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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze29.0ms (0.9%)

Memory

-8.2MiB live, 30.7MiB 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)

sample939.0ms (29.6%)

Memory

33.1MiB live, 982.9MiB allocated

Samples

455.0ms	8 256×	0	valid
12.0ms	325×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 200.0ms

ival-add: 64.0ms (32% of total)

ival-sqrt: 64.0ms (32% of total)

ival-mult: 63.0ms (31.5% of total)

ival-true: 6.0ms (3% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain302.0ms (9.5%)

Memory

5.3MiB live, 88.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
87	-	-	`(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	87	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	87
↳	`(*.f64 x x)`	overflow	87

Confusion

	Predicted +	Predicted -
+	87	0
-	0	169

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	87	0	0
-	0	0	169

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	169
1	87

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

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

ival-add: 11.0ms (58.5% of total)

ival-mult: 4.0ms (21.3% of total)

ival-sqrt: 3.0ms (16% of total)

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

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

preprocess22.0ms (0.7%)

Memory

-8.8MiB live, 29.2MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.4%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB 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

localize18.0ms (0.6%)

Memory

-14.7MiB live, 23.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.01953125	(+.f64 (*.f64 x x) y)
accuracy	20.20339642193439	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

13.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (43% of total)

ival-sqrt: 2.0ms (43% of total)

ival-add: 1.0ms (21.5% of total)

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

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

series6.0ms (0.2%)

Memory

7.4MiB live, 7.4MiB 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
1.0ms	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))

simplify220.0ms (6.9%)

Memory

-3.5MiB live, 306.0MiB 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)

rewrite182.0ms (5.7%)

Memory

-10.7MiB live, 278.3MiB 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
#<batchref>
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eval35.0ms (1.1%)

Memory: 2.2MiB live, 80.9MiB allocated
Compiler: Compiled 6 400 to 869 computations (86.4% saved)

prune10.0ms (0.3%)

Memory

-0.6MiB live, 36.1MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	278	5	283
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	279	5	284

Accuracy

100.0%

Counts

284 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.4%	(sqrt.f64 (fma.f64 x x y))
▶	35.6%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
▶	67.7%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
▶	35.6%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 46 to 46 computations (0% saved)

simplify27.0ms (0.9%)

Memory

11.6MiB live, 51.2MiB 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

localize61.0ms (1.9%)

Memory

9.0MiB live, 48.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.0859375	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
accuracy	20.40967488355311	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
accuracy	0	(*.f64 x x)
accuracy	10.17418621416735	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
accuracy	20.831085961927045	#s(approx (+ (* x x) y) (*.f64 x x))
accuracy	0	(sqrt.f64 y)
accuracy	21.959304504301283	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0	(neg.f64 x)
accuracy	44.12337074395303	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
accuracy	0	(fma.f64 x x y)
accuracy	10.17418621416735	(sqrt.f64 (fma.f64 x x y))

Samples

46.0ms	179×	0	valid
6.0ms	77×	0	invalid

Compiler

Compiled 67 to 13 computations (80.6% saved)

Precisions

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

ival-mult: 3.0ms (26.1% of total)

ival-sqrt: 3.0ms (26.1% of total)

ival-div: 2.0ms (17.4% of total)

ival-add: 2.0ms (17.4% of total)

ival-neg: 1.0ms (8.7% of total)

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

exact: 0.0ms (0% of total)

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

series16.0ms (0.5%)

Memory

-20.1MiB live, 25.4MiB 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>) () ())) ())
#s(alt (+ x (* 1/2 (/ y 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>) () ())) ())
#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)) (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 (* 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)) (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 0 y) (#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 (+ x (* 1/2 (/ y x))) (taylor 0 y) (#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 (+ x (* 1/2 (/ y x))) (taylor 0 y) (#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 (+ x (* 1/2 (/ y x))) (taylor 0 y) (#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 (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (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 (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (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 (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (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 (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<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 (sqrt y) (taylor inf 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 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf 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 (* 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 #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) #<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 #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf 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 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf 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 (* 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 #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (patch #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 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 #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 inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf 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 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf 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 (* 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 #s(approx (+ (* x x) y) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<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 #s(approx (+ (* x x) y) (.f64 x x))) (patch (sqrt.f64 #s(approx (+ ( x x) y) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt y (taylor inf 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 (+ 1 (/ (pow x 2) y))) (taylor inf 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 (+ 1 (/ (pow x 2) y))) (taylor inf 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 (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt #s(approx (+ (* x x) y) (.f64 x x)) (patch #s(approx (+ ( x x) y) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf 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>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf 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>) () ())) ())
#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 #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 (* 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 #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 (* 1/2 (/ y x)) (taylor inf y) (#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 (* y (+ (* 1/2 (/ 1 x)) (/ x y))) (taylor inf y) (#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 (* y (+ (* 1/2 (/ 1 x)) (/ x y))) (taylor inf y) (#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 (* y (+ (* 1/2 (/ 1 x)) (/ x y))) (taylor inf y) (#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 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.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 (fma.f64 x x y)) (patch (sqrt.f64 (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))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (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 (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<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>) () ())) ())
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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 #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 (+ (* -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 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 (* 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 (* 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 (* 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 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 (* 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 (* 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 (* 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 (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (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 (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (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 (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (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>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.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 (fma.f64 x x y)) (patch (sqrt.f64 (fma.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 (fma.f64 x x y)) (patch (sqrt.f64 (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 #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 (* 1/2 (/ 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))) (* 1/2 (/ 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	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	@	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	@	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))

simplify252.0ms (8%)

