Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze19.0ms (0.5%)

Memory

12.6MiB live, 50.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample712.0ms (18.8%)

Memory

-22.6MiB live, 1 410.5MiB allocated

Samples

436.0ms	8 256×	0	valid
18.0ms	311×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 255.0ms

ival-mult: 106.0ms (41.6% of total)

ival-add: 75.0ms (29.4% of total)

ival-sqrt: 64.0ms (25.1% of total)

ival-true: 7.0ms (2.7% of total)

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

Bogosity

explain61.0ms (1.6%)

Memory

7.8MiB live, 168.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
92	-	-	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
0	-	-	`(+.f64 (*.f64 x x) y)`
0	-	-	`y`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) y))`	oflow-rescue	92	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	92
↳	`(*.f64 x x)`	overflow	92

Confusion

	Predicted +	Predicted -
+	92	0
-	0	164

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	92	0	0
-	0	0	164

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	164
1	92

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

23.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 5.0ms (43.1% of total)

ival-sqrt: 4.0ms (34.5% of total)

ival-add: 2.0ms (17.3% of total)

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

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

preprocess25.0ms (0.7%)

Memory

3.8MiB live, 47.4MiB allocated

Algorithm

1×	egg-herbie

Rules

64×	`sub-neg`
34×	`distribute-lft-neg-in`
34×	`associate-+l-`
32×	`associate--r+`
32×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

4×	`lower-+.f32`
2×	`lift-sqrt.f64`
2×	`lift-+.f64`
2×	`lower-fma.f64`
2×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	9	16
0	9	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.4%)

Memory

7.2MiB live, 45.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (*.f64 x x) y)
accuracy	0	(*.f64 x x)
accuracy	21.411506137199893	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

11.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 2.0ms (36% of total)

ival-sqrt: 2.0ms (36% of total)

ival-add: 1.0ms (18% of total)

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

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

series7.0ms (0.2%)

Memory

-21.9MiB live, 16.9MiB allocated

Counts

3 → 60

Calls

Call 1

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

Inputs

#s(alt (+.f64 (*.f64 x x) y) (patch (+.f64 (*.f64 x x) y) #<representation binary64>) () ())

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

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) 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 x 2) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) 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) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) 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>) () ())) ())

Calls

6 calls:

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

simplify254.0ms (6.7%)

Memory

11.8MiB live, 321.4MiB allocated

Algorithm

1×	egg-herbie

Rules

23 502×	`lower-fma.f64`
23 502×	`lower-fma.f32`
5 416×	`lower-*.f64`
5 416×	`lower-*.f32`
2 450×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	615
1	383	600
2	1202	592
3	4035	567
0	8298	515

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 55

Calls

Call 1

Inputs
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite192.0ms (5.1%)

Memory

-29.6MiB live, 269.5MiB allocated

Rules

5 034×	`lower-fma.f64`
5 034×	`lower-fma.f32`
4 204×	`lower-/.f64`
4 204×	`lower-/.f32`
3 240×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12

Stop Event

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

Counts

3 → 228

Calls

Call 1

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

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

eval53.0ms (1.4%)

Memory: 27.1MiB live, 64.7MiB allocated
Compiler: Compiled 6 400 to 869 computations (86.4% saved)

prune36.0ms (0.9%)

Memory

-12.4MiB live, 26.1MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	277	6	283
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	278	6	284

Accuracy

100.0%

Counts

284 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.5%	(sqrt.f64 (fma.f64 x x y))
	31.8%	(sqrt.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 x x) y)))
▶	31.7%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
▶	65.5%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
▶	37.7%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 74 to 66 computations (10.8% saved)

simplify31.0ms (0.8%)

Memory

-4.7MiB live, 37.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

384×	`lower-fma.f32`
380×	`lower-fma.f64`
264×	`lower-*.f32`
262×	`lower-*.f64`
164×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	78
0	27	78
1	36	78
2	42	78
3	45	78
4	47	78
5	51	78
6	66	78
7	103	78
8	133	78
9	242	78
10	391	78
11	678	78
12	960	78
13	1021	78
14	1035	78
15	1047	78
0	1047	78

