Metrics for Optimisation.CirclePacking:place from circle-packing-0.1.0.4, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze16.0ms (0.4%)

Memory

-14.3MiB live, 24.6MiB 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
25%	25%	74.9%	0.1%	0%	0%	0%	3
28.6%	25%	62.4%	0.1%	0%	12.5%	0%	4
46.2%	37.5%	43.7%	0.1%	0%	18.7%	0%	5
52.2%	37.5%	34.3%	0.1%	0%	28.1%	0%	6
65.1%	43.7%	23.4%	0.1%	0%	32.8%	0%	7
70.9%	43.7%	18%	0.1%	0%	38.2%	0%	8
79.5%	46.8%	12.1%	0.1%	0%	41%	0%	9
83.6%	46.8%	9.2%	0.1%	0%	43.9%	0%	10
88.7%	48.4%	6.1%	0.1%	0%	45.4%	0%	11
91.3%	48.4%	4.6%	0.1%	0%	46.9%	0%	12

Compiler

Compiled 6 to 6 computations (0% saved)

sample1.0s (24.3%)

Memory

16.8MiB live, 482.2MiB allocated

Samples

609.0ms	8 256×	0	valid
15.0ms	488×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 369.0ms

ival-add: 303.0ms (82.1% of total)

ival-sqrt: 57.0ms (15.4% of total)

ival-true: 5.0ms (1.4% of total)

ival-assert: 4.0ms (1.1% of total)

Bogosity

explain35.0ms (0.8%)

Memory

20.1MiB live, 20.1MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(sqrt.f64 (+.f64 x y))`
-	-	`y`
-	-	`(+.f64 x y)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

17.0ms

512×

valid

Compiler

Compiled 26 to 16 computations (38.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-add: 3.0ms (45.3% of total)

ival-sqrt: 3.0ms (45.3% of total)

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

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

preprocess16.0ms (0.4%)

Memory

6.8MiB live, 6.8MiB allocated

Algorithm

1×	egg-herbie

Rules

44×	`sub-neg`
28×	`associate--r+`
24×	`neg-mul-1`
22×	`cancel-sign-sub-inv`
22×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort x y)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify3.0ms (0.1%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
1	7	9
0	7	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize92.0ms (2.2%)

Memory

-31.3MiB live, 7.8MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

89.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 2.0ms (60.9% of total)

ival-add: 1.0ms (30.4% of total)

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

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

series5.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB allocated

Counts

2 → 48

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	y	@	inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	inf	((sqrt (+ x y)) (+ x y))
0.0ms	y	@	0	((sqrt (+ x y)) (+ x y))

simplify366.0ms (8.8%)

Memory

-15.3MiB live, 81.9MiB allocated

Algorithm

1×	egg-herbie

Rules

27 648×	`lower-fma.f64`
27 648×	`lower-fma.f32`
5 638×	`lower-*.f64`
5 638×	`lower-*.f32`
2 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	630
1	454	600
2	1426	582
3	4628	570
0	8167	534

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 42

Calls

Call 1

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

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

rewrite258.0ms (6.2%)

Memory

14.8MiB live, 85.7MiB allocated

Rules

5 128×	`lower-fma.f64`
5 128×	`lower-fma.f32`
4 292×	`lower-/.f64`
4 292×	`lower-/.f32`
3 378×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	22	7
2	145	7
3	1366	7
0	8310	7

Stop Event

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

Counts

2 → 226

Calls

Call 1

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

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

eval117.0ms (2.8%)

Memory: -17.8MiB live, 35.1MiB allocated
Compiler: Compiled 5 681 to 881 computations (84.5% saved)

prune71.0ms (1.7%)

Memory

2.4MiB live, 78.4MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	266	2	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	266	3	269

Accuracy

100.0%

Counts

269 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.7%	(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	98.4%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 14 to 14 computations (0% saved)

simplify4.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score
cost-diff	5824	(pow.f64 x #s(literal 1/2 binary64))
cost-diff	5824	(pow.f64 y #s(literal 1/2 binary64))
cost-diff	6912	(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Rules

8×	`lower-pow.f32`
6×	`lower-sqrt.f32`
4×	`lower-hypot.f32`
4×	`lower-sqrt.f64`
4×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
0	17	22
1	26	21
2	28	21
3	30	21
0	30	21

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize28.0ms (0.7%)

Memory

-15.1MiB live, 66.6MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 y #s(literal 1/2 binary64))
accuracy	0	(pow.f64 x #s(literal 1/2 binary64))
accuracy	0.00390625	(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
accuracy	0	(sqrt.f64 y)
accuracy	0.8403529509589929	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Samples

14.0ms	135×	0	valid
8.0ms	121×	0	invalid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

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

ival-hypot: 5.0ms (44.5% of total)

ival-sqrt: 4.0ms (35.6% of total)

ival-add: 1.0ms (8.9% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB allocated

Counts

5 → 84

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((sqrt (+ x y)) (sqrt y) (sqrt (+ (* (pow y 1/2) (pow y 1/2)) (* (pow x 1/2) (pow x 1/2)))) (pow y 1/2) (pow x 1/2))
1.0ms	y	@	0	((sqrt (+ x y)) (sqrt y) (sqrt (+ (* (pow y 1/2) (pow y 1/2)) (* (pow x 1/2) (pow x 1/2)))) (pow y 1/2) (pow x 1/2))
1.0ms	x	@	-inf	((sqrt (+ x y)) (sqrt y) (sqrt (+ (* (pow y 1/2) (pow y 1/2)) (* (pow x 1/2) (pow x 1/2)))) (pow y 1/2) (pow x 1/2))
0.0ms	y	@	inf	((sqrt (+ x y)) (sqrt y) (sqrt (+ (* (pow y 1/2) (pow y 1/2)) (* (pow x 1/2) (pow x 1/2)))) (pow y 1/2) (pow x 1/2))
0.0ms	x	@	0	((sqrt (+ x y)) (sqrt y) (sqrt (+ (* (pow y 1/2) (pow y 1/2)) (* (pow x 1/2) (pow x 1/2)))) (pow y 1/2) (pow x 1/2))

simplify259.0ms (6.2%)

