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)

sample677.0ms (2.3%)

Memory

9.9MiB live, 850.8MiB allocated

Samples

500.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 241.0ms

ival-hypot: 232.0ms (96.3% of total)

ival-true: 6.0ms (2.5% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain115.0ms (0.4%)

Memory

0.4MiB live, 122.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
119	-	4	(-8.283170884990739e-159 1.7411038653422418e-230)	`(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	101	0
↳	`(*.f64 y y)`	overflow	54
↳	`(*.f64 x x)`	overflow	58
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	101
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	14	0
↳	`(*.f64 y y)`	underflow	61
↳	`(*.f64 x x)`	underflow	67
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	14

Confusion

	Predicted +	Predicted -
+	115	4
-	0	137

Precision

1.0

Recall

0.9663865546218487

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	115	0	4
-	0	0	137

Precision?

1.0

Recall?

0.9663865546218487

Freqs

test

number	freq
0	141
1	115

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

31.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-hypot: 8.0ms (44.3% of total)

ival-mult: 7.0ms (38.8% of total)

ival-add: 2.0ms (11.1% of total)

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

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

preprocess19.0ms (0.1%)

Memory

-7.1MiB live, 30.6MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`sub-neg`
30×	`distribute-lft-neg-in`
30×	`neg-sub0`
28×	`unsub-neg`
24×	`neg-mul-1`

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	4

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

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	-5632	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Rules

4×	`lower-hypot.f32`
4×	`lower-hypot.f64`
4×	`lower-fma.f64`
4×	`lift-*.f64`
4×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	11	23
0	11	15

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

localize22.0ms (0.1%)

Memory

-5.9MiB live, 37.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(+.f64 (.f64 x x) (.f64 y y))
accuracy	27.13272370161774	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

17.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 5.0ms (45.1% of total)

ival-hypot: 4.0ms (36.1% of total)

ival-add: 1.0ms (9% of total)

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

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

series6.0ms (0%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())
#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())

Outputs
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (+ 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))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* 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))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 1/2 (/ (pow x 2) y))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (+ 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))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* 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))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation:binary64>) () ())) ())

Calls

6 calls:

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

simplify507.0ms (1.7%)

Memory

-161.5MiB live, 296.5MiB allocated

Algorithm

1×	egg-herbie

Rules

18 004×	`lower-fma.f64`
18 004×	`lower-fma.f32`
5 072×	`lower-*.f64`
5 072×	`lower-*.f32`
2 260×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	620
1	296	620
2	956	618
3	3671	584
4	6436	582
0	8062	476

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

Calls

Call 1

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

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

rewrite499.0ms (1.7%)

Memory

-2.1MiB live, 201.6MiB allocated

Rules

5 720×	`lower-fma.f64`
5 720×	`lower-fma.f32`
4 038×	`lower-/.f64`
4 038×	`lower-/.f32`
3 184×	`lower-*.f32`

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	13

Stop Event

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

Counts

4 → 245

Calls

Call 1

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

Outputs
(.f64 (sqrt.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))))) (sqrt.f64 (fma.f64 (.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 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))))) (sqrt.f64 (-.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))))))
(.f64 (sqrt.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (hypot.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 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))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (sqrt.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))))) (sqrt.f64 (hypot.f64 y x)))
(*.f64 (sqrt.f64 (/.f64 (hypot.f64 y x) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.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))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.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)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 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)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.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))))))
(.f64 (pow.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (hypot.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.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))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (pow.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)))) #s(literal 1/2 binary64)) (sqrt.f64 (hypot.f64 y x)))
(*.f64 (pow.f64 (/.f64 (hypot.f64 y x) (+.f64 y x)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 y x)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (hypot.f64 y x)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (.f64 (+.f64 y x) (-.f64 y x)) #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 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (pow.f64 (pow.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (pow.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)))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (pow.f64 (pow.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)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64)) (sqrt.f64 (-.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 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(*.f64 (pow.f64 (hypot.f64 y x) #s(literal 1/4 binary64)) (pow.f64 (hypot.f64 y x) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (hypot.f64 y x)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64)))
(.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)))) (sqrt.f64 (/.f64 (hypot.f64 y x) (+.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 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (.f64 (hypot.f64 y x) (pow.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))) #s(literal -1 binary64)))))
(.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)))) (pow.f64 (/.f64 (hypot.f64 y x) (+.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)))) #s(literal 1/2 binary64)))
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eval147.0ms (0.5%)

Memory: -8.8MiB live, 29.7MiB allocated
Compiler: Compiled 7 493 to 988 computations (86.8% saved)

prune87.0ms (0.3%)

Memory

-23.6MiB live, 16.2MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	307	6	313
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	308	6	314

Accuracy

99.9%

Counts

314 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	27.2%	(sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))))
▶	57.6%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	57.0%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	4.6%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
▶	99.4%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
▶	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 114 to 78 computations (31.6% saved)

simplify9.0ms (0%)

Memory

7.3MiB live, 7.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	-5760	(fma.f64 y y (*.f64 x x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
cost-diff	0	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
cost-diff	0	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
cost-diff	0	(/.f64 x y)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))

Rules

68×	`lower-fma.f32`
64×	`lower-fma.f64`
60×	`lower-+.f64`
60×	`lower-+.f32`
48×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	120
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	136	114
8	145	114
9	151	114
10	151	114
0	151	90

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize82.0ms (0.3%)

Memory

9.8MiB live, 46.1MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	27.13272370161774	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0	(*.f64 y y)
accuracy	0.43418934781515567	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	27.13272370161774	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0	(*.f64 x x)
accuracy	27.13272370161774	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
accuracy	55.007370467474736	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
accuracy	0	(neg.f64 x)
accuracy	62.80120203657372	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
accuracy	0	(/.f64 x y)
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.36158795398427857	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))

Samples

70.0ms

256×

valid

Compiler

Compiled 97 to 16 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 45.0ms (75.2% of total)

ival-hypot: 9.0ms (15% of total)

ival-add: 3.0ms (5% of total)

ival-div: 2.0ms (3.3% of total)

ival-neg: 1.0ms (1.7% of total)

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

exact: 0.0ms (0% of total)

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

series15.0ms (0.1%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

14 → 288

Calls

Call 1

Inputs
#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation:binary64>) () ())
#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation:binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation:binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())
#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 x x))) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation:binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())
#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation:binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 y y (.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (.f64 x x))) #<representation:binary64>) () ())
#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())

Outputs
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (+ 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))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (/ x y) (taylor 0 y) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (+ 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))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (+ 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))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (+ 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))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (+ 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))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 y y (.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (* 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))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) (patch #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (/ x y) (taylor -inf x) (#s(alt (/.f64 x y) (patch (/.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 x x)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y))) (patch (sqrt.f64 #s(approx (+ ( x x) (* y y)) (*.f64 y y))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) (* y y)) (.f64 y y)) (patch #s(approx (+ ( x x) (* y y)) (*.f64 y y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 y y (.f64 x x))) (patch (sqrt.f64 (fma.f64 y y (.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation:binary64>) () ())) ())

Calls

6 calls:

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

simplify5.0s (16.6%)