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize38.0ms (1%)

Memory

-3.8MiB live, 70.4MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.0703125	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
accuracy	21.968894656801748	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
accuracy	0	(*.f64 x x)
accuracy	10.194191532143472	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
accuracy	22.207496552879373	#s(approx (+ (* x x) y) (*.f64 x x))
accuracy	0	(sqrt.f64 y)
accuracy	19.346233620042753	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0	(neg.f64 x)
accuracy	42.84666688491707	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
accuracy	0	(fma.f64 x x y)
accuracy	10.194191532143472	(sqrt.f64 (fma.f64 x x y))

Samples

19.0ms	174×	0	valid
7.0ms	82×	0	invalid

Compiler

Compiled 67 to 13 computations (80.6% saved)

Precisions

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

ival-mult: 7.0ms (41.8% of total)

ival-sqrt: 4.0ms (23.9% of total)

ival-div: 2.0ms (11.9% of total)

ival-add: 2.0ms (11.9% of total)

ival-neg: 1.0ms (6% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.4%)

Memory

3.0MiB live, 41.9MiB allocated

Counts

12 → 240

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) y) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) y) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (+ (* x x) y) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (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) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) 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 #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) y) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) y) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) y) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (* x x) y) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) 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 #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y 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 (/ 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>) () ())) ())

Calls

6 calls:

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

simplify202.0ms (5.3%)

Memory

24.6MiB live, 336.1MiB allocated

Algorithm

1×	egg-herbie

Rules

23 474×	`lower-fma.f64`
23 474×	`lower-fma.f32`
5 372×	`lower-*.f64`
5 372×	`lower-*.f32`
2 410×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	2889
1	425	2814
2	1315	2774
3	4486	2654
0	8715	2430

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 221

Calls

Call 1

Inputs
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* 1/2 (/ y x))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 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 (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* 1/2 (/ y x))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(* 1/2 (/ y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)

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

rewrite181.0ms (4.8%)

Memory

2.3MiB live, 286.9MiB allocated

Rules

5 804×	`lower-fma.f32`
5 800×	`lower-fma.f64`
4 018×	`lower-*.f32`
4 016×	`lower-*.f64`
1 916×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	70
0	27	70
1	73	70
2	408	70
3	4494	70
0	8359	70