Memory

-4.2MiB live, 388.4MiB allocated

Algorithm

1×	egg-herbie

Rules

30 238×	`lower-fma.f64`
30 238×	`lower-fma.f32`
5 102×	`lower-*.f64`
5 102×	`lower-*.f32`
3 164×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	141	1212
1	405	1152
2	1310	1116
3	3611	1072
4	7975	1072
0	8051	1004

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

rewrite251.0ms (6%)

Memory

23.4MiB live, 264.4MiB allocated

Rules

4 838×	`lower-fma.f64`
4 838×	`lower-fma.f32`
3 762×	`lower-*.f64`
3 762×	`lower-*.f32`
2 448×	`lower-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	22
0	17	18
1	70	17
2	414	17
3	4121	17
0	8473	17

Stop Event

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

Counts

5 → 103

Calls

Call 1

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

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

eval21.0ms (0.5%)

Memory: -20.7MiB live, 56.8MiB allocated
Compiler: Compiled 2 223 to 391 computations (82.4% saved)

prune19.0ms (0.4%)

Memory

29.3MiB live, 68.3MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	187	3	190

Accuracy

100.0%

Counts

190 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.7%	(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.4%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 12 to 13 computations (-8.3% saved)

simplify5.0ms (0.1%)

Memory

-32.6MiB live, 10.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(sqrt.f64 y)
cost-diff	6912	(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
0	11	10
1	13	10
2	15	10
0	15	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (0.4%)

Memory

10.9MiB live, 50.0MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 y)
accuracy	0	(sqrt.f64 x)
accuracy	0.00390625	(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))

Samples

8.0ms	135×	0	valid
6.0ms	121×	0	invalid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

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

ival-hypot: 5.0ms (62.9% of total)

ival-sqrt: 3.0ms (37.8% of total)

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

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

series3.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Counts

3 → 48

Calls

Call 1

Inputs

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

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

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((sqrt (+ (* (sqrt y) (sqrt y)) (* (sqrt x) (sqrt x)))) (sqrt y) (sqrt x))
1.0ms	y	@	-inf	((sqrt (+ (* (sqrt y) (sqrt y)) (* (sqrt x) (sqrt x)))) (sqrt y) (sqrt x))
0.0ms	y	@	inf	((sqrt (+ (* (sqrt y) (sqrt y)) (* (sqrt x) (sqrt x)))) (sqrt y) (sqrt x))
0.0ms	x	@	inf	((sqrt (+ (* (sqrt y) (sqrt y)) (* (sqrt x) (sqrt x)))) (sqrt y) (sqrt x))
0.0ms	y	@	0	((sqrt (+ (* (sqrt y) (sqrt y)) (* (sqrt x) (sqrt x)))) (sqrt y) (sqrt x))

simplify265.0ms (6.4%)

Memory

-11.8MiB live, 383.5MiB allocated

Algorithm

1×	egg-herbie

Rules

30 238×	`lower-fma.f64`
30 238×	`lower-fma.f32`
5 102×	`lower-*.f64`
5 102×	`lower-*.f32`
3 164×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	141	618
1	405	588
2	1310	570
3	3611	548
4	7975	548
0	8051	514

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite137.0ms (3.3%)

Memory

28.6MiB live, 303.1MiB allocated

Rules

5 088×	`lower-fma.f64`
5 088×	`lower-fma.f32`
3 410×	`lower-*.f64`
3 410×	`lower-*.f32`
2 868×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
0	11	8
1	35	8
2	234	8
3	2168	8
0	8135	8