Memory

-14.1MiB live, 259.0MiB allocated

Algorithm

1×	egg-herbie

Rules

16 212×	`lower-fma.f64`
16 212×	`lower-fma.f32`
4 244×	`lower-*.f64`
4 244×	`lower-*.f32`
2 514×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	2908
1	326	2908
2	1025	2898
3	3967	2668
4	7526	2668
0	8271	2274

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 265

Calls

Call 1

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

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

rewrite18.2s (60.6%)

Memory

32.5MiB live, 231.4MiB allocated

Rules

6 574×	`lower-fma.f32`
6 570×	`lower-fma.f64`
4 274×	`lower-*.f32`
4 268×	`lower-*.f64`
2 716×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	109
0	31	103
1	89	103
2	570	103
3	6804	103
0	8330	79

Stop Event

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

Counts

14 → 340

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (-.f64 (.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y))))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x))) y) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (.f64 (/.f64 x y) 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 y) x))))))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x))) y) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x))) y) (-.f64 (.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x))) y) (.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y))) (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y))
(.f64 (fma.f64 y y (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 y (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x)))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y)) (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)))
(.f64 (pow.f64 (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (.f64 (/.f64 x y) #s(literal 1/2 binary64))) x)) #s(literal -1 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 x y) 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 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y)))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (*.f64 (/.f64 x y) #s(literal 1/2 binary64))) x)))))
(.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y)))
(.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y))
(.f64 (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (.f64 (/.f64 x y) #s(literal 1/2 binary64))) x)) (/.f64 (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y) (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (.f64 (/.f64 x y) #s(literal 1/2 binary64))) x))))
(.f64 (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (.f64 (/.f64 x y) #s(literal 1/2 binary64))) x)) (.f64 (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y) (pow.f64 (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (*.f64 (/.f64 x y) #s(literal 1/2 binary64))) x)) #s(literal -1 binary64))))
(.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (*.f64 (/.f64 x y) #s(literal 1/2 binary64))) x)) #s(literal -1 binary64)))
(.f64 (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y) (/.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y))))
(.f64 (fma.f64 (/.f64 x y) (.f64 #s(literal 1/2 binary64) x) y) (.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x y) (*.f64 #s(literal 1/2 binary64) x) y)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y))) (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y))) (fma.f64 (.f64 y y) (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (pow.f64 (.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (.f64 (/.f64 x y) #s(literal 1/2 binary64))) x)) #s(literal -1 binary64))) (-.f64 (.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (pow.f64 y #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #s(literal 9 binary64))) (pow.f64 (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (.f64 (/.f64 x y) #s(literal 1/2 binary64))) x)) #s(literal -1 binary64))) (-.f64 (hypot.f64 (.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (pow.f64 y #s(literal 3 binary64))) (.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (*.f64 (/.f64 x y) x) y) #s(literal 3 binary64)))))
(/.f64 (.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) #s(literal 1 binary64)) (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)))
(/.f64 (.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))) #s(literal 1 binary64)) (-.f64 (hypot.f64 (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) y) (.f64 (.f64 y (*.f64 (/.f64 x y) #s(literal 1/2 binary64))) x)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)))) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y))))) (.f64 (/.f64 (.f64 (neg.f64 y) y) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y)) (/.f64 (.f64 (neg.f64 y) y) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y))) (/.f64 (.f64 (neg.f64 y) y) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (neg.f64 y) y) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)))) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)))) (fma.f64 (/.f64 (.f64 (neg.f64 y) y) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y)) (/.f64 (.f64 (neg.f64 y) y) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x) y)) (.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)))) (/.f64 (.f64 (neg.f64 y) y) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y))))))
(/.f64 (neg.f64 (fma.f64 y y (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 x y) x) #s(literal 2 binary64))))) (neg.f64 (+.f64 y (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x y) x)))))
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eval248.0ms (0.8%)

Memory: -19.4MiB live, 105.1MiB allocated
Compiler: Compiled 10 504 to 1 292 computations (87.7% saved)

prune87.0ms (0.3%)

Memory

16.6MiB live, 52.6MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	630	1	631
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	630	7	637

Accuracy

99.9%

Counts

637 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	27.2%	(sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))))
✓	57.6%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	57.0%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	4.6%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
▶	98.6%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
✓	1.9%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 72 to 48 computations (33.3% saved)

simplify433.0ms (1.4%)

Memory

-16.7MiB live, 102.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x y)
cost-diff	0	(*.f64 (-.f64 x y) (+.f64 y x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))))
cost-diff	0	(.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
cost-diff	1600	(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))
cost-diff	5824	(pow.f64 y #s(literal 1/2 binary64))

Rules

8 932×	`lower-fma.f32`
8 928×	`lower-fma.f64`
2 776×	`lower-*.f32`
2 768×	`lower-*.f64`
1 660×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	169
0	41	162
1	88	158
2	205	154
3	515	149
4	1145	149
5	2781	149
6	4679	149
7	6495	149
8	7656	149
0	8028	143

Stop Event

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

Calls

Call 1

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

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

localize93.0ms (0.3%)

Memory

-3.9MiB live, 76.2MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	2.1953125000000004	(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))
accuracy	16.756164018075633	(/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x)))
accuracy	27.13272370161774	(sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))))
accuracy	45.66943996685318	(/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 y x)))
accuracy	0.0078125	(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
accuracy	0.125	(.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)
accuracy	0.36158795398427857	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
accuracy	0.53515625	(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))

Samples

41.0ms

256×

valid

Compiler

Compiled 159 to 24 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 8.0ms (26.8% of total)

ival-div: 5.0ms (16.7% of total)

ival-hypot: 4.0ms (13.4% of total)

ival-add: 3.0ms (10% of total)

ival-sqrt: 3.0ms (10% of total)

ival-pow: 3.0ms (10% of total)

ival-sub: 1.0ms (3.3% of total)

ival-neg: 1.0ms (3.3% of total)

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

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

exact: 0.0ms (0% of total)

series39.0ms (0.1%)

Memory

6.1MiB live, 43.2MiB allocated

Counts

12 → 264

Calls

Call 1

Inputs
#s(alt (pow.f64 y #s(literal 1/2 binary64)) (patch (pow.f64 y #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) (patch (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) #<representation:binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation:binary64>) () ())
#s(alt (.f64 (-.f64 x y) (+.f64 y x)) (patch (.f64 (-.f64 x y) (+.f64 y x)) #<representation:binary64>) () ())
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation:binary64>) () ())
#s(alt (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 x y) #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())
#s(alt (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) (patch (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) #<representation:binary64>) () ())