Stop Event

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

Counts

12 → 282

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (fma.f64 x x y)))
(pow.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 x x) y)) (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 y (.f64 x x))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (*.f64 x x) y)) (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))))
(sqrt.f64 (fma.f64 x x y))
(exp.f64 (fma.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/4 binary64) (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/2 binary64)))
(.f64 (exp.f64 (log.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (exp.f64 (neg.f64 (log.f64 (-.f64 (.f64 x x) y)))))
(.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))))
(*.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y (*.f64 x x)) y)))
(.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (-.f64 y (.f64 x x)) y) (-.f64 (.f64 (-.f64 y (*.f64 x x)) y) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x y))
(.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (-.f64 y (*.f64 x x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64)) (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))
(.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (neg.f64 (-.f64 (.f64 x x) y)) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 x x y))
(.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 x x y) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 x x y) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 x x y) (/.f64 (-.f64 (.f64 x x) y) (-.f64 (*.f64 x x) y)))
(.f64 (fma.f64 x x y) (.f64 (-.f64 (.f64 x x) y) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 y (.f64 x x)) (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (exp.f64 (log.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))))) (exp.f64 (log.f64 (-.f64 y (.f64 x x)))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))))) (exp.f64 (log.f64 (neg.f64 (-.f64 (*.f64 x x) y)))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (exp.f64 (log.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (exp.f64 (log.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (exp.f64 (log.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (exp.f64 (log.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64))) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64))) (fma.f64 (*.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 3 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))))
(/.f64 (neg.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 y (.f64 x x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (neg.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 x x) y)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (-.f64 (.f64 x x) y)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 y y))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 (*.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
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(/.f64 (neg.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))) (neg.f64 (-.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) y (*.f64 x x))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 x x (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (neg.f64 (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) y (.f64 x x)))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) y (.f64 x x)))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x)) (.f64 x x))) (pow.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x)) (fma.f64 x x (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x)) (+.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) y (*.f64 x x))) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (neg.f64 (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (-.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y)))
(/.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 9 binary64))) (.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) y (.f64 x x))) (-.f64 (+.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/8 binary64) (pow.f64 y #s(literal 3 binary64))))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) y (*.f64 x x)))))
(/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) (-.f64 (.f64 x x) (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) #s(literal -1 binary64)))
(/.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) y (*.f64 x x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) y (*.f64 x x)))))
(neg.f64 (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)))
(neg.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) y (*.f64 x x))))))
(fma.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) (exp.f64 (log.f64 (/.f64 y x))) x)
(fma.f64 (exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) y))) (pow.f64 x #s(literal -1 binary64)) x)
(fma.f64 (/.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (neg.f64 x) x)) x x)
(fma.f64 (/.f64 (.f64 #s(literal -1/2 binary64) y) (neg.f64 (pow.f64 x #s(literal 3 binary64)))) (.f64 x x) x)
(fma.f64 (/.f64 y #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x) x)
(fma.f64 (/.f64 y (neg.f64 x)) #s(literal -1/2 binary64) x)
(fma.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (neg.f64 (pow.f64 x #s(literal 3 binary64))))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 y x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) y (.f64 x x))) (neg.f64 (*.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 (neg.f64 x) x (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) (neg.f64 (*.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(fma.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) x) x)
(fma.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64)) y) (/.f64 y (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (neg.f64 (*.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x)
(fma.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) y) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (neg.f64 (*.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 y #s(literal -1 binary64)) x)
(fma.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64)) (/.f64 (.f64 y y) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (neg.f64 (*.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) y) (/.f64 #s(literal -1 binary64) x) x)
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (pow.f64 x #s(literal -1 binary64)) x)
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 y #s(literal 2 binary64)) x)
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) y) x)
(fma.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)
(fma.f64 #s(literal 1 binary64) x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(fma.f64 (.f64 y y) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (neg.f64 (*.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)) (neg.f64 (.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 y (neg.f64 x)) x)
(fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 #s(literal -1 binary64) x) y) x)
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (neg.f64 (*.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) y) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (neg.f64 (*.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(fma.f64 #s(literal 1/2 binary64) (/.f64 y x) x)
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(fma.f64 y (/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -2 binary64)) y) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (neg.f64 (*.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y))) (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y))))
(-.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))) (neg.f64 (.f64 x (/.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x))))))
(+.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)
(+.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 (neg.f64 x) x)) x)
(.f64 (/.f64 #s(literal -1/2 binary64) (neg.f64 (pow.f64 x #s(literal 3 binary64)))) (.f64 x x))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -2 binary64)))
(/.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 x))
(/.f64 #s(literal 1/2 binary64) x)
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) x)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(neg.f64 (/.f64 #s(literal -1/2 binary64) x))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) x))
(exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))

eval137.0ms (3.6%)

Memory: -5.4MiB live, 116.9MiB allocated
Compiler: Compiled 7 683 to 1 037 computations (86.5% saved)

prune18.0ms (0.5%)

Memory

11.2MiB live, 47.9MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	502	1	503
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	503	6	509

Accuracy

100.0%

Counts

509 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))))
✓	66.5%	(sqrt.f64 (fma.f64 x x y))
✓	31.7%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	65.5%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	37.7%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 32 to 31 computations (3.1% saved)

simplify5.0ms (0.1%)

Memory

-30.2MiB live, 8.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

4×	`lower-+.f64`
4×	`lower-/.f32`
4×	`lower-+.f32`
2×	`lift-sqrt.f64`
2×	`lift-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
0	13	30
1	17	30
0	17	30