Stop Event

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

Counts

3 → 122

Calls

Call 1

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

Outputs
(.f64 (sqrt.f64 (/.f64 (.f64 (-.f64 y x) (+.f64 x y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 x (+.f64 x y) (*.f64 y y))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 x y) x) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (.f64 y y) (.f64 (-.f64 x y) x))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 x y) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (.f64 (-.f64 x y) x) (-.f64 (.f64 (-.f64 x y) x) (*.f64 y y)) (pow.f64 y #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (/.f64 (.f64 (-.f64 y x) (+.f64 x y)) (*.f64 (-.f64 y x) (+.f64 x y)))) (sqrt.f64 (+.f64 x y)))
(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
(.f64 (sqrt.f64 (.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (.f64 (-.f64 y x) (+.f64 x y)))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 y x)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (fma.f64 (-.f64 x y) x (.f64 y y))) #s(literal -1 binary64))))
(.f64 (pow.f64 (-.f64 y x) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (-.f64 y x) (+.f64 x y))))
(.f64 (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1/2 binary64)) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 (-.f64 y x) (+.f64 x y))) (pow.f64 (-.f64 y x) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (.f64 y y))) (sqrt.f64 (/.f64 (+.f64 x y) (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (.f64 y y))) (sqrt.f64 (.f64 (+.f64 x y) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64)))))
(.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x y)))
(*.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (/.f64 (-.f64 y x) (-.f64 y x))))
(.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (.f64 (-.f64 y x) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (+.f64 x y)))
(pow.f64 (sqrt.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (+.f64 x y) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 y x) (+.f64 x y))))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 y x)))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y)))) (neg.f64 (sqrt.f64 (-.f64 x y))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 x y))))) (neg.f64 (sqrt.f64 (neg.f64 (-.f64 y x)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))) (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (-.f64 y x) (+.f64 x y)) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))) (hypot.f64 x y))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x x (*.f64 y y)) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 x y) #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (-.f64 x y) x (.f64 y y))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 y x))) #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 x (-.f64 y x))) #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 y (/.f64 y (-.f64 y x)) (*.f64 x (/.f64 x (-.f64 y x))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (-.f64 y x) #s(literal 3 binary64))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 y x) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 y x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 y x))) #s(literal 2 binary64)) (.f64 (.f64 y (/.f64 y (-.f64 y x))) (*.f64 x (/.f64 x (-.f64 y x))))))))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 x y)))) (sqrt.f64 (neg.f64 (-.f64 x y))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 x y))))) (sqrt.f64 (neg.f64 (neg.f64 (-.f64 y x)))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (fma.f64 x x (*.f64 y y)) (-.f64 y x))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (fma.f64 x x (.f64 y y)) (pow.f64 y #s(literal 4 binary64))) (-.f64 y x))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (.f64 x y) #s(literal 3 binary64))) (fma.f64 (-.f64 x y) x (.f64 y y)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 y y) (-.f64 y x)) (.f64 (-.f64 y x) (.f64 x x)))) (sqrt.f64 (pow.f64 (-.f64 y x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 y x) (+.f64 x y)))) (neg.f64 (sqrt.f64 (-.f64 y x))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (.f64 (-.f64 y x) (fma.f64 (.f64 x x) (fma.f64 x x (*.f64 y y)) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (sqrt.f64 (.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (-.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (*.f64 x y) #s(literal 3 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 x y)))) (sqrt.f64 (neg.f64 (-.f64 y x))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (.f64 (-.f64 y x) (fma.f64 x x (.f64 y y)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 y x) (+.f64 x y))) (sqrt.f64 (-.f64 y x)))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x y) (*.f64 (+.f64 x y) (-.f64 x y)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (+.f64 x y) #s(literal -1 binary64))))
(sqrt.f64 (+.f64 x y))
(hypot.f64 (neg.f64 (sqrt.f64 y)) (neg.f64 (sqrt.f64 x)))
(hypot.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 x))
(hypot.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 y)))
(hypot.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 y))
(hypot.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 y)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 y))
(hypot.f64 (sqrt.f64 y) (neg.f64 (sqrt.f64 x)))
(hypot.f64 (sqrt.f64 y) (sqrt.f64 x))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x y) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 x y)) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 (pow.f64 y #s(literal 3/8 binary64))) (pow.f64 y #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 (pow.f64 y #s(literal 3/4 binary64))) (pow.f64 y #s(literal 1/8 binary64)))
(*.f64 (pow.f64 y #s(literal 3/8 binary64)) (pow.f64 y #s(literal 1/8 binary64)))
(*.f64 (pow.f64 y #s(literal 1/8 binary64)) (fabs.f64 (pow.f64 y #s(literal 3/8 binary64))))
(*.f64 (pow.f64 y #s(literal 1/8 binary64)) (sqrt.f64 (pow.f64 y #s(literal 3/4 binary64))))
(*.f64 (pow.f64 y #s(literal 1/8 binary64)) (pow.f64 y #s(literal 3/8 binary64)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (log.f64 y) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (sqrt.f64 y)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y))
(pow.f64 (pow.f64 y #s(literal 8 binary64)) #s(literal 1/16 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64))
(pow.f64 y #s(literal 1/2 binary64))
(sqrt.f64 y)
(fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 y))))
(fabs.f64 (neg.f64 (sqrt.f64 y)))
(fabs.f64 (sqrt.f64 y))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 y)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 y #s(literal 4 binary64))) #s(literal 1/8 binary64)))
(exp.f64 (log.f64 (sqrt.f64 y)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (fabs.f64 (pow.f64 x #s(literal 3/8 binary64))))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (sqrt.f64 x)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/16 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (-.f64 (sqrt.f64 x) #s(literal 0 binary64)))
(fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 x))))
(fabs.f64 (neg.f64 (sqrt.f64 x)))
(fabs.f64 (sqrt.f64 x))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))

eval66.0ms (1.6%)

Memory: -29.5MiB live, 101.9MiB allocated
Compiler: Compiled 2 312 to 541 computations (76.6% saved)

prune19.0ms (0.4%)

Memory

31.4MiB live, 69.3MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	170	3	173

Accuracy

100.0%

Counts

173 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.4%	(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.4%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 24 to 18 computations (25% saved)

simplify5.0ms (0.1%)

Memory

-28.7MiB live, 9.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

8×	`lift-sqrt.f64`
8×	`lower-sqrt.f32`
8×	`lower-+.f32`
4×	`lift-+.f64`
4×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	56
0	18	56
1	21	56
0	21	56

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize31.0ms (0.7%)

Memory

-6.0MiB live, 73.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.03515625	(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))
accuracy	0.0390625	(sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
accuracy	0.21550751953688402	(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
accuracy	0.2578125	(/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))

Samples

13.0ms	135×	0	valid
9.0ms	121×	0	invalid

Compiler

Compiled 58 to 12 computations (79.3% saved)

Precisions

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

ival-sqrt: 6.0ms (54.7% of total)

ival-add: 2.0ms (18.2% of total)

ival-div: 1.0ms (9.1% of total)

ival-mult: 1.0ms (9.1% of total)

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

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

series22.0ms (0.5%)