Outputs
#s(alt (sqrt y) (taylor 0 y) (#s(alt (pow.f64 y #s(literal 1/2 binary64)) (patch (pow.f64 y #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (pow.f64 y #s(literal 1/2 binary64)) (patch (pow.f64 y #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (pow.f64 y #s(literal 1/2 binary64)) (patch (pow.f64 y #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (pow.f64 y #s(literal 1/2 binary64)) (patch (pow.f64 y #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor 0 y) (#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (pow x 2)) (pow y 2)) y) (taylor 0 y) (#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ (pow y 2) x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (+ 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))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor 0 y) (#s(alt (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) (patch (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor 0 y) (#s(alt (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) (patch (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor 0 y) (#s(alt (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) (patch (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor 0 y) (#s(alt (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) (patch (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* -1/2 (/ (* y (+ x (* -1 x))) x))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/2 (/ (+ x (* -1 x)) x)) (* 1/2 (/ (* y (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))))) x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/2 (/ (+ x (* -1 x)) x)) (* y (+ (* -1/2 (/ (* y (+ (* -1/2 (/ (* (+ x (* -1 x)) (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))))) (pow x 2))) (/ (* (+ x (* -1 x)) (- 1 (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (pow x 2)))) x)) (* 1/2 (/ (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) x))))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 y x)) (patch (.f64 (-.f64 x y) (+.f64 y x)) #<representation:binary64>) () ())) ())
#s(alt (+ (* y (+ x (* -1 x))) (pow x 2)) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 y x)) (patch (.f64 (-.f64 x y) (+.f64 y x)) #<representation:binary64>) () ())) ())
#s(alt (+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2)) (taylor 0 y) (#s(alt (.f64 (-.f64 x y) (+.f64 y x)) (patch (.f64 (-.f64 x y) (+.f64 y x)) #<representation:binary64>) () ())) ())
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#s(alt (* 1/2 (/ x y)) (taylor -inf x) (#s(alt (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 x y) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (/ (pow y 4) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (* (pow y 4) (+ y (* -1 y))) x)) (pow y 4)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* (pow y 4) (pow (+ y (* -1 y)) 2)) (pow y 6)) x)) (* (pow y 4) (+ y (* -1 y)))) x)) (pow y 4)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* (+ y (* -1 y)) (+ (* (pow y 4) (pow (+ y (* -1 y)) 2)) (pow y 6))) (* (pow y 6) (+ y (* -1 y)))) x)) (+ (* (pow y 4) (pow (+ y (* -1 y)) 2)) (pow y 6))) x)) (* (pow y 4) (+ y (* -1 y)))) x)) (pow y 4)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ y (* -1 y)) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (+ (* -1 (/ (pow y 2) x)) (* -1 (/ (pow (+ y (* -1 y)) 2) x))) (* -1 (+ y (* -1 y)))) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x)) (/ (* (+ y (* -1 y)) (+ (* -1 (pow y 2)) (* -1 (pow (+ y (* -1 y)) 2)))) x)) (+ (* -1 (pow y 2)) (* -1 (pow (+ y (* -1 y)) 2)))) x)) (* -1 (+ y (* -1 y)))) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (patch (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) (patch (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ y (* -1 y)) x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) (patch (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (+ (pow y 2) (pow (+ y (* -1 y)) 2)) x)))) x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) (patch (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) (* (pow y 2) (+ y (* -1 y)))) x)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) x)))) x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) (patch (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))) #<representation:binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	((pow y 1/2) (+ (* (pow y 1/2) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (* (/ x y) 1/2) x) (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (* x x) (* (- x y) (+ y x)) (- x y) (* (/ x y) 1/2) (/ (pow y 4) (* (- x y) (+ y x))) (/ (* x x) (* (- x y) (+ y x))) (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x))))))
4.0ms	y	@	0	((pow y 1/2) (+ (* (pow y 1/2) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (* (/ x y) 1/2) x) (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (* x x) (* (- x y) (+ y x)) (- x y) (* (/ x y) 1/2) (/ (pow y 4) (* (- x y) (+ y x))) (/ (* x x) (* (- x y) (+ y x))) (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x))))))
4.0ms	x	@	-inf	((pow y 1/2) (+ (* (pow y 1/2) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (* (/ x y) 1/2) x) (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (* x x) (* (- x y) (+ y x)) (- x y) (* (/ x y) 1/2) (/ (pow y 4) (* (- x y) (+ y x))) (/ (* x x) (* (- x y) (+ y x))) (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x))))))
4.0ms	y	@	inf	((pow y 1/2) (+ (* (pow y 1/2) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (* (/ x y) 1/2) x) (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (* x x) (* (- x y) (+ y x)) (- x y) (* (/ x y) 1/2) (/ (pow y 4) (* (- x y) (+ y x))) (/ (* x x) (* (- x y) (+ y x))) (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x))))))
3.0ms	y	@	-inf	((pow y 1/2) (+ (* (pow y 1/2) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (* (/ x y) 1/2) x) (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (* x x) (* (- x y) (+ y x)) (- x y) (* (/ x y) 1/2) (/ (pow y 4) (* (- x y) (+ y x))) (/ (* x x) (* (- x y) (+ y x))) (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x))))))

simplify118.0ms (0.4%)

Memory

11.6MiB live, 134.2MiB allocated

Algorithm

1×	egg-herbie

Rules

5 420×	`lower-fma.f64`
5 420×	`lower-fma.f32`
2 640×	`lower-*.f64`
2 640×	`lower-*.f32`
1 926×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	663	3130
1	2174	2313
0	9858	2193

