) (*.f64 y #s(literal -2 binary64)))
(/.f64 (*.f64 #s(literal -1/2 binary64) x) (neg.f64 y))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x)))
(/.f64 (/.f64 x y) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) y) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) y) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
(/.f64 x (*.f64 #s(literal 2 binary64) y))
(neg.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) x) y))
(neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (neg.f64 y)))
(neg.f64 (*.f64 x (/.f64 #s(literal -1/2 binary64) y)))
(neg.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) y) x))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 #s(literal 2 binary64) y) x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) y) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) y) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1/2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) y))
(*.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) y))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (pow.f64 y #s(literal -1 binary64)))
(pow.f64 (*.f64 #s(literal 2 binary64) y) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (*.f64 y #s(literal -2 binary64)))
(/.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 #s(literal 1/2 binary64) y)
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) y)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) y)))
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) y))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) y)) #s(literal -1 binary64)))

eval46.0ms (0.2%)

Memory: -14.4MiB live, 75.7MiB allocated
Compiler: Compiled 7 871 to 995 computations (87.4% saved)

prune13.0ms (0.1%)

Memory

-7.3MiB live, 31.4MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	263	2	265
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	264	7	271

Accuracy

100.0%

Counts

271 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	56.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.9%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) y) x) x y))
	3.9%	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x))))
	3.9%	#s(approx (sqrt (+ (* y y) (* x x))) #s(approx (+ (* (/ 1/2 y) (* x x)) y) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) y) x) x)))
✓	2.0%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 383 to 136 computations (64.5% saved)

regimes34.0ms (0.2%)

Memory

-18.0MiB live, 61.9MiB allocated

Counts

16 → 1

Calls

Call 1

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

Outputs
(hypot.f64 y x)

Calls

6 calls:

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

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes30.0ms (0.2%)

Memory

20.3MiB live, 58.9MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.9%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.9%	1	`(*.f64 x x)`
99.9%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes36.0ms (0.2%)

Memory

-6.8MiB live, 32.1MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

6 calls:

19.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	x
3.0ms	y
3.0ms	(*.f64 y y)
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
93.4%	1	`x`
93.4%	1	`y`
93.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
93.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
93.4%	1	`(*.f64 x x)`
93.4%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes45.0ms (0.2%)

Memory

-7.3MiB live, 31.7MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

30.0ms	x
3.0ms	y
3.0ms	(*.f64 y y)
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
56.8%	1	`x`
56.8%	1	`y`
56.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
56.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
56.8%	1	`(*.f64 x x)`
56.8%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes14.0ms (0.1%)

Memory

34.0MiB live, 34.0MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

6 calls:

2.0ms	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
56.8%	1	`y`
56.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
56.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
56.8%	1	`(*.f64 x x)`
56.8%	1	`(*.f64 y y)`
56.8%	1	`x`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes38.0ms (0.2%)

Memory

-30.8MiB live, 51.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

28.0ms	(*.f64 y y)
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	x
1.0ms	y
1.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify24.0ms (0.1%)

Memory

20.1MiB live, 57.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	67
1	29	67
2	31	67
3	32	67

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness789.0ms (4%)

Memory

14.2MiB live, 609.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	254
0	68	197
1	268	196
2	1829	193
0	8610	168
0	104	429
1	296	429
2	953	427
3	3667	393
4	6426	391
0	8051	354
0	117	479
1	326	479
2	1025	477
3	3967	435
4	7531	435
0	8293	397
0	6	21
0	10	21
1	29	21
2	196	21
3	1788	21
0	8624	15

Stop Event

1×	fuel
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×	node limit
1×	iter limit

Compiler

Compiled 143 to 76 computations (46.9% saved)

preprocess51.0ms (0.3%)

Memory

8.6MiB live, 81.2MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 206 to 104 computations (49.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.0s (5.2%)

explain117.0ms (0.6%)

preprocess24.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize24.0ms (0.1%)

series5.0ms (0%)

simplify179.0ms (0.9%)

rewrite287.0ms (1.4%)

eval68.0ms (0.3%)

prune10.0ms (0%)

simplify55.0ms (0.3%)

localize47.0ms (0.2%)

series9.0ms (0%)

simplify264.0ms (1.3%)

rewrite295.0ms (1.5%)

eval139.0ms (0.7%)

prune10.0ms (0%)

simplify171.0ms (0.9%)

localize119.0ms (0.6%)

series4.8s (24%)

simplify9.8s (49.2%)

rewrite522.0ms (2.6%)

eval389.0ms (2%)

prune27.0ms (0.1%)

simplify5.0ms (0%)

localize45.0ms (0.2%)

series9.0ms (0%)

simplify191.0ms (1%)

rewrite153.0ms (0.8%)

eval46.0ms (0.2%)

prune13.0ms (0.1%)

regimes34.0ms (0.2%)

regimes30.0ms (0.2%)

regimes36.0ms (0.2%)

regimes45.0ms (0.2%)

regimes14.0ms (0.1%)

regimes38.0ms (0.2%)

simplify24.0ms (0.1%)

soundness789.0ms (4%)

preprocess51.0ms (0.3%)

end0.0ms (0%)

Profiling