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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze20.0ms (0.7%)

Memory

-1.1MiB live, 37.1MiB 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)

sample673.0ms (22.7%)

Memory

28.8MiB live, 1 012.7MiB allocated

Samples

445.0ms	8 256×	0	valid
14.0ms	334×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 252.0ms

ival-mult: 103.0ms (40.8% of total)

ival-sqrt: 97.0ms (38.4% of total)

ival-add: 43.0ms (17% of total)

ival-true: 6.0ms (2.4% of total)

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

Bogosity

explain122.0ms (4.1%)

Memory

-5.3MiB live, 147.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
79	-	-	`(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	79	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	79
↳	`(*.f64 x x)`	overflow	79

Confusion

	Predicted +	Predicted -
+	79	0
-	0	177

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	79	0	0
-	0	0	177

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	177
1	79

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

40.0ms

512×

valid

Compiler

Compiled 90 to 34 computations (62.2% saved)

Precisions

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

ival-mult: 4.0ms (36% of total)

ival-sqrt: 4.0ms (36% of total)

ival-add: 2.0ms (18% of total)

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

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

preprocess35.0ms (1.2%)

Memory

-23.3MiB live, 27.9MiB allocated

Algorithm

1×	egg-herbie

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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.2%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Memory

1.1MiB live, 1.1MiB 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)

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.6%)

Memory

11.2MiB live, 11.2MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (*.f64 x x) y)
accuracy	18.44686660214092	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

12.0ms

256×

valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

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

ival-mult: 2.0ms (36.1% of total)

ival-sqrt: 2.0ms (36.1% of total)

ival-add: 1.0ms (18.1% of total)

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

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

series6.0ms (0.2%)

Memory

4.4MiB live, 4.4MiB 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))

simplify190.0ms (6.4%)

Memory

8.3MiB live, 203.1MiB allocated

Algorithm

1×	egg-herbie

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)

rewrite163.0ms (5.5%)

Memory

9.3MiB live, 130.6MiB allocated

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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eval48.0ms (1.6%)

Memory: -27.0MiB live, 47.8MiB allocated
Compiler: Compiled 6 400 to 869 computations (86.4% saved)

prune7.0ms (0.2%)

Memory

17.8MiB live, 17.8MiB 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
▶	71.2%	(sqrt.f64 (fma.f64 x x y))
▶	34.9%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
▶	64.5%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
▶	37.9%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 46 to 46 computations (0% saved)

simplify29.0ms (1%)

Memory

-15.0MiB live, 23.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

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

localize50.0ms (1.7%)

Memory

-5.5MiB live, 38.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.046875	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
accuracy	22.508387614283173	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
accuracy	0	(*.f64 x x)
accuracy	9.101487123797698	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
accuracy	22.91828745147333	#s(approx (+ (* x x) y) (*.f64 x x))
accuracy	0	(sqrt.f64 y)
accuracy	19.474241678073795	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0	(neg.f64 x)
accuracy	43.06672672293504	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
accuracy	0	(fma.f64 x x y)
accuracy	9.101487123797698	(sqrt.f64 (fma.f64 x x y))

Samples

15.0ms	175×	0	valid
7.0ms	81×	0	invalid

Compiler

Compiled 122 to 28 computations (77% saved)

Precisions

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

ival-mult: 3.0ms (24.4% of total)

ival-sqrt: 3.0ms (24.4% of total)

ival-div: 2.0ms (16.2% of total)

ival-add: 2.0ms (16.2% of total)

ival-neg: 1.0ms (8.1% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.4%)

Memory

18.5MiB live, 18.5MiB 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>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (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 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) (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 (* -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 #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) (patch #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) #<representation binary64>) () ())) ())
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#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))

simplify274.0ms (9.2%)

Memory

-26.6MiB live, 204.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 221

Calls

Call 1

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

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

rewrite218.0ms (7.3%)

Memory

-20.1MiB live, 55.2MiB allocated

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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eval100.0ms (3.4%)

Memory: 3.7MiB live, 82.4MiB allocated
Compiler: Compiled 7 683 to 1 038 computations (86.5% saved)

prune16.0ms (0.6%)

Memory

24.7MiB live, 24.7MiB 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
✓	71.2%	(sqrt.f64 (fma.f64 x x y))
✓	34.9%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	64.5%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	37.9%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 52 to 40 computations (23.1% saved)

regimes14.0ms (0.5%)

Memory

9.4MiB live, 9.4MiB 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 (+.f64 (*.f64 x x) y))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
100.0%	2	`x`
85.4%	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)

regimes23.0ms (0.8%)