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 251

Calls

Call 1

Inputs
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* 1/2 (/ (pow x 2) y))
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
x
(+ 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) y))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
x
(+ x (* -1/2 (/ (* y (+ x (* -1 x))) x)))
(+ x (* y (+ (* -1/2 (/ (+ x (* -1 x)) x)) (* 1/2 (/ (* y (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))))) x)))))
(+ x (* y (+ (* -1/2 (/ (+ x (* -1 x)) x)) (* y (+ (* -1/2 (/ (* y (+ (* -1/2 (/ (* (+ x (* -1 x)) (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))))) (pow x 2))) (/ (* (+ x (* -1 x)) (- 1 (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (pow x 2)))) x)) (* 1/2 (/ (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) x)))))))
(pow x 2)
(+ (* y (+ x (* -1 x))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(/ (pow y 4) (pow x 2))
(* (pow y 4) (+ (/ 1 (pow x 2)) (/ (pow y 2) (pow x 4))))
(* (pow y 4) (+ (* (pow y 2) (+ (/ 1 (pow x 4)) (/ (pow y 2) (pow x 6)))) (/ 1 (pow x 2))))
(* (pow y 4) (+ (* (pow y 2) (+ (* (pow y 2) (+ (/ 1 (pow x 6)) (/ (pow y 2) (pow x 8)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2))))
1
(+ 1 (/ (pow y 2) (pow x 2)))
(+ 1 (* (pow y 2) (+ (/ 1 (pow x 2)) (/ (pow y 2) (pow x 4)))))
(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (/ 1 (pow x 4)) (/ (pow y 2) (pow x 6)))) (/ 1 (pow x 2)))))
(pow x 2)
(+ (* -1 (* y (+ x (* -1 x)))) (pow x 2))
(+ (* y (- (* y (- 1 (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (+ x (* -1 x)))) (pow x 2))
(+ (* y (- (* y (- (+ 1 (* -1 (/ (* y (* (+ x (* -1 x)) (- 1 (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))))) (pow x 2)))) (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (+ x (* -1 x)))) (pow x 2))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
y
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y))))
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (+ (* 1/2 (/ (- (+ (* (+ x (* -1 x)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (* (pow x 2) (+ x (* -1 x)))) (* 1/2 (* (+ x (* -1 x)) (- (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) (pow y 3))) (* 1/2 (/ (- (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))))
(* -1 (pow y 2))
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* -1 (pow y 2))
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(* (pow y 2) (- (* -1 (/ (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (pow y 2))) (+ 1 (+ (* -1 (/ x y)) (/ x y)))))
(* (pow y 2) (- (* -1 (/ (+ (* (+ x (* -1 x)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (* (pow x 2) (+ x (* -1 x)))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (+ (/ x y) (+ (/ (pow x 2) (pow y 2)) (/ (pow (+ x (* -1 x)) 2) (pow y 2))))))))
(* -1 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) y)) (* -1 (pow x 2))) (pow y 2))
(/ (- (+ (* -1 (/ (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4)) (pow y 2))) (* -1 (pow x 2))) (/ (* (pow x 2) (+ x (* -1 x))) y)) (pow y 2))
(/ (- (+ (* -1 (/ (+ (* (+ x (* -1 x)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) (* (pow x 4) (+ x (* -1 x)))) (pow y 3))) (* -1 (pow x 2))) (+ (/ (* (pow x 2) (+ x (* -1 x))) y) (+ (/ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow y 2)) (/ (pow x 4) (pow y 2))))) (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (/ x y))))
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (+ (/ x y) (+ (/ (pow x 2) (pow y 2)) (/ (pow (+ x (* -1 x)) 2) (pow y 2)))))))
(* (pow y 2) (+ 1 (+ (* -1 (/ x y)) (+ (/ x y) (+ (/ (* (+ x (* -1 x)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (pow y 3)) (+ (/ (* (pow x 2) (+ x (* -1 x))) (pow y 3)) (+ (/ (pow x 2) (pow y 2)) (/ (pow (+ x (* -1 x)) 2) (pow y 2)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (pow x 2) (pow y 2))) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1/2 (/ (pow x 2) (pow y 2))) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1/2 (/ (pow x 2) (pow y 2))) (pow (sqrt -1) 2))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
(* -1 y)
(* -1 (* y (+ 1 (* -1/2 (/ (+ x (* -1 x)) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1/2 (/ (- (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) y)) (* 1/2 (+ x (* -1 x)))) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (+ (* (+ x (* -1 x)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (* (pow x 2) (+ x (* -1 x)))) (* 1/2 (* (+ x (* -1 x)) (- (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) y)) (* 1/2 (- (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (* 1/4 (pow (+ x (* -1 x)) 2))))) y)) (* 1/2 (+ x (* -1 x)))) y)))))
(* -1 (pow y 2))
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* -1 (pow y 2))
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(* (pow y 2) (- (* -1 (/ (- (+ (/ (pow x 2) y) (/ (pow (+ x (* -1 x)) 2) y)) (+ x (* -1 x))) y)) 1))
(* (pow y 2) (- (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ x (* -1 x)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) y) (/ (* (pow x 2) (+ x (* -1 x))) y)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) y)) (+ x (* -1 x))) y)) 1))
(* -1 (/ (pow x 2) (pow y 2)))
(/ (+ (* -1 (pow x 2)) (/ (* (pow x 2) (+ x (* -1 x))) y)) (pow y 2))
(/ (+ (* -1 (/ (- (+ (/ (* (pow x 2) (pow (+ x (* -1 x)) 2)) y) (/ (pow x 4) y)) (* (pow x 2) (+ x (* -1 x)))) y)) (* -1 (pow x 2))) (pow y 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ x (* -1 x)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) y) (/ (* (pow x 4) (+ x (* -1 x))) y)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) y)) (* (pow x 2) (+ x (* -1 x)))) y)) (* -1 (pow x 2))) (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (+ x (* -1 x)) y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (+ (pow x 2) (pow (+ x (* -1 x)) 2)) y)))) y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (+ (* (+ x (* -1 x)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (* (pow x 2) (+ x (* -1 x)))) y)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) y)))) y))))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* 1/2 (/ (pow x 2) y)))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
y
(+ y (* 1/2 (/ (* x (+ y (* -1 y))) y)))
(+ y (* x (+ (* 1/2 (/ (* x (- (+ 1 (/ (pow (+ y (* -1 y)) 2) (pow y 2))) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y)))))
(+ y (* x (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* x (+ (* 1/2 (/ (* x (- (/ (* (+ 1 (/ (pow (+ y (* -1 y)) 2) (pow y 2))) (+ y (* -1 y))) (pow y 2)) (* 1/2 (/ (* (+ y (* -1 y)) (- (+ 1 (/ (pow (+ y (* -1 y)) 2) (pow y 2))) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) (pow y 2))))) y)) (* 1/2 (/ (- (+ 1 (/ (pow (+ y (* -1 y)) 2) (pow y 2))) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (pow y 2))
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(* -1 y)
(- x y)
(- x y)
(- x y)
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* 1/2 (/ x y))
(* -1 (pow y 2))
(+ (* -1 (* x (+ y (* -1 y)))) (* -1 (pow y 2)))
(+ (* -1 (pow y 2)) (* x (- (* -1 (* x (+ 1 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) (+ y (* -1 y)))))
(+ (* -1 (pow y 2)) (* x (- (* x (- (* -1 (/ (* x (* (+ 1 (/ (pow (+ y (* -1 y)) 2) (pow y 2))) (+ y (* -1 y)))) (pow y 2))) (+ 1 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) (+ y (* -1 y)))))
(* -1 (/ (pow x 2) (pow y 2)))
(* (pow x 2) (- (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 2))))
(* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow y 6))) (/ 1 (pow y 4)))) (/ 1 (pow y 2))))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow y 8))) (/ 1 (pow y 6)))) (/ 1 (pow y 4)))) (/ 1 (pow y 2))))
(pow y 2)
(- (* x (+ y (* -1 y))) (* -1 (pow y 2)))
(- (* x (+ y (+ (* -1 y) (* x (+ 1 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))))) (* -1 (pow y 2)))
(- (* x (+ y (+ (* -1 y) (* x (+ 1 (+ (/ (* x (* (+ 1 (/ (pow (+ y (* -1 y)) 2) (pow y 2))) (+ y (* -1 y)))) (pow y 2)) (/ (pow (+ y (* -1 y)) 2) (pow y 2)))))))) (* -1 (pow y 2)))