Memory

1.9MiB live, 277.4MiB 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)
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(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
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(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/2 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 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 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)))
(* 1/2 (/ y x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (fma.f64 y #s(literal 1/2 binary64) (*.f64 x x)) 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)
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 (.f64 #s(literal -1/8 binary64) x) (.f64 (/.f64 y (pow.f64 x #s(literal 4 binary64))) y) (fma.f64 (/.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 (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)) 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)
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 (.f64 #s(literal -1/8 binary64) x) (.f64 (/.f64 y (pow.f64 x #s(literal 4 binary64))) y) (fma.f64 (/.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 (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)) 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)
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 (.f64 #s(literal -1/8 binary64) x) (.f64 (/.f64 y (pow.f64 x #s(literal 4 binary64))) y) (fma.f64 (/.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 (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)) x (.f64 (/.f64 #s(literal 1/2 binary64) 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 (.f64 #s(literal -1/8 binary64) x) (.f64 (/.f64 y (pow.f64 x #s(literal 4 binary64))) y) (fma.f64 (/.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 (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)) 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)
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 (.f64 #s(literal -1/8 binary64) x) (.f64 (/.f64 y (pow.f64 x #s(literal 4 binary64))) y) (fma.f64 (/.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 (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)) x (.f64 (/.f64 #s(literal 1/2 binary64) x) y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(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)
(* -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)
(* -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)

rewrite176.0ms (5.5%)

Memory

30.1MiB live, 232.1MiB 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
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eval72.0ms (2.3%)

Memory: -25.0MiB live, 130.5MiB allocated
Compiler: Compiled 7 683 to 1 037 computations (86.5% saved)

prune17.0ms (0.5%)

Memory

14.1MiB live, 53.7MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	503	0	503
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	503	5	508

Accuracy

100.0%

Counts

508 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.4%	(sqrt.f64 (fma.f64 x x y))
✓	35.6%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	67.7%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	35.6%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 52 to 40 computations (23.1% saved)

regimes15.0ms (0.5%)

Memory

2.7MiB live, 41.6MiB allocated

Counts

6 → 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))

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

Results

Accuracy	Segments	Branch
100.0%	2	`x`
84.8%	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)

regimes12.0ms (0.4%)

Memory

-6.1MiB live, 32.6MiB 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:

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

Results

Accuracy	Segments	Branch
68.4%	1	`y`
68.4%	1	`x`
68.4%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
68.4%	1	`(+.f64 (*.f64 x x) y)`
68.4%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes14.0ms (0.4%)

Memory

-24.4MiB live, 25.5MiB 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:

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

Results

Accuracy	Segments	Branch
58.0%	2	`x`
53.7%	2	`y`
45.7%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
45.7%	2	`(+.f64 (*.f64 x x) y)`
58.0%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes43.0ms (1.3%)

Memory

27.9MiB live, 66.2MiB 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:

36.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	x
2.0ms	y
2.0ms	(+.f64 (*.f64 x x) y)

Results

Accuracy	Segments	Branch
35.6%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
35.6%	1	`(+.f64 (*.f64 x x) y)`
35.6%	1	`y`
35.6%	1	`x`
35.6%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes9.0ms (0.3%)

Memory

-15.0MiB live, 23.3MiB 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:

3.0ms	x
1.0ms	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
1.2%	1	`y`
1.2%	1	`x`
1.2%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.2%	1	`(+.f64 (*.f64 x x) y)`
1.2%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	5.941811018132124e+244	1.8931982645481765e+248

Compiler

Compiled 9 to 10 computations (-11.1% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.548591428703371e-99	2.2712783010812868e-95

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify29.0ms (0.9%)

Memory

-12.1MiB live, 68.2MiB 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 100000000000000004432795665958347438500428966608636256080197937830963477082618911859584178365170076692451010888562841972100410265623306726829729177688912148325455279810104971033102576911999816916636238052732752107272876955671430431745947427930112 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 6156563468186637/615656346818663737691860001564743965704370926101022604186692084441339402679643915803347910232576806887603562348544 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 100000000000000004432795665958347438500428966608636256080197937830963477082618911859584178365170076692451010888562841972100410265623306726829729177688912148325455279810104971033102576911999816916636238052732752107272876955671430431745947427930112 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 6156563468186637/615656346818663737691860001564743965704370926101022604186692084441339402679643915803347910232576806887603562348544 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))

soundness574.0ms (18.1%)

Memory

18.2MiB live, 372.4MiB 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)

preprocess86.0ms (2.7%)

Memory: -14.0MiB live, 163.9MiB 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%)

analyze29.0ms (0.9%)

sample939.0ms (29.6%)

explain302.0ms (9.5%)

preprocess22.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize18.0ms (0.6%)

series6.0ms (0.2%)

simplify220.0ms (6.9%)

rewrite182.0ms (5.7%)

eval35.0ms (1.1%)

prune10.0ms (0.3%)

simplify27.0ms (0.9%)

localize61.0ms (1.9%)

series16.0ms (0.5%)

simplify252.0ms (8%)

rewrite176.0ms (5.5%)

eval72.0ms (2.3%)

prune17.0ms (0.5%)

regimes15.0ms (0.5%)

regimes12.0ms (0.4%)

regimes14.0ms (0.4%)

regimes43.0ms (1.3%)

regimes9.0ms (0.3%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify29.0ms (0.9%)

soundness574.0ms (18.1%)

preprocess86.0ms (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