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))
(pow.f64 (fma.f64 x x y) #s(literal -1 binary64))
(fma.f64 x x y)
x
y
#s(literal -1 binary64)

localize24.0ms (0.6%)

Memory

-6.5MiB live, 40.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x y)
accuracy	0.20703125	(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))))
accuracy	0.30560304665014004	(pow.f64 (fma.f64 x x y) #s(literal -1 binary64))
accuracy	20.971744777811256	(sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))

Samples

16.0ms

256×

valid

Compiler

Compiled 36 to 11 computations (69.4% saved)

Precisions

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

ival-div: 2.0ms (21.5% of total)

ival-mult: 2.0ms (21.5% of total)

ival-sqrt: 2.0ms (21.5% of total)

ival-pow: 2.0ms (21.5% of total)

ival-add: 1.0ms (10.8% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

13.6MiB live, 13.6MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ y (pow x 3))) (/ 1 x)) (taylor 0 y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (- (* 3/8 (/ y (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x)) (taylor 0 y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (- (* y (+ (* -5/16 (/ y (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x)) (taylor 0 y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 2))) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (- (/ y (pow x 6)) (/ 1 (pow x 4)))) (/ 1 (pow x 2))) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (- (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2))) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor inf y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))) (taylor inf y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))))) (taylor inf y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 4) y)) (pow x 6)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5)))))))) (taylor inf y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 y) (taylor inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (pow x 2) y))) y) (taylor inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y)) y) (taylor inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (* -1 (/ (pow x 6) (pow y 3)))) (+ (* -1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y))) y) (taylor inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) (taylor -inf y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) (taylor -inf y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1/2 (* (pow x 4) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 4) y) (pow (sqrt -1) 2))) (pow x 6))))) (pow y 3))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) (taylor -inf y) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 y) (taylor -inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ (pow x 2) y) 1) y)) (taylor -inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 2)) y)) 1) y)) (taylor -inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) y) (pow x 4)) y)) (pow x 2)) y)) 1) y)) (taylor -inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor 0 x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))) (taylor 0 x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) (taylor 0 x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* (pow x 2) (+ (* -5/16 (* (pow x 2) (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 y) (taylor 0 x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (pow x 2) (pow y 2))) (/ 1 y)) (taylor 0 x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (- (/ (pow x 2) (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y)) (taylor 0 x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y)) (taylor 0 x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x) (taylor inf x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x) (taylor inf x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x) (taylor inf x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2)) (taylor inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) (patch (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify167.0ms (4.4%)

Memory

-10.2MiB live, 225.0MiB allocated

Algorithm

1×	egg-herbie

Rules

11 592×	`lower-fma.f64`
11 592×	`lower-fma.f32`
4 132×	`lower-*.f64`
4 132×	`lower-*.f32`
3 602×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	298	1500
1	871	1439
2	2637	1413
3	6279	1393
0	8403	1296

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 91

Calls

Call 1

Inputs
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(/ 1 x)
(+ (* -1/2 (/ y (pow x 3))) (/ 1 x))
(+ (* y (- (* 3/8 (/ y (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+ (* y (- (* y (+ (* -5/16 (/ y (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(/ 1 (pow x 2))
(+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 2)))
(+ (* y (- (/ y (pow x 6)) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(+ (* y (- (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5)))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 4) y)) (pow x 6)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))))))
(/ 1 y)
(/ (+ 1 (* -1 (/ (pow x 2) y))) y)
(/ (- (+ 1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y)) y)
(/ (- (+ 1 (* -1 (/ (pow x 6) (pow y 3)))) (+ (* -1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y))) y)
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (pow x 4) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 4) y) (pow (sqrt -1) 2))) (pow x 6))))) (pow y 3))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(/ 1 y)
(* -1 (/ (- (/ (pow x 2) y) 1) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 2)) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) y) (pow x 4)) y)) (pow x 2)) y)) 1) y))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* (pow x 2) (+ (* -5/16 (* (pow x 2) (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))
(/ 1 y)
(+ (* -1 (/ (pow x 2) (pow y 2))) (/ 1 y))
(+ (* (pow x 2) (- (/ (pow x 2) (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(/ 1 x)
(/ (+ 1 (* -1/2 (/ y (pow x 2)))) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x)
(/ 1 (pow x 2))
(/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(/ -1 x)
(* -1 (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x))
(/ 1 (pow x 2))
(/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))