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x
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(* 1/2 (/ (pow x 2) y))
(* 1/2 (/ (pow x 2) y))
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(* 1/2 (/ (pow x 2) y))
x
(* x (+ 1 (* -1/2 (/ (+ y (* -1 y)) x))))
(* x (+ 1 (+ (* -1/2 (/ (+ y (* -1 y)) x)) (* -1/2 (/ (+ (* -1 (pow y 2)) (+ (* -1 (pow (+ y (* -1 y)) 2)) (* 1/4 (pow (+ y (* -1 y)) 2)))) (pow x 2))))))
(* x (+ 1 (+ (* -1/2 (/ (+ y (* -1 y)) x)) (+ (* -1/2 (/ (+ (* -1 (* (+ y (* -1 y)) (+ (* -1 (pow y 2)) (* -1 (pow (+ y (* -1 y)) 2))))) (+ (* 1/2 (* (+ y (* -1 y)) (+ (* -1 (pow y 2)) (+ (* -1 (pow (+ y (* -1 y)) 2)) (* 1/4 (pow (+ y (* -1 y)) 2)))))) (* (pow y 2) (+ y (* -1 y))))) (pow x 3))) (* -1/2 (/ (+ (* -1 (pow y 2)) (+ (* -1 (pow (+ y (* -1 y)) 2)) (* 1/4 (pow (+ y (* -1 y)) 2)))) (pow x 2)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
x
(* x (+ 1 (* -1 (/ y x))))
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(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))) (+ (pow y 2) (pow (+ y (* -1 y)) 2)))) (* 1/2 (/ (+ (* 1/2 (/ (* (+ y (* -1 y)) (+ (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))) (+ (pow y 2) (pow (+ y (* -1 y)) 2)))) (pow (sqrt -1) 2))) (+ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) (* (pow y 2) (+ y (* -1 y))))) x))) x)) (* -1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2))))
(pow x 2)
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Outputs
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* 1/2 (/ (pow x 2) y))
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(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 y y)) y)
x
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(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
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(+ x (* y (+ (* -1/2 (/ (+ x (* -1 x)) x)) (* 1/2 (/ (* y (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))))) x)))))
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(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
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(/ (pow y 4) (pow x 2))
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1
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(+ 1 (* (pow y 2) (+ (* (pow y 2) (+ (/ 1 (pow x 4)) (/ (pow y 2) (pow x 6)))) (/ 1 (pow x 2)))))
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(pow x 2)
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(hypot.f64 x y)
(sqrt y)
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(sqrt y)
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(sqrt y)
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y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
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(fma.f64 (.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64)) y y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64)) y y)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
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y
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y
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(* -1 (pow y 2))
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(.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 x x) y) y)) y) y)
(* (pow y 2) (- (* -1 (/ (+ (* (+ x (* -1 x)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (* (pow x 2) (+ x (* -1 x)))) (pow y 3))) (+ 1 (+ (* -1 (/ x y)) (+ (/ x y) (+ (/ (pow x 2) (pow y 2)) (/ (pow (+ x (* -1 x)) 2) (pow y 2))))))))
(.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 x x) y) y)) y) y)
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(- (+ 1 (* -1 (/ (+ (* -1 (* (+ y (* -1 y)) (+ (* -1 (pow y 2)) (* -1 (pow (+ y (* -1 y)) 2))))) (* (pow y 2) (+ y (* -1 y)))) (pow x 3)))) (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (+ (* -1 (/ (pow (+ y (* -1 y)) 2) (pow x 2))) (/ y x)))))
(fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ y (* -1 y)) x))))
(*.f64 x x)
(* (pow x 2) (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (* -1 (pow (+ y (* -1 y)) 2))) (pow x 2)))) (+ (* -1 (/ y x)) (/ y x))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (- (+ 1 (* -1 (/ (+ (* -1 (* (+ y (* -1 y)) (+ (* -1 (pow y 2)) (* -1 (pow (+ y (* -1 y)) 2))))) (* (pow y 2) (+ y (* -1 y)))) (pow x 3)))) (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (+ (* -1 (/ (pow (+ y (* -1 y)) 2) (pow x 2))) (/ y x))))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* 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 #s(literal 1/2 binary64) x) (.f64 y (/.f64 y x)) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 y (/.f64 y x)) (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* 1/2 (/ (+ y (* -1 y)) x)) (pow (sqrt -1) 2))))
x
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (+ y (* -1 y))) (* 1/2 (/ (+ (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) x))) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 (fma.f64 (*.f64 y (/.f64 y x)) #s(literal 1/2 binary64) #s(literal 0 binary64)) (neg.f64 x)) (neg.f64 x) x)
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))) (+ (pow y 2) (pow (+ y (* -1 y)) 2)))) (* 1/2 (/ (+ (* 1/2 (/ (* (+ y (* -1 y)) (+ (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))) (+ (pow y 2) (pow (+ y (* -1 y)) 2)))) (pow (sqrt -1) 2))) (+ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) (* (pow y 2) (+ y (* -1 y))))) x))) x)) (* -1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 y y)) (neg.f64 x)) (neg.f64 x)) (neg.f64 x) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 y x) (/.f64 y x))) (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 y x) (/.f64 y x))) (*.f64 x x))
x
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (* x (- (/ y x) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(/ (pow y 4) (pow x 2))
(/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) x)
(/ (+ (* -1 (/ (* (pow y 4) (+ y (* -1 y))) x)) (pow y 4)) (pow x 2))
(/.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 5 binary64)) (pow.f64 y #s(literal 4 binary64))) x) x)
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* (pow y 4) (pow (+ y (* -1 y)) 2)) (pow y 6)) x)) (* (pow y 4) (+ y (* -1 y)))) x)) (pow y 4)) (pow x 2))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 5 binary64)) (/.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 5 binary64)) (pow.f64 y #s(literal 6 binary64))) (neg.f64 x))) x)) (*.f64 x x))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* (+ y (* -1 y)) (+ (* (pow y 4) (pow (+ y (* -1 y)) 2)) (pow y 6))) (* (pow y 6) (+ y (* -1 y)))) x)) (+ (* (pow y 4) (pow (+ y (* -1 y)) 2)) (pow y 6))) x)) (* (pow y 4) (+ y (* -1 y)))) x)) (pow y 4)) (pow x 2))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 5 binary64)) (/.f64 (-.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 5 binary64)) (pow.f64 y #s(literal 6 binary64))) (/.f64 (.f64 #s(literal 0 binary64) (+.f64 (fma.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 5 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 y #s(literal 6 binary64)))) x)) (neg.f64 x))) x)) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (+ y (* -1 y)) x)))
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (+ (* -1 (/ (pow y 2) x)) (* -1 (/ (pow (+ y (* -1 y)) 2) x))) (* -1 (+ y (* -1 y)))) x)))
(fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64))
(+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow y 2) (+ y (* -1 y))) x)) (/ (* (+ y (* -1 y)) (+ (* -1 (pow y 2)) (* -1 (pow (+ y (* -1 y)) 2)))) x)) (+ (* -1 (pow y 2)) (* -1 (pow (+ y (* -1 y)) 2)))) x)) (* -1 (+ y (* -1 y)))) x)))
(fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ y (* -1 y)) x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (+ (pow y 2) (pow (+ y (* -1 y)) 2)) x)))) x))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) (* (pow y 2) (+ y (* -1 y)))) x)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) x)))) x))))
(.f64 (.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 1 binary64)) x) x)

