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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze129.0ms (3.4%)

Memory

-45.1MiB live, 14.6MiB 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)

sample861.0ms (22.4%)

Memory

17.0MiB live, 486.4MiB allocated

Samples

579.0ms	8 256×	0	valid
17.0ms	516×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 360.0ms

ival-add: 224.0ms (62.2% of total)

ival-sqrt: 127.0ms (35.3% of total)

ival-true: 6.0ms (1.7% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain94.0ms (2.4%)

Memory

-0.8MiB live, 75.0MiB 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

18.0ms

512×

valid

Compiler

Compiled 26 to 16 computations (38.5% saved)

Precisions

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

ival-sqrt: 4.0ms (56.2% of total)

ival-add: 3.0ms (42.1% of total)

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

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

preprocess16.0ms (0.4%)

Memory

29.0MiB live, 29.0MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB 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

5.1MiB live, 5.1MiB 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

localize57.0ms (1.5%)

Memory

-13.0MiB live, 24.7MiB 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

53.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add: 2.0ms (45.8% of total)

ival-sqrt: 2.0ms (45.8% of total)

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

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

series6.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB 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	y	@	inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	inf	((sqrt (+ x y)) (+ x y))
0.0ms	y	@	0	((sqrt (+ x y)) (+ x y))

simplify623.0ms (16.2%)

Memory

-7.3MiB live, 272.6MiB 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)

rewrite332.0ms (8.6%)

Memory

-11.5MiB live, 303.7MiB 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 (+.f64 (hypot.f64 y x) (*.f64 y x))))
(.f64 (sqrt.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y 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 (+.f64 (hypot.f64 y x) (*.f64 y x))))
(.f64 (pow.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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 (sqrt.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 (-.f64 (hypot.f64 y x) (.f64 y 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 (-.f64 (hypot.f64 y x) (.f64 y 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) (-.f64 (hypot.f64 y x) (.f64 y 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) (-.f64 (hypot.f64 y x) (.f64 y 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 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1/2 binary64)) (sqrt.f64 (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 (-.f64 (hypot.f64 y x) (.f64 y x))) (sqrt.f64 (/.f64 (+.f64 y x) (-.f64 (hypot.f64 y x) (*.f64 y x)))))
(.f64 (sqrt.f64 (-.f64 (hypot.f64 y x) (.f64 y x))) (pow.f64 (/.f64 (+.f64 y x) (-.f64 (hypot.f64 y x) (*.f64 y x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y 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 (sqrt.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 (-.f64 (hypot.f64 y x) (*.f64 y 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 (-.f64 (hypot.f64 y x) (*.f64 y x))))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 x y))) (sqrt.f64 (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) (hypot.f64 y 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))) (-.f64 (hypot.f64 y x) (*.f64 y x)))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (-.f64 (hypot.f64 y x) (.f64 y x)))) (sqrt.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 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 (sqrt.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (hypot.f64 y 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) (hypot.f64 y 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) (hypot.f64 y 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))) (-.f64 (hypot.f64 y x) (.f64 y 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) (hypot.f64 y 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 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (.f64 y x)))))
(/.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) (hypot.f64 y 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 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))) (neg.f64 (.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (*.f64 y x)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))) (neg.f64 (.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 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) (hypot.f64 y x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (*.f64 (hypot.f64 y 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) (hypot.f64 y 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 (-.f64 (hypot.f64 y x) (.f64 y 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) (hypot.f64 y 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))) (-.f64 (hypot.f64 y x) (.f64 y 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 (-.f64 (hypot.f64 y x) (*.f64 y x)) #s(literal -1 binary64)) (pow.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 y 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) (hypot.f64 y 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))) (-.f64 (hypot.f64 y x) (*.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (/.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (-.f64 (hypot.f64 y x) (.f64 y 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 (hypot.f64 y 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) (hypot.f64 y 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))) (-.f64 (hypot.f64 y x) (.f64 y x))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (*.f64 y x))) (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 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) (hypot.f64 y x)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 x y) (fma.f64 (.f64 y y) (hypot.f64 y 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 (-.f64 (hypot.f64 y x) (.f64 y 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 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))) (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 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 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (*.f64 y 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 (-.f64 (hypot.f64 y x) (*.f64 y x))))
(/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 x y))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (hypot.f64 y x) (*.f64 y 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)))) (+.f64 (hypot.f64 y x) (.f64 y 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) (hypot.f64 y x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (hypot.f64 y x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (-.f64 x y) (fma.f64 (.f64 y y) (hypot.f64