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

rewrite147.0ms (3.9%)

Memory

28.7MiB live, 182.4MiB allocated

Rules

3 460×	`lower-*.f64`
3 460×	`lower-*.f32`
2 380×	`lower-fma.f32`
2 378×	`lower-fma.f64`
2 348×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	26
0	13	24
1	48	22
2	262	21
3	2334	21
0	8534	21

Stop Event

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

Counts

4 → 595

Calls

Call 1

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

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

eval137.0ms (3.6%)

Memory: 6.4MiB live, 162.6MiB allocated
Compiler: Compiled 15 563 to 2 599 computations (83.3% saved)

prune13.0ms (0.3%)

Memory

4.6MiB live, 41.7MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	685	1	686
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	686	6	692

Accuracy

100.0%

Counts

692 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
✓	66.5%	(sqrt.f64 (fma.f64 x x y))
✓	31.7%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	65.5%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	37.7%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 32 to 30 computations (6.3% saved)

simplify4.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

4×	`lift-/.f64`
4×	`lower-+.f64`
4×	`lower-/.f32`
4×	`lower-+.f32`
2×	`lift-sqrt.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
0	12	29
1	15	29
0	15	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))
(/.f64 #s(literal 1 binary64) (fma.f64 x x y))
(fma.f64 x x y)
x
y

Outputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))
(/.f64 #s(literal 1 binary64) (fma.f64 x x y))
(fma.f64 x x y)
x
y

localize24.0ms (0.6%)

Memory

-6.5MiB live, 43.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x y)
accuracy	0.20703125	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
accuracy	0.30560304665014004	(/.f64 #s(literal 1 binary64) (fma.f64 x x y))
accuracy	20.971744777811256	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))

Samples

14.0ms

256×

valid

Compiler

Compiled 35 to 10 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 3.0ms (37% of total)

ival-mult: 2.0ms (24.7% of total)

ival-sqrt: 2.0ms (24.7% of total)

ival-add: 1.0ms (12.3% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

-24.7MiB live, 11.1MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())
#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ y (pow x 3))) (/ 1 x)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (- (* 3/8 (/ y (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (- (* y (+ (* -5/16 (/ y (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (- (/ y (pow x 6)) (/ 1 (pow x 4)))) (/ 1 (pow x 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (- (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
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#s(alt (/ 1 y) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (pow x 2) y))) y) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
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#s(alt (/ (- (+ 1 (* -1 (/ (pow x 6) (pow y 3)))) (+ (* -1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y))) y) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
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#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) (taylor -inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) (taylor -inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1/2 (* (pow x 4) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 4) y) (pow (sqrt -1) 2))) (pow x 6))))) (pow y 3))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) (taylor -inf y) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (/ 1 y) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ (pow x 2) y) 1) y)) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) y) (pow x 4)) y)) (pow x 2)) y)) 1) y)) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
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#s(alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
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#s(alt (+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* (pow x 2) (+ (* -5/16 (* (pow x 2) (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
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#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))
0.0ms	x	@	inf	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))
0.0ms	y	@	inf	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))
0.0ms	y	@	-inf	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))
0.0ms	y	@	0	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))

simplify208.0ms (5.5%)

Memory

20.8MiB live, 258.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 592×	`lower-fma.f64`
11 592×	`lower-fma.f32`
4 132×	`lower-*.f64`
4 132×	`lower-*.f32`
3 602×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	298	1500
1	871	1439
2	2637	1413
3	6279	1393
0	8403	1296