rewrite228.0ms (0.8%)

Memory

16.8MiB live, 397.1MiB allocated

Rules

4 996×	`lower-/.f32`
4 990×	`lower-/.f64`
3 358×	`lower-*.f32`
3 350×	`lower-*.f64`
2 840×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	142
0	41	135
1	176	91
2	1381	91
0	8139	77

Stop Event

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

Counts

12 → 987

Calls

Call 1

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

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

eval316.0ms (1.1%)

Memory: -10.0MiB live, 504.0MiB allocated
Compiler: Compiled 56 067 to 5 127 computations (90.9% saved)

prune43.0ms (0.1%)

Memory

19.1MiB live, 102.7MiB allocated

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1 471	5	1 476
Fresh	0	0	0
Picked	2	0	2
Done	3	2	5
Total	1 476	7	1 483

Accuracy

99.9%

Counts

1 483 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.6%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	27.2%	(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))))
▶	98.8%	#s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y)
▶	91.2%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
▶	92.0%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
▶	98.6%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))

Compiler

Compiled 164 to 122 computations (25.6% saved)

simplify185.0ms (0.6%)

Memory

8.1MiB live, 238.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
cost-diff	1600	(fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))
cost-diff	5824	(pow.f64 y #s(literal 1/2 binary64))
cost-diff	18624	(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y))
cost-diff	320	(.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))
cost-diff	1600	(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))
cost-diff	5824	(pow.f64 y #s(literal 1/2 binary64))
cost-diff	12480	(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))))
cost-diff	256	(-.f64 (.f64 (.f64 (neg.f64 x) x) (*.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64))))
cost-diff	0	(.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
cost-diff	1600	(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))
cost-diff	0	#s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y)

Rules

9 844×	`lower-fma.f32`
9 842×	`lower-fma.f64`
3 010×	`lower-*.f32`
2 994×	`lower-*.f64`
1 152×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	346
0	82	295
1	164	282
2	427	269
3	1435	258
4	3933	258
5	6059	258
0	8105	240

Stop Event

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

Calls

Call 1

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

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

localize208.0ms (0.7%)

Memory

-28.6MiB live, 343.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.125	(.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)
accuracy	0.36158795398427857	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
accuracy	0.53515625	(fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))
accuracy	5.326564812463393	(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y))
accuracy	0.125	(.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)
accuracy	0.36158795398427857	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
accuracy	0.53515625	(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))
accuracy	4.767610590535813	(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
accuracy	0.10775375976844202	(.f64 (.f64 (neg.f64 x) x) (*.f64 x x))
accuracy	5.98046875	(-.f64 (.f64 (.f64 (neg.f64 x) x) (*.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64))))
accuracy	27.13272370161774	(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))))
accuracy	40.54074219800233	(/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y)))
accuracy	0.0078125	(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
accuracy	0.125	(.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)
accuracy	0.36158795398427857	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
accuracy	0.53515625	(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))
accuracy	0.7527039774449018	#s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y)

Samples

152.0ms

256×

valid

Compiler

Compiled 300 to 46 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-mult: 21.0ms (23% of total)

ival-neg: 21.0ms (23% of total)

ival-pow: 10.0ms (11% of total)

ival-div: 9.0ms (9.9% of total)

ival-add: 9.0ms (9.9% of total)

ival-exp: 6.0ms (6.6% of total)

ival-sqrt: 5.0ms (5.5% of total)

ival-hypot: 4.0ms (4.4% of total)

ival-log: 3.0ms (3.3% of total)

ival-sub: 2.0ms (2.2% of total)

exact: 1.0ms (1.1% of total)

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

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

series327.0ms (1.1%)

Memory

2.2MiB live, 373.6MiB allocated

Counts

20 → 384

Calls

Call 1

Inputs
#s(alt #s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y) (patch #s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y) #<representation:binary64>) () ())
#s(alt (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())
#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) (patch (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x) #<representation:binary64>) () ())
#s(alt (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (patch (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) #<representation:binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y)))) (patch (sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y)))) #<representation:binary64>) () ())
#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation:binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())
#s(alt (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (patch (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #<representation:binary64>) () ())
#s(alt (pow.f64 y #s(literal 1/2 binary64)) (patch (pow.f64 y #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (patch (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #<representation:binary64>) () ())
#s(alt (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (patch (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) #<representation:binary64>) () ())
#s(alt (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())
#s(alt (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 x y) #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) (patch (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (patch (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) #<representation:binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())

Outputs
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y) (patch #s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y) #<representation:binary64>) () ())) ())
#s(alt (+ x (* -1/2 (/ (* y (+ x (* -1 x))) x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y) (patch #s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y) #<representation:binary64>) () ())) ())
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#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ (pow x 2) y)) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) (patch (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 y #s(literal 1/2 binary64)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ x y)) (taylor -inf x) (#s(alt (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 x y) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ x y)) (taylor -inf x) (#s(alt (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 x y) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ x y)) (taylor -inf x) (#s(alt (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 x y) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (/ x y)) (taylor -inf x) (#s(alt (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 x y) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) (patch (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) (patch (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (pow y 2) (pow (+ y (* -1 y)) 2)) x))) x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) (patch (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2)))) (* -1 (* (pow y 2) (+ y (* -1 y))))) x)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) x))) x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) (patch (/.f64 (-.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (.f64 (neg.f64 (+.f64 x y)) (-.f64 x y))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (patch (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (patch (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (patch (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (patch (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) (patch #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x))) #<representation:binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
173.0ms	y	@	-inf	((sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (+ (* (sqrt y) (sqrt y)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ x y) 1/2) x) (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (sqrt (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y)))) (* (neg x) x) (neg x) (exp (* (* (log y) 2) 1/4)) (pow y 1/2) (+ (* (pow y 1/2) (exp (* (* (log y) 2) 1/4))) (* (* (/ x y) 1/2) x)) (* (* (log y) 2) 1/4) (pow (exp 1/2) (log y)) (+ (* (pow (exp 1/2) (log y)) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (/ x y) 1/2) (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y))) (* (* (neg x) x) (* x x)) (sqrt (+ (* x x) (* y y))))
57.0ms	y	@	0	((sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (+ (* (sqrt y) (sqrt y)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ x y) 1/2) x) (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (sqrt (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y)))) (* (neg x) x) (neg x) (exp (* (* (log y) 2) 1/4)) (pow y 1/2) (+ (* (pow y 1/2) (exp (* (* (log y) 2) 1/4))) (* (* (/ x y) 1/2) x)) (* (* (log y) 2) 1/4) (pow (exp 1/2) (log y)) (+ (* (pow (exp 1/2) (log y)) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (/ x y) 1/2) (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y))) (* (* (neg x) x) (* x x)) (sqrt (+ (* x x) (* y y))))
43.0ms	x	@	0	((sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (+ (* (sqrt y) (sqrt y)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ x y) 1/2) x) (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (sqrt (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y)))) (* (neg x) x) (neg x) (exp (* (* (log y) 2) 1/4)) (pow y 1/2) (+ (* (pow y 1/2) (exp (* (* (log y) 2) 1/4))) (* (* (/ x y) 1/2) x)) (* (* (log y) 2) 1/4) (pow (exp 1/2) (log y)) (+ (* (pow (exp 1/2) (log y)) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (/ x y) 1/2) (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y))) (* (* (neg x) x) (* x x)) (sqrt (+ (* x x) (* y y))))
17.0ms	y	@	inf	((sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (+ (* (sqrt y) (sqrt y)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ x y) 1/2) x) (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (sqrt (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y)))) (* (neg x) x) (neg x) (exp (* (* (log y) 2) 1/4)) (pow y 1/2) (+ (* (pow y 1/2) (exp (* (* (log y) 2) 1/4))) (* (* (/ x y) 1/2) x)) (* (* (log y) 2) 1/4) (pow (exp 1/2) (log y)) (+ (* (pow (exp 1/2) (log y)) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (/ x y) 1/2) (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y))) (* (* (neg x) x) (* x x)) (sqrt (+ (* x x) (* y y))))
6.0ms	x	@	inf	((sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) (+ (* (sqrt y) (sqrt y)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (sqrt y) (* (* (/ x y) 1/2) x) (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (sqrt (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y)))) (* (neg x) x) (neg x) (exp (* (* (log y) 2) 1/4)) (pow y 1/2) (+ (* (pow y 1/2) (exp (* (* (log y) 2) 1/4))) (* (* (/ x y) 1/2) x)) (* (* (log y) 2) 1/4) (pow (exp 1/2) (log y)) (+ (* (pow (exp 1/2) (log y)) (pow y 1/2)) (* (* (/ x y) 1/2) x)) (sqrt (+ (* x x) (* y y))) (* (/ x y) 1/2) (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y))) (* (* (neg x) x) (* x x)) (sqrt (+ (* x x) (* y y))))

simplify89.0ms (0.3%)