Memory

-31.6MiB live, 8.0MiB allocated

Counts

5 → 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))

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

4 calls:

15.0ms	(*.f64 x x)
2.0ms	(+.f64 (*.f64 x x) y)
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

Results

Accuracy	Segments	Branch
100.0%	2	`x`
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 15 to 14 computations (6.7% saved)

regimes11.0ms (0.4%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
71.2%	1	`y`
71.2%	1	`x`
71.2%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
71.2%	1	`(+.f64 (*.f64 x x) y)`
71.2%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes10.0ms (0.3%)

Memory

16.6MiB live, 16.6MiB 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	y
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	x
2.0ms	(+.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
60.9%	2	`x`
44.1%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
44.1%	2	`(+.f64 (*.f64 x x) y)`
60.9%	2	`(*.f64 x x)`
58.3%	2	`y`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes48.0ms (1.6%)

Memory

-26.6MiB live, 12.6MiB 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:

41.0ms	x
2.0ms	y
2.0ms	(+.f64 (*.f64 x x) y)
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
37.9%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
37.9%	1	`(+.f64 (*.f64 x x) y)`
37.9%	1	`y`
37.9%	1	`x`
37.9%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes7.0ms (0.2%)

Memory

14.0MiB live, 14.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

1.0ms	x
1.0ms	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
1.3%	1	`x`
1.3%	1	`y`
1.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.3%	1	`(+.f64 (*.f64 x x) y)`
1.3%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.558792571223761e+237	1.4743328926559202e+238

Compiler

Compiled 9 to 10 computations (-11.1% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.558792571223761e+237	1.4743328926559202e+238

Compiler

Compiled 9 to 10 computations (-11.1% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.8280504536820937e-91	1.0640962191042392e-87

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify39.0ms (1.3%)

Memory

-12.9MiB live, 34.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	97
1	32	97
2	34	97
3	35	97

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) #s(literal 5000000000000000243237986643632505202424076549985527579867655198709325563678867350395951502785064455265869472944416071214292298582754854311598233227483074357337160490771542905278506610019687651036675311822945811815559589454503326152392704 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(if (<=.f64 (.f64 x x) #s(literal 5000000000000000243237986643632505202424076549985527579867655198709325563678867350395951502785064455265869472944416071214292298582754854311598233227483074357337160490771542905278506610019687651036675311822945811815559589454503326152392704 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 4586997231980143/9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496 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 5000000000000000243237986643632505202424076549985527579867655198709325563678867350395951502785064455265869472944416071214292298582754854311598233227483074357337160490771542905278506610019687651036675311822945811815559589454503326152392704 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(if (<=.f64 (.f64 x x) #s(literal 5000000000000000243237986643632505202424076549985527579867655198709325563678867350395951502785064455265869472944416071214292298582754854311598233227483074357337160490771542905278506610019687651036675311822945811815559589454503326152392704 binary64)) (sqrt.f64 (+.f64 y (.f64 x x))) #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(if (<=.f64 (.f64 x x) #s(literal 5000000000000000243237986643632505202424076549985527579867655198709325563678867350395951502785064455265869472944416071214292298582754854311598233227483074357337160490771542905278506610019687651036675311822945811815559589454503326152392704 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 4586997231980143/9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496 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))

soundness669.0ms (22.5%)

Memory

-3.4MiB live, 265.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 106 to 61 computations (42.5% saved)

preprocess164.0ms (5.5%)

Memory: 18.5MiB live, 141.4MiB allocated
Compiler: Compiled 232 to 114 computations (50.9% 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%)

analyze20.0ms (0.7%)

sample673.0ms (22.7%)

explain122.0ms (4.1%)

preprocess35.0ms (1.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize17.0ms (0.6%)

series6.0ms (0.2%)

simplify190.0ms (6.4%)

rewrite163.0ms (5.5%)

eval48.0ms (1.6%)

prune7.0ms (0.2%)

simplify29.0ms (1%)

localize50.0ms (1.7%)

series12.0ms (0.4%)

simplify274.0ms (9.2%)

rewrite218.0ms (7.3%)

eval100.0ms (3.4%)

prune16.0ms (0.6%)

regimes14.0ms (0.5%)

regimes23.0ms (0.8%)

regimes11.0ms (0.4%)

regimes10.0ms (0.3%)

regimes48.0ms (1.6%)

regimes7.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify39.0ms (1.3%)

soundness669.0ms (22.5%)

preprocess164.0ms (5.5%)

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