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 91

Calls

Call 1

Inputs
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(/ 1 x)
(+ (* -1/2 (/ y (pow x 3))) (/ 1 x))
(+ (* y (- (* 3/8 (/ y (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+ (* y (- (* y (+ (* -5/16 (/ y (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(/ 1 (pow x 2))
(+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 2)))
(+ (* y (- (/ y (pow x 6)) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(+ (* y (- (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5)))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 4) y)) (pow x 6)))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))))))
(/ 1 y)
(/ (+ 1 (* -1 (/ (pow x 2) y))) y)
(/ (- (+ 1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y)) y)
(/ (- (+ 1 (* -1 (/ (pow x 6) (pow y 3)))) (+ (* -1 (/ (pow x 4) (pow y 2))) (/ (pow x 2) y))) y)
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (pow x 4) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 4) y) (pow (sqrt -1) 2))) (pow x 6))))) (pow y 3))) (+ (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(/ 1 y)
(* -1 (/ (- (/ (pow x 2) y) 1) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 2)) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) y) (pow x 4)) y)) (pow x 2)) y)) 1) y))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* (pow x 2) (+ (* -5/16 (* (pow x 2) (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))
(/ 1 y)
(+ (* -1 (/ (pow x 2) (pow y 2))) (/ 1 y))
(+ (* (pow x 2) (- (/ (pow x 2) (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(+ (* (pow x 2) (- (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(/ 1 x)
(/ (+ 1 (* -1/2 (/ y (pow x 2)))) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x)
(/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x)
(/ 1 (pow x 2))
(/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(/ -1 x)
(* -1 (/ (+ 1 (* -1/2 (/ y (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))) (pow x 4))) (* -1/2 (/ (+ (* 1/2 (* y (+ (* -1 (pow y 2)) (* 1/4 (pow y 2))))) (pow y 3)) (pow x 6)))))) x))
(/ 1 (pow x 2))
(/ (+ 1 (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))) (pow x 2))
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 6)))) (+ (* -1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2)))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))

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

rewrite119.0ms (3.1%)

Memory

-14.6MiB live, 74.0MiB allocated

Rules

1 392×	`lower-*.f64`
1 392×	`lower-*.f32`
1 204×	`lower-fma.f32`
1 202×	`lower-fma.f64`
1 002×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	26
0	12	26
1	49	21
2	277	21
0	2317	21

Stop Event

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

Counts

4 → 282

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))
(/.f64 #s(literal 1 binary64) (fma.f64 x x y))
(fma.f64 x x y)

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

eval62.0ms (1.6%)

Memory: 4.4MiB live, 76.3MiB allocated
Compiler: Compiled 7 238 to 1 356 computations (81.3% saved)

prune16.0ms (0.4%)

Memory

-17.4MiB live, 28.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	373	0	373
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	373	6	379

Accuracy

100.0%

Counts

379 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
✓	66.5%	(sqrt.f64 (fma.f64 x x y))
✓	31.7%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	65.5%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	37.7%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 93 to 62 computations (33.3% saved)

regimes17.0ms (0.5%)

Memory

32.2MiB live, 32.2MiB allocated

Counts

9 → 2

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
100.0%	2	`x`
84.3%	2	`y`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes14.0ms (0.4%)

Memory

-9.3MiB live, 27.1MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
66.5%	1	`y`
66.5%	1	`x`
66.5%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
66.5%	1	`(+.f64 (*.f64 x x) y)`
66.5%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes12.0ms (0.3%)

Memory

-17.9MiB live, 20.5MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	(+.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
53.6%	2	`y`
55.4%	2	`x`
42.1%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
42.1%	2	`(+.f64 (*.f64 x x) y)`
55.4%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes8.0ms (0.2%)

Memory

14.1MiB live, 14.1MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	x
2.0ms	y
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
37.7%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
37.7%	1	`(+.f64 (*.f64 x x) y)`
37.7%	1	`y`
37.7%	1	`x`
37.7%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes7.0ms (0.2%)