Memory

-14.2MiB live, 183.3MiB allocated

Algorithm

1×	egg-herbie

Rules

3 402×	`lower-fma.f64`
3 402×	`lower-fma.f32`
2 146×	`lower-*.f64`
2 146×	`lower-*.f32`
1 308×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	589	5302
1	2053	3361
0	10142	3184

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 362

Calls

Call 1

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

Outputs
x
(+ x (* -1/2 (/ (* y (+ x (* -1 x))) x)))
x
(+ x (* y (+ (* -1/2 (/ (+ x (* -1 x)) x)) (* 1/2 (/ (* y (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))))) x)))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)
(+ x (* y (+ (* -1/2 (/ (+ x (* -1 x)) x)) (* y (+ (* -1/2 (/ (* y (+ (* -1/2 (/ (* (+ x (* -1 x)) (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))))) (pow x 2))) (/ (* (+ x (* -1 x)) (- 1 (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) (pow x 2)))) x)) (* 1/2 (/ (- 1 (+ (* -1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) x)))))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(/ (+ (* 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 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 y y)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 y y)) y)
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 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 y (/.f64 y (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(+ (* -1 (pow x 4)) (pow y 4))
(-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))
(+ (* -1 (pow x 4)) (pow y 4))
(-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))
(+ (* -1 (pow x 4)) (pow y 4))
(-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* x (pow (sqrt -1) 2))
(neg.f64 x)
(+ (* 1/2 (/ (* y (+ x (* -1 x))) x)) (* x (pow (sqrt -1) 2)))
(neg.f64 x)
(+ (* x (pow (sqrt -1) 2)) (* y (+ (* -1/2 (/ (* y (+ 1 (+ (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))) (/ (pow (+ x (* -1 x)) 2) (pow x 2))))) x)) (* 1/2 (/ (+ x (* -1 x)) x)))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -1/2 binary64)) y (neg.f64 x))
(+ (* x (pow (sqrt -1) 2)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) x)) (* y (+ (* -1/2 (/ (* y (+ (* -1 (/ (* (+ 1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (+ x (* -1 x))) (pow x 2))) (+ (* -1 (/ (+ x (* -1 x)) (pow x 2))) (* -1/2 (/ (* (+ 1 (+ (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))) (/ (pow (+ x (* -1 x)) 2) (pow x 2)))) (+ x (* -1 x))) (* (pow x 2) (pow (sqrt -1) 2))))))) x)) (* -1/2 (/ (+ 1 (+ (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))) (/ (pow (+ x (* -1 x)) 2) (pow x 2)))) x)))))))
(fma.f64 (*.f64 (/.f64 y x) #s(literal -1/2 binary64)) y (neg.f64 x))
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(/ (+ (* 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 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 y y)) y)
(/ (+ (* 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 (log y))
(*.f64 (log.f64 y) #s(literal 1/2 binary64))
(* 1/2 (log y))
(*.f64 (log.f64 y) #s(literal 1/2 binary64))
(* 1/2 (log y))
(*.f64 (log.f64 y) #s(literal 1/2 binary64))
(* 1/2 (log y))
(*.f64 (log.f64 y) #s(literal 1/2 binary64))
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(/ (+ (* 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 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 y y)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 y y)) y)
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 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 y (/.f64 y (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 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 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(pow x 2)
(*.f64 x x)
(+ (* -1 (* y (+ x (* -1 x)))) (pow x 2))
(*.f64 x x)
(+ (* y (+ (* -1 (+ x (* -1 x))) (* y (+ 1 (/ (pow (+ x (* -1 x)) 2) (pow x 2)))))) (pow x 2))
(hypot.f64 y x)
(+ (* y (+ (* -1 (+ x (* -1 x))) (* y (+ 1 (+ (* y (+ (* -1 (/ (* (+ 1 (/ (pow (+ x (* -1 x)) 2) (pow x 2))) (+ x (* -1 x))) (pow x 2))) (* -1 (/ (+ x (* -1 x)) (pow x 2))))) (/ (pow (+ x (* -1 x)) 2) (pow x 2))))))) (pow x 2))
(hypot.f64 y x)
x
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (*.f64 (/.f64 y x) #s(literal 1/2 binary64)) y x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 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 y (/.f64 y (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
y
(* y (+ 1 (* 1/2 (/ (+ x (* -1 x)) y))))
y
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))
(fma.f64 (.f64 y (/.f64 (/.f64 (.f64 x x) y) y)) #s(literal 1/2 binary64) y)
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (+ (* 1/2 (/ (- (+ (* (+ x (* -1 x)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (* (pow x 2) (+ x (* -1 x)))) (* 1/2 (* (+ x (* -1 x)) (- (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))))) (pow y 3))) (* 1/2 (/ (- (+ (pow x 2) (pow (+ x (* -1 x)) 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))))
(fma.f64 (.f64 y (/.f64 (/.f64 (.f64 x x) y) y)) #s(literal 1/2 binary64) y)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 y (/.f64 (/.f64 (.f64 x x) y) y)) #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 y (/.f64 (/.f64 (.f64 x x) y) y)) #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 y (/.f64 (/.f64 (.f64 x x) y) y)) #s(literal 1/2 binary64) y)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 y (/.f64 (/.f64 (.f64 x x) y) y)) #s(literal 1/2 binary64) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) y y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64))))) y y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(pow y 4)
(pow.f64 y #s(literal 4 binary64))
(* (pow y 4) (+ 1 (* -1 (/ (pow x 4) (pow y 4)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 y #s(literal 4 binary64)))
(* (pow y 4) (+ 1 (* -1 (/ (pow x 4) (pow y 4)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 y #s(literal 4 binary64)))
(* (pow y 4) (+ 1 (* -1 (/ (pow x 4) (pow y 4)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 y #s(literal 4 binary64)))
(* y (pow (sqrt -1) 2))
(neg.f64 y)
(* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (pow (sqrt -1) 2)))
(neg.f64 y)
(* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (+ (* -1/2 (/ (+ (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (pow y 2))) (pow (sqrt -1) 2))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) y)
(* y (+ (* -1/2 (/ (+ x (* -1 x)) y)) (+ (* -1/2 (/ (+ (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (pow y 2))) (+ (* -1/2 (/ (+ (* 1/2 (/ (* (+ x (* -1 x)) (+ (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))) (+ (pow x 2) (pow (+ x (* -1 x)) 2)))) (pow (sqrt -1) 2))) (+ (* (+ x (* -1 x)) (+ (pow x 2) (pow (+ x (* -1 x)) 2))) (* (pow x 2) (+ x (* -1 x))))) (pow y 3))) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal -1 binary64)) y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
y
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 y (/.f64 (/.f64 (.f64 x x) y) y)) #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
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(* -1 (* x (+ (* -1 (/ (+ (* 1/2 (+ y (* -1 y))) (* 1/2 (/ (+ (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) x))) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 y (/.f64 y x) #s(literal 0 binary64))) x) (neg.f64 x) x)
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))) (+ (pow y 2) (pow (+ y (* -1 y)) 2)))) (* 1/2 (/ (+ (* -1 (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2)))) (+ (* -1 (* (pow y 2) (+ y (* -1 y)))) (* -1/2 (/ (* (+ y (* -1 y)) (+ (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))) (+ (pow y 2) (pow (+ y (* -1 y)) 2)))) (pow (sqrt -1) 2))))) x))) x)) (* 1/2 (+ y (* -1 y)))) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 (/.f64 (.f64 (.f64 y y) #s(literal -1/2 binary64)) (neg.f64 x)) (neg.f64 x)) (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* 1/2 (/ (pow x 2) y))
(.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* 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 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (.f64 (.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64)))) x x))
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(* 1/2 (/ x y))
(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (pow y 2) (pow (+ y (* -1 y)) 2)) x))) x))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (neg.f64 y) y) x) x)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (+ y (* -1 y)) (+ (pow y 2) (pow (+ y (* -1 y)) 2)))) (* -1 (* (pow y 2) (+ y (* -1 y))))) x)) (+ (pow y 2) (pow (+ y (* -1 y)) 2))) x))) x))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (neg.f64 y) y) x) x)) x) x)
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 (pow x 4))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* 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 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (.f64 (.f64 y (/.f64 y (*.f64 x x))) #s(literal 1/2 binary64)))) x x))