Memory

10.9MiB live, 49.1MiB allocated

Counts

5 → 120

Calls

Call 1

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

Outputs
#s(alt (sqrt x) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ x (+ (sqrt x) (sqrt y)))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ x (+ (sqrt x) (sqrt y)))) (* 1/2 (* (sqrt (/ 1 (* x (+ (sqrt x) (sqrt y))))) y))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ x (+ (sqrt x) (sqrt y)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (+ (sqrt x) (sqrt y))))) y)) (* 1/2 (sqrt (/ 1 (* x (+ (sqrt x) (sqrt y))))))))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ x (+ (sqrt x) (sqrt y)))) (* y (+ (* 1/2 (sqrt (/ 1 (* x (+ (sqrt x) (sqrt y)))))) (* y (+ (* -1/8 (sqrt (/ 1 (* (pow x 3) (+ (sqrt x) (sqrt y)))))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (+ (sqrt x) (sqrt y))))) y))))))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (/ x (+ (sqrt x) (sqrt y))) (taylor 0 y) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y)))) (taylor 0 y) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y)))) (taylor 0 y) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y)))) (taylor 0 y) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (sqrt x) (sqrt y))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (sqrt x) (sqrt y))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (sqrt x) (sqrt y))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (sqrt x) (sqrt y))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 y) 1/4) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (- (* x (sqrt y)) (* (sqrt x) y)))) (pow (* 1 y) 1/4)) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow (/ 1 (pow y 9)) 1/4) (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) y)) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) y)))))) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (- (* x (sqrt y)) (* (sqrt x) y)))) (pow (* 1 y) 1/4))) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow (/ 1 (pow y 9)) 1/4) (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) y)) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) y)))))) (+ (* -1/2 (* (pow (/ 1 (pow y 13)) 1/4) (+ (* -1 (* x (* y (- (* x (sqrt y)) (* (sqrt x) y))))) (* -1/2 (* (sqrt (/ 1 y)) (* (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) y)) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) y)))) (- (* x (sqrt y)) (* (sqrt x) y)))))))) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (- (* x (sqrt y)) (* (sqrt x) y)))) (pow (* 1 y) 1/4)))) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt y) (* x (sqrt (/ 1 y)))) (sqrt x)) (taylor inf y) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt y) (+ (* -1 (* (sqrt (/ x (pow y 3))) (- (* x (sqrt y)) (* (sqrt x) y)))) (* x (sqrt (/ 1 y))))) (sqrt x)) (taylor inf y) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt y) (+ (* x (sqrt (/ 1 y))) (/ (* x (- (* x (sqrt y)) (* (sqrt x) y))) (pow y 2)))) (+ (sqrt x) (* (sqrt (/ x (pow y 3))) (- (* x (sqrt y)) (* (sqrt x) y))))) (taylor inf y) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 y) 1/4) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (sqrt x))) (pow (/ 1 (pow y 3)) 1/4))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* -1/8 (* (pow (/ 1 (pow y 7)) 1/4) x)) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (sqrt x))) (pow (/ 1 (pow y 3)) 1/4)))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* -1/8 (* (pow (/ 1 (pow y 7)) 1/4) x)) (+ (* 1/16 (* (pow (/ 1 (pow y 9)) 1/4) (sqrt (pow x 3)))) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (sqrt x))) (pow (/ 1 (pow y 3)) 1/4))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) (taylor -inf y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) (taylor -inf y) (#s(alt (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* -1 y) 1/4) (sqrt (sqrt -1))) (taylor -inf y) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
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#s(alt (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (pow (/ -1 (pow x 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))) (* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* 1/2 (* (pow (/ -1 x) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))) (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))))))) x)) (* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (pow (/ -1 x) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))))) (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 x)) (* (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))) (/ (* x (* y (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) (pow (sqrt -1) 2))))))) x)) (* 1/2 (* (pow (/ -1 x) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))))) x)) (* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (patch (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt x)) (taylor -inf x) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) x))) (taylor -inf x) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* (sqrt x) y) (* (sqrt (/ y x)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) x))) (taylor -inf x) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* -1 (/ (- (/ (* y (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))) (pow (sqrt -1) 2)) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) x)) (* (sqrt x) y)) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) x))) (taylor -inf x) (#s(alt (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (sqrt (/ y (sqrt -1))))) (* (pow (/ -1 (pow x 3)) 1/4) (sqrt (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (pow (/ -1 (pow x 7)) 1/4) (* y (sqrt (/ 1 (pow (sqrt -1) 3)))))) (+ (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (sqrt (/ y (sqrt -1))))) (* (pow (/ -1 (pow x 3)) 1/4) (sqrt (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (pow (/ -1 (pow x 7)) 1/4) (* y (sqrt (/ 1 (pow (sqrt -1) 3)))))) (+ (* 1/16 (* (pow (/ -1 (pow x 9)) 1/4) (sqrt (/ (pow y 3) (pow (sqrt -1) 5))))) (+ (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (sqrt (/ y (sqrt -1))))) (* (pow (/ -1 (pow x 3)) 1/4) (sqrt (sqrt -1)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) (patch (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((* (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (sqrt (+ (sqrt x) (sqrt y)))) (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (/ (+ x y) (+ (sqrt x) (sqrt y))) (+ x y) (sqrt (+ (sqrt x) (sqrt y))))
4.0ms	y	@	inf	((* (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (sqrt (+ (sqrt x) (sqrt y)))) (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (/ (+ x y) (+ (sqrt x) (sqrt y))) (+ x y) (sqrt (+ (sqrt x) (sqrt y))))
4.0ms	y	@	-inf	((* (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (sqrt (+ (sqrt x) (sqrt y)))) (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (/ (+ x y) (+ (sqrt x) (sqrt y))) (+ x y) (sqrt (+ (sqrt x) (sqrt y))))
3.0ms	x	@	inf	((* (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (sqrt (+ (sqrt x) (sqrt y)))) (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (/ (+ x y) (+ (sqrt x) (sqrt y))) (+ x y) (sqrt (+ (sqrt x) (sqrt y))))
1.0ms	y	@	0	((* (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (sqrt (+ (sqrt x) (sqrt y)))) (sqrt (/ (+ x y) (+ (sqrt x) (sqrt y)))) (/ (+ x y) (+ (sqrt x) (sqrt y))) (+ x y) (sqrt (+ (sqrt x) (sqrt y))))

simplify174.0ms (4.2%)

Memory

21.8MiB live, 254.3MiB allocated

Algorithm

1×	egg-herbie

Rules

10 338×	`lower-fma.f64`
10 338×	`lower-fma.f32`
7 468×	`lower-*.f64`
7 468×	`lower-*.f32`
2 570×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	548	3236
1	1623	3016
2	6501	2976
0	8518	2816

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 114

Calls

Call 1

Inputs
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(sqrt (/ x (+ (sqrt x) (sqrt y))))
(+ (sqrt (/ x (+ (sqrt x) (sqrt y)))) (* 1/2 (* (sqrt (/ 1 (* x (+ (sqrt x) (sqrt y))))) y)))
(+ (sqrt (/ x (+ (sqrt x) (sqrt y)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (+ (sqrt x) (sqrt y))))) y)) (* 1/2 (sqrt (/ 1 (* x (+ (sqrt x) (sqrt y)))))))))
(+ (sqrt (/ x (+ (sqrt x) (sqrt y)))) (* y (+ (* 1/2 (sqrt (/ 1 (* x (+ (sqrt x) (sqrt y)))))) (* y (+ (* -1/8 (sqrt (/ 1 (* (pow x 3) (+ (sqrt x) (sqrt y)))))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (+ (sqrt x) (sqrt y))))) y)))))))
(/ x (+ (sqrt x) (sqrt y)))
(+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y))))
(+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y))))
(+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y))))
x
(+ x y)
(+ x y)
(+ x y)
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(pow (* 1 y) 1/4)
(+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (- (* x (sqrt y)) (* (sqrt x) y)))) (pow (* 1 y) 1/4))
(+ (* -1/2 (* (pow (/ 1 (pow y 9)) 1/4) (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) y)) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) y)))))) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (- (* x (sqrt y)) (* (sqrt x) y)))) (pow (* 1 y) 1/4)))
(+ (* -1/2 (* (pow (/ 1 (pow y 9)) 1/4) (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) y)) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) y)))))) (+ (* -1/2 (* (pow (/ 1 (pow y 13)) 1/4) (+ (* -1 (* x (* y (- (* x (sqrt y)) (* (sqrt x) y))))) (* -1/2 (* (sqrt (/ 1 y)) (* (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) y)) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) y)))) (- (* x (sqrt y)) (* (sqrt x) y)))))))) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (- (* x (sqrt y)) (* (sqrt x) y)))) (pow (* 1 y) 1/4))))
(sqrt y)
(- (+ (sqrt y) (* x (sqrt (/ 1 y)))) (sqrt x))
(- (+ (sqrt y) (+ (* -1 (* (sqrt (/ x (pow y 3))) (- (* x (sqrt y)) (* (sqrt x) y)))) (* x (sqrt (/ 1 y))))) (sqrt x))
(- (+ (sqrt y) (+ (* x (sqrt (/ 1 y))) (/ (* x (- (* x (sqrt y)) (* (sqrt x) y))) (pow y 2)))) (+ (sqrt x) (* (sqrt (/ x (pow y 3))) (- (* x (sqrt y)) (* (sqrt x) y)))))
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(pow (* 1 y) 1/4)
(* y (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (sqrt x))) (pow (/ 1 (pow y 3)) 1/4)))
(* y (+ (* -1/8 (* (pow (/ 1 (pow y 7)) 1/4) x)) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (sqrt x))) (pow (/ 1 (pow y 3)) 1/4))))
(* y (+ (* -1/8 (* (pow (/ 1 (pow y 7)) 1/4) x)) (+ (* 1/16 (* (pow (/ 1 (pow y 9)) 1/4) (sqrt (pow x 3)))) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (sqrt x))) (pow (/ 1 (pow y 3)) 1/4)))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* (pow (* -1 y) 1/4) (sqrt (sqrt -1)))
(+ (* -1/2 (* (pow (/ -1 (pow y 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2))))))) (* (pow (* -1 y) 1/4) (sqrt (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (* (pow (/ -1 y) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2))))))) (* 1/2 (* (pow (/ -1 (pow y 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))))))))) y)) (* (pow (* -1 y) 1/4) (sqrt (sqrt -1))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (pow (/ -1 y) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2))))))))) (* 1/2 (* (pow (/ -1 (pow y 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 y)) (* (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))))) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2))))))) (/ (* x (* y (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))))))) y)) (* 1/2 (* (pow (/ -1 y) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))))))) y)) (* (pow (* -1 y) 1/4) (sqrt (sqrt -1))))
(* -1 (sqrt y))
(+ (* -1 (sqrt y)) (* -1 (/ (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))) y)))
(+ (* -1 (sqrt y)) (* -1 (/ (- (+ (* x (sqrt y)) (* (sqrt (/ x y)) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))))) (* (sqrt x) (/ y (pow (sqrt -1) 2)))) y)))
(+ (* -1 (sqrt y)) (* -1 (/ (- (+ (* -1 (/ (- (/ (* x (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))))) y)) (* x (sqrt y))) (* (sqrt x) (/ y (pow (sqrt -1) 2)))) y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* (pow (* -1 y) 1/4) (sqrt (sqrt -1))))
(* -1 (* y (+ (* 1/2 (* (pow (/ -1 (pow y 5)) 1/4) (sqrt (/ x (sqrt -1))))) (* (pow (/ -1 (pow y 3)) 1/4) (sqrt (sqrt -1))))))
(* -1 (* y (+ (* -1/8 (* (pow (/ -1 (pow y 7)) 1/4) (* x (sqrt (/ 1 (pow (sqrt -1) 3)))))) (+ (* 1/2 (* (pow (/ -1 (pow y 5)) 1/4) (sqrt (/ x (sqrt -1))))) (* (pow (/ -1 (pow y 3)) 1/4) (sqrt (sqrt -1)))))))
(* -1 (* y (+ (* -1/8 (* (pow (/ -1 (pow y 7)) 1/4) (* x (sqrt (/ 1 (pow (sqrt -1) 3)))))) (+ (* 1/16 (* (pow (/ -1 (pow y 9)) 1/4) (sqrt (/ (pow x 3) (pow (sqrt -1) 5))))) (+ (* 1/2 (* (pow (/ -1 (pow y 5)) 1/4) (sqrt (/ x (sqrt -1))))) (* (pow (/ -1 (pow y 3)) 1/4) (sqrt (sqrt -1))))))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(sqrt (/ y (+ (sqrt x) (sqrt y))))
(+ (sqrt (/ y (+ (sqrt x) (sqrt y)))) (* 1/2 (* x (sqrt (/ 1 (* y (+ (sqrt x) (sqrt y))))))))
(+ (sqrt (/ y (+ (sqrt x) (sqrt y)))) (* x (+ (* -1/8 (* x (sqrt (/ 1 (* (pow y 3) (+ (sqrt x) (sqrt y))))))) (* 1/2 (sqrt (/ 1 (* y (+ (sqrt x) (sqrt y)))))))))
(+ (sqrt (/ y (+ (sqrt x) (sqrt y)))) (* x (+ (* 1/2 (sqrt (/ 1 (* y (+ (sqrt x) (sqrt y)))))) (* x (+ (* -1/8 (sqrt (/ 1 (* (pow y 3) (+ (sqrt x) (sqrt y)))))) (* 1/16 (* x (sqrt (/ 1 (* (pow y 5) (+ (sqrt x) (sqrt y))))))))))))
(/ y (+ (sqrt x) (sqrt y)))
(+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y))))
(+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y))))
(+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y))))
y
(+ x y)
(+ x y)
(+ x y)
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(pow (* 1 x) 1/4)
(+ (* 1/2 (* (pow (/ 1 (pow x 5)) 1/4) (- (* (sqrt x) y) (* x (sqrt y))))) (pow (* 1 x) 1/4))
(+ (* -1/2 (* (pow (/ 1 (pow x 9)) 1/4) (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* x (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* x (sqrt y))))))) (+ (* 1/2 (* (pow (/ 1 (pow x 5)) 1/4) (- (* (sqrt x) y) (* x (sqrt y))))) (pow (* 1 x) 1/4)))
(+ (* -1/2 (* (pow (/ 1 (pow x 9)) 1/4) (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* x (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* x (sqrt y))))))) (+ (* -1/2 (* (pow (/ 1 (pow x 13)) 1/4) (+ (* -1 (* x (* y (- (* (sqrt x) y) (* x (sqrt y)))))) (* -1/2 (* (sqrt (/ 1 x)) (* (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* x (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* x (sqrt y))))) (- (* (sqrt x) y) (* x (sqrt y))))))))) (+ (* 1/2 (* (pow (/ 1 (pow x 5)) 1/4) (- (* (sqrt x) y) (* x (sqrt y))))) (pow (* 1 x) 1/4))))
(sqrt x)
(- (+ (sqrt x) (* (sqrt (/ 1 x)) y)) (sqrt y))
(- (+ (sqrt x) (+ (* -1 (* (sqrt (/ y (pow x 3))) (- (* (sqrt x) y) (* x (sqrt y))))) (* (sqrt (/ 1 x)) y))) (sqrt y))
(- (+ (sqrt x) (+ (* (sqrt (/ 1 x)) y) (/ (* y (- (* (sqrt x) y) (* x (sqrt y)))) (pow x 2)))) (+ (sqrt y) (* (sqrt (/ y (pow x 3))) (- (* (sqrt x) y) (* x (sqrt y))))))
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(pow (* 1 x) 1/4)
(* x (+ (* 1/2 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt y))) (pow (/ 1 (pow x 3)) 1/4)))
(* x (+ (* -1/8 (* (pow (/ 1 (pow x 7)) 1/4) y)) (+ (* 1/2 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt y))) (pow (/ 1 (pow x 3)) 1/4))))
(* x (+ (* -1/8 (* (pow (/ 1 (pow x 7)) 1/4) y)) (+ (* 1/16 (* (pow (/ 1 (pow x 9)) 1/4) (sqrt (pow y 3)))) (+ (* 1/2 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt y))) (pow (/ 1 (pow x 3)) 1/4)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))
(+ (* -1/2 (* (pow (/ -1 (pow x 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))) (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (* (pow (/ -1 x) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))) (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))))))) x)) (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (pow (/ -1 x) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))))) (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 x)) (* (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))) (/ (* x (* y (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) (pow (sqrt -1) 2))))))) x)) (* 1/2 (* (pow (/ -1 x) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))))) x)) (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (* -1 (/ (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* (sqrt x) y) (* (sqrt (/ y x)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) x)))
(+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* -1 (/ (- (/ (* y (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))) (pow (sqrt -1) 2)) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) x)) (* (sqrt x) y)) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(* -1 (* x (+ (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (sqrt (/ y (sqrt -1))))) (* (pow (/ -1 (pow x 3)) 1/4) (sqrt (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (pow (/ -1 (pow x 7)) 1/4) (* y (sqrt (/ 1 (pow (sqrt -1) 3)))))) (+ (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (sqrt (/ y (sqrt -1))))) (* (pow (/ -1 (pow x 3)) 1/4) (sqrt (sqrt -1)))))))
(* -1 (* x (+ (* -1/8 (* (pow (/ -1 (pow x 7)) 1/4) (* y (sqrt (/ 1 (pow (sqrt -1) 3)))))) (+ (* 1/16 (* (pow (/ -1 (pow x 9)) 1/4) (sqrt (/ (pow y 3) (pow (sqrt -1) 5))))) (+ (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (sqrt (/ y (sqrt -1))))) (* (pow (/ -1 (pow x 3)) 1/4) (sqrt (sqrt -1))))))))

Outputs
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 y #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(sqrt (/ x (+ (sqrt x) (sqrt y))))
(sqrt.f64 (/.f64 x (+.f64 (sqrt.f64 y) (sqrt.f64 x))))
(+ (sqrt (/ x (+ (sqrt x) (sqrt y)))) (* 1/2 (* (sqrt (/ 1 (* x (+ (sqrt x) (sqrt y))))) y)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))) (sqrt.f64 (/.f64 x (+.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+ (sqrt (/ x (+ (sqrt x) (sqrt y)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (* (pow x 3) (+ (sqrt x) (sqrt y))))) y)) (* 1/2 (sqrt (/ 1 (* x (+ (sqrt x) (sqrt y)))))))))
(fma.f64 (fma.f64 (.f64 y #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))) #s(literal 1/2 binary64))) y (sqrt.f64 (/.f64 x (+.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(+ (sqrt (/ x (+ (sqrt x) (sqrt y)))) (* y (+ (* 1/2 (sqrt (/ 1 (* x (+ (sqrt x) (sqrt y)))))) (* y (+ (* -1/8 (sqrt (/ 1 (* (pow x 3) (+ (sqrt x) (sqrt y)))))) (* 1/16 (* (sqrt (/ 1 (* (pow x 5) (+ (sqrt x) (sqrt y))))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 y) (sqrt.f64 x)))) #s(literal 1/2 binary64))) y (sqrt.f64 (/.f64 x (+.f64 (sqrt.f64 y) (sqrt.f64 x)))))
(/ x (+ (sqrt x) (sqrt y)))
(/.f64 x (+.f64 (sqrt.f64 y) (sqrt.f64 x)))
(+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y))))
(+.f64 (/.f64 y (+.f64 (sqrt.f64 y) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 y) (sqrt.f64 x))))
(+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y))))
(+.f64 (/.f64 y (+.f64 (sqrt.f64 y) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 y) (sqrt.f64 x))))
(+ (/ x (+ (sqrt x) (sqrt y))) (/ y (+ (sqrt x) (sqrt y))))
(+.f64 (/.f64 y (+.f64 (sqrt.f64 y) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 y) (sqrt.f64 x))))
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)))
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)))
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)))
(sqrt (+ (sqrt x) (sqrt y)))
(sqrt.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)))
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) 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 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (.f64 x x) #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) 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 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(.f64 (+.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 (.f64 (.f64 x x) #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) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(pow (* 1 y) 1/4)
(pow.f64 y #s(literal 1/4 binary64))
(+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (- (* x (sqrt y)) (* (sqrt x) y)))) (pow (* 1 y) 1/4))
(fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x)) (pow.f64 y #s(literal 1/4 binary64)))
(+ (* -1/2 (* (pow (/ 1 (pow y 9)) 1/4) (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) y)) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) y)))))) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (- (* x (sqrt y)) (* (sqrt x) y)))) (pow (* 1 y) 1/4)))
(fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 9 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (fma.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (.f64 y x)) (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x)))) (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x)) (pow.f64 y #s(literal 1/4 binary64))))
(+ (* -1/2 (* (pow (/ 1 (pow y 9)) 1/4) (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) y)) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) y)))))) (+ (* -1/2 (* (pow (/ 1 (pow y 13)) 1/4) (+ (* -1 (* x (* y (- (* x (sqrt y)) (* (sqrt x) y))))) (* -1/2 (* (sqrt (/ 1 y)) (* (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) y)) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) y)))) (- (* x (sqrt y)) (* (sqrt x) y)))))))) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (- (* x (sqrt y)) (* (sqrt x) y)))) (pow (* 1 y) 1/4))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (.f64 y x)) (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 9 binary64))) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x))) (fma.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (.f64 y x)) (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x))))) #s(literal -1/2 binary64) (.f64 (.f64 (neg.f64 x) y) (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 13 binary64))) #s(literal 1/4 binary64)))) (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 (sqrt.f64 y) x)) (pow.f64 y #s(literal 1/4 binary64))))
(sqrt y)
(sqrt.f64 y)
(- (+ (sqrt y) (* x (sqrt (/ 1 y)))) (sqrt x))
(-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x (sqrt.f64 y)) (sqrt.f64 x))
(- (+ (sqrt y) (+ (* -1 (* (sqrt (/ x (pow y 3))) (- (* x (sqrt y)) (* (sqrt x) y)))) (* x (sqrt (/ 1 y))))) (sqrt x))
(-.f64 (fma.f64 (neg.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 (sqrt.f64 y) x))) (sqrt.f64 (/.f64 x (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x (sqrt.f64 y))) (sqrt.f64 x))
(- (+ (sqrt y) (+ (* x (sqrt (/ 1 y))) (/ (* x (- (* x (sqrt y)) (* (sqrt x) y))) (pow y 2)))) (+ (sqrt x) (* (sqrt (/ x (pow y 3))) (- (* x (sqrt y)) (* (sqrt x) y)))))
(fma.f64 x (+.f64 (/.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) (.f64 (sqrt.f64 y) x)) (.f64 y y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (-.f64 (sqrt.f64 y) (fma.f64 (sqrt.f64 (/.f64 x (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (neg.f64 y) (sqrt.f64 x) (*.f64 (sqrt.f64 y) x)) (sqrt.f64 x))))
y
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(* y (+ 1 (/ x y)))
(fma.f64 (/.f64 x y) y y)
(pow (* 1 y) 1/4)
(pow.f64 y #s(literal 1/4 binary64))
(* y (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (sqrt x))) (pow (/ 1 (pow y 3)) 1/4)))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64))) y)
(* y (+ (* -1/8 (* (pow (/ 1 (pow y 7)) 1/4) x)) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (sqrt x))) (pow (/ 1 (pow y 3)) 1/4))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))) #s(literal 1/4 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64)))) y)
(* y (+ (* -1/8 (* (pow (/ 1 (pow y 7)) 1/4) x)) (+ (* 1/16 (* (pow (/ 1 (pow y 9)) 1/4) (sqrt (pow x 3)))) (+ (* 1/2 (* (pow (/ 1 (pow y 5)) 1/4) (sqrt x))) (pow (/ 1 (pow y 3)) 1/4)))))
(.f64 (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 9 binary64))) #s(literal 1/4 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64))))) y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (neg.f64 y) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 (.f64 x (neg.f64 x)) #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) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 (.f64 x (neg.f64 x)) #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) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))
(* (pow (* -1 y) 1/4) (sqrt (sqrt -1)))
(*.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (neg.f64 y) #s(literal 1/4 binary64)))
(+ (* -1/2 (* (pow (/ -1 (pow y 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2))))))) (* (pow (* -1 y) 1/4) (sqrt (sqrt -1))))
(fma.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 5 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (neg.f64 y) #s(literal 1/4 binary64))))
(+ (* -1 (/ (+ (* 1/2 (* (pow (/ -1 y) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2))))))) (* 1/2 (* (pow (/ -1 (pow y 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 y)) (pow (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))) 2))) (* (sqrt (* x y)) (- (* x (sqrt y)) (* (sqrt x) (/ y (pow (sqrt -1) 2)))))))))) y)) (* (pow (* -1 y) 1/4) (sqrt (sqrt -1))))
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(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)))) x)
(* x (+ (* -1/8 (* (pow (/ 1 (pow x 7)) 1/4) y)) (+ (* 1/16 (* (pow (/ 1 (pow x 9)) 1/4) (sqrt (pow y 3)))) (+ (* 1/2 (* (pow (/ 1 (pow x 5)) 1/4) (sqrt y))) (pow (/ 1 (pow x 3)) 1/4)))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64))) #s(literal 1/4 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (pow.f64 y #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64))))) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (neg.f64 x) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (neg.f64 x) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (neg.f64 y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (neg.f64 x) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (neg.f64 y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1/2 (* (pow (/ -1 (pow x 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))) (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(fma.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (* -1 (/ (+ (* 1/2 (* (pow (/ -1 x) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))) (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))))))) x)) (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (sqrt.f64 (.f64 y x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))))) (.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (pow (/ -1 x) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))))) (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (* (sqrt (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 x)) (* (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) 2))) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))))) (/ (* x (* y (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) (pow (sqrt -1) 2))))))) x)) (* 1/2 (* (pow (/ -1 x) 1/4) (* (sqrt (/ 1 (sqrt -1))) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))))) x)) (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(fma.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (/.f64 (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (fma.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (sqrt.f64 (.f64 y x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (sqrt.f64 (.f64 y x))))) #s(literal -1/2 binary64) (.f64 (.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) y) (neg.f64 x))))) (neg.f64 x))) (neg.f64 x)))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 y) x (*.f64 y (sqrt.f64 x))) (neg.f64 x)) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* (sqrt x) y) (* (sqrt (/ y x)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 y x)) (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x)))) (neg.f64 x)) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* -1 (/ (- (/ (* y (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y)))) (pow (sqrt -1) 2)) (* (sqrt (* x y)) (- (* (sqrt x) y) (* (/ x (pow (sqrt -1) 2)) (sqrt y))))) x)) (* (sqrt x) y)) (* (/ x (pow (sqrt -1) 2)) (sqrt y))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 y) x (fma.f64 y (sqrt.f64 x) (/.f64 (-.f64 (.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (neg.f64 y)) (.f64 (fma.f64 (sqrt.f64 y) x (.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 y x)))) (neg.f64 x)))) (neg.f64 x)) (sqrt.f64 x))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)
(* -1 (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(*.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (sqrt (/ y (sqrt -1))))) (* (pow (/ -1 (pow x 3)) 1/4) (sqrt (sqrt -1))))))
(.f64 (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (pow (/ -1 (pow x 7)) 1/4) (* y (sqrt (/ 1 (pow (sqrt -1) 3)))))) (+ (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (sqrt (/ y (sqrt -1))))) (* (pow (/ -1 (pow x 3)) 1/4) (sqrt (sqrt -1)))))))
(.f64 (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -1/8 binary64)) y) (sqrt.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (pow (/ -1 (pow x 7)) 1/4) (* y (sqrt (/ 1 (pow (sqrt -1) 3)))))) (+ (* 1/16 (* (pow (/ -1 (pow x 9)) 1/4) (sqrt (/ (pow y 3) (pow (sqrt -1) 5))))) (+ (* 1/2 (* (pow (/ -1 (pow x 5)) 1/4) (sqrt (/ y (sqrt -1))))) (* (pow (/ -1 (pow x 3)) 1/4) (sqrt (sqrt -1))))))))
(.f64 (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) y (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 9 binary64))) #s(literal 1/4 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))))) (neg.f64 x))

rewrite351.0ms (8.4%)

Memory

-16.9MiB live, 187.8MiB allocated

Rules

3 928×	`lower-*.f32`
3 926×	`lower-*.f64`
3 084×	`lower-fma.f64`
3 084×	`lower-fma.f32`
2 892×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	45
0	18	44
1	63	32
2	472	32
3	5361	32
0	8058	32

Stop Event

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

Counts

5 → 527

Calls

Call 1

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

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

eval83.0ms (2%)

Memory: 5.4MiB live, 119.9MiB allocated
Compiler: Compiled 19 542 to 2 643 computations (86.5% saved)

prune122.0ms (2.9%)

Memory

30.3MiB live, 142.6MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	641	0	641
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	641	3	644

Accuracy

100.0%

Counts

644 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.4%	(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (+.f64 (sqrt.f64 x) (sqrt.f64 y)))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 y))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.4%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 60 to 35 computations (41.7% saved)

regimes23.0ms (0.5%)

Memory

-25.2MiB live, 22.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

15.0ms	(+.f64 x y)
3.0ms	(sqrt.f64 (+.f64 x y))
2.0ms	y
2.0ms	x

Results

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

Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes5.0ms (0.1%)

Memory

15.6MiB live, 15.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`y`
98.4%	1	`(sqrt.f64 (+.f64 x y))`
98.4%	1	`(+.f64 x y)`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify26.0ms (0.6%)

Memory

-15.0MiB live, 60.8MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness201.0ms (4.8%)

Memory

-14.9MiB live, 106.7MiB allocated

Rules

27 648×	`lower-fma.f64`
27 648×	`lower-fma.f32`
5 638×	`lower-*.f64`
5 638×	`lower-*.f32`
2 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	630
1	454	600
2	1426	582
3	4628	570
0	8167	534

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 9 to 9 computations (0% saved)

preprocess23.0ms (0.6%)

Memory: 13.5MiB live, 50.4MiB allocated
Remove: (sort x y)
Compiler: Compiled 38 to 36 computations (5.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4

start0.0ms (0%)

analyze16.0ms (0.4%)

sample1.0s (24.3%)

explain35.0ms (0.8%)

preprocess16.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize92.0ms (2.2%)

series5.0ms (0.1%)

simplify366.0ms (8.8%)

rewrite258.0ms (6.2%)

eval117.0ms (2.8%)

prune71.0ms (1.7%)

simplify4.0ms (0.1%)

localize28.0ms (0.7%)

series6.0ms (0.1%)

simplify259.0ms (6.2%)

rewrite251.0ms (6%)

eval21.0ms (0.5%)

prune19.0ms (0.4%)

simplify5.0ms (0.1%)

localize18.0ms (0.4%)

series3.0ms (0.1%)

simplify265.0ms (6.4%)

rewrite137.0ms (3.3%)

eval66.0ms (1.6%)

prune19.0ms (0.4%)

simplify5.0ms (0.1%)

localize31.0ms (0.7%)

series22.0ms (0.5%)

simplify174.0ms (4.2%)

rewrite351.0ms (8.4%)

eval83.0ms (2%)

prune122.0ms (2.9%)

regimes23.0ms (0.5%)

regimes5.0ms (0.1%)

simplify26.0ms (0.6%)

soundness201.0ms (4.8%)

preprocess23.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4