Memory

14.7MiB live, 14.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
1.3%	1	`x`
1.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.3%	1	`(+.f64 (*.f64 x x) y)`
1.3%	1	`(*.f64 x x)`
1.3%	1	`y`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.3071917975844144e+235	1.0094853176135619e+239

Compiler

Compiled 9 to 10 computations (-11.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.0202488389491196e-207	1.0902167525169235e-174

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify36.0ms (1%)

Memory

-36.8MiB live, 47.3MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`-commutative-binary64-.f64`
2×	`neg-sub0-binary64--.f64-neg.f64`
2×	`+-commutative-binary64-+.f64`
2×	`neg-mul-1-binary64-*.f64-neg.f64`
2×	`sub-neg-binary64-neg.f64-+.f64--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	72
1	28	72
2	30	72
3	31	72

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) #s(literal 50000000000000002658300983132982451780169472876225504866784864935219457611460827972975021456746524545128608409062560469814752225690268269365846081545102019383495851986671117567248753418814166156177318917645740336056184652851795690782720 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 (.f64 x x) #s(literal 7229475734293037/1445895146858607358437943727208769466035893202868007692637901788601699241144933631951807447549557758449099707135121406247999127995329736165184795181305316406492567598839150653733187621116264206194563768053163279547256274944 binary64)) #s(approx (sqrt (+ ( x x) y)) (sqrt.f64 y)) (sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Outputs
(if (<=.f64 (.f64 x x) #s(literal 50000000000000002658300983132982451780169472876225504866784864935219457611460827972975021456746524545128608409062560469814752225690268269365846081545102019383495851986671117567248753418814166156177318917645740336056184652851795690782720 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 (.f64 x x) #s(literal 7229475734293037/1445895146858607358437943727208769466035893202868007692637901788601699241144933631951807447549557758449099707135121406247999127995329736165184795181305316406492567598839150653733187621116264206194563768053163279547256274944 binary64)) #s(approx (sqrt (+ ( x x) y)) (sqrt.f64 y)) (sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

soundness652.0ms (17.2%)

Memory

0.6MiB live, 367.7MiB allocated

Rules

23 502×	`lower-fma.f64`
23 502×	`lower-fma.f32`
5 416×	`lower-*.f64`
5 416×	`lower-*.f32`
5 034×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12
0	133	615
1	383	600
2	1202	592
3	4035	567
0	8298	515

Stop Event

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

Compiler

Compiled 81 to 53 computations (34.6% saved)

preprocess102.0ms (2.7%)

Memory: 6.1MiB live, 78.8MiB allocated
Compiler: Compiled 192 to 108 computations (43.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

start0.0ms (0%)

analyze19.0ms (0.5%)

sample712.0ms (18.8%)

explain61.0ms (1.6%)

preprocess25.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize17.0ms (0.4%)

series7.0ms (0.2%)

simplify254.0ms (6.7%)

rewrite192.0ms (5.1%)

eval53.0ms (1.4%)

prune36.0ms (0.9%)

simplify31.0ms (0.8%)

localize38.0ms (1%)

series14.0ms (0.4%)

simplify202.0ms (5.3%)

rewrite181.0ms (4.8%)

eval137.0ms (3.6%)

prune18.0ms (0.5%)

simplify5.0ms (0.1%)

localize24.0ms (0.6%)

series9.0ms (0.2%)

simplify167.0ms (4.4%)

rewrite147.0ms (3.9%)

eval137.0ms (3.6%)

prune13.0ms (0.3%)

simplify4.0ms (0.1%)

localize24.0ms (0.6%)

series8.0ms (0.2%)

simplify208.0ms (5.5%)

rewrite119.0ms (3.1%)

eval62.0ms (1.6%)

prune16.0ms (0.4%)

regimes17.0ms (0.5%)

regimes14.0ms (0.4%)

regimes12.0ms (0.3%)

regimes8.0ms (0.2%)

regimes7.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify36.0ms (1%)

soundness652.0ms (17.2%)

preprocess102.0ms (2.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5