rewrite383.0ms (1.3%)

Memory

18.0MiB live, 456.1MiB allocated

Rules

4 900×	`lower-/.f32`
4 896×	`lower-/.f64`
4 542×	`lower-*.f32`
4 526×	`lower-*.f64`
4 120×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	257
0	82	207
1	305	148
2	2337	147
0	9955	117

Stop Event

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

Counts

20 → 1 137

Calls

Call 1

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

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

eval722.0ms (2.4%)

Memory: 27.4MiB live, 557.2MiB allocated
Compiler: Compiled 49 870 to 4 358 computations (91.3% saved)

prune102.0ms (0.3%)

Memory

-11.3MiB live, 124.4MiB allocated

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	1 746	7	1 753
Fresh	0	0	0
Picked	3	2	5
Done	0	2	2
Total	1 749	11	1 760

Accuracy

99.9%

Counts

1 760 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.6%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
	25.7%	(sqrt.f64 #s(approx (/ (- (* (* (neg x) x) (* x x)) (neg (pow y 4))) (* (neg (+ x y)) (- x y))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 y (/.f64 y (.f64 x x)))) x) x)))
✓	98.8%	#s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y)
	89.7%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
	91.2%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y)) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
	87.2%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (pow.f64 (exp.f64 #s(literal 1/4 binary64)) (.f64 #s(literal 2 binary64) (log.f64 y))) (sqrt.f64 y) (.f64 (*.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
✓	98.6%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
	92.0%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
	86.7%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (sqrt.f64 y) (exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/4 binary64))) (.f64 #s(literal 2 binary64) (log.f64 y)))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))
	86.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/4 binary64))) (.f64 #s(literal 2 binary64) (log.f64 y)))) (exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x)))

Compiler

Compiled 447 to 209 computations (53.2% saved)

regimes225.0ms (0.7%)

Memory

3.6MiB live, 42.9MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

6 calls:

196.0ms	(*.f64 x x)
6.0ms	y
6.0ms	x
5.0ms	(*.f64 y y)
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes31.0ms (0.1%)

Memory

-15.5MiB live, 25.3MiB allocated

Accuracy

Total -62.0b remaining (-8243.4%)

Threshold costs -62b (-8243.4%)

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y)
#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
(sqrt.f64 (fma.f64 y y (*.f64 x x)))

Outputs
#s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y)

Calls

6 calls:

20.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`y`
98.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
98.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.8%	1	`(*.f64 x x)`
98.8%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify74.0ms (0.2%)

Memory

12.3MiB live, 50.6MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	48
1	24	48

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

#s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y)

Outputs

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

#s(approx (sqrt (+ (* (* x x) (/ (* x x) (* (- x y) (+ y x)))) (neg (/ (pow y 4) (* (- x y) (+ y x)))))) y)

soundness611.0ms (2%)

Memory

-15.9MiB live, 217.2MiB allocated

Rules

18 004×	`lower-fma.f64`
18 004×	`lower-fma.f32`
5 720×	`lower-fma.f64`
5 720×	`lower-fma.f32`
5 420×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	663	3130
1	2174	2313
0	9858	2193
0	6	21
0	10	21
1	29	21
2	196	21
3	1788	21
0	8624	13
0	104	620
1	296	620
2	956	618
3	3671	584
4	6436	582
0	8062	476

Stop Event

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

Compiler

Compiled 28 to 22 computations (21.4% saved)

preprocess126.0ms (0.4%)

Memory: 8.8MiB live, 163.2MiB allocated
Compiler: Compiled 130 to 96 computations (26.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	120
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	136	114
8	145	114
9	151	114
10	151	114
0	151	90

Iter	Nodes	Cost
0	21	120
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	136	114
8	145	114
9	151	114
10	151	114
0	151	90

start0.0ms (0%)

analyze0.0ms (0%)

sample677.0ms (2.3%)

explain115.0ms (0.4%)

preprocess19.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize22.0ms (0.1%)

series6.0ms (0%)

simplify507.0ms (1.7%)

rewrite499.0ms (1.7%)

eval147.0ms (0.5%)

prune87.0ms (0.3%)

simplify9.0ms (0%)

localize82.0ms (0.3%)

series15.0ms (0.1%)

simplify5.0s (16.6%)

rewrite18.2s (60.6%)

eval248.0ms (0.8%)

prune87.0ms (0.3%)

simplify433.0ms (1.4%)

localize93.0ms (0.3%)

series39.0ms (0.1%)

simplify118.0ms (0.4%)

rewrite228.0ms (0.8%)

eval316.0ms (1.1%)

prune43.0ms (0.1%)

simplify185.0ms (0.6%)

localize208.0ms (0.7%)

series327.0ms (1.1%)

simplify89.0ms (0.3%)

rewrite383.0ms (1.3%)

eval722.0ms (2.4%)

prune102.0ms (0.3%)

regimes225.0ms (0.7%)

regimes31.0ms (0.1%)

simplify74.0ms (0.2%)

soundness611.0ms (2%)

preprocess126.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	120
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	136	114
8	145	114
9	151	114
10	151	114
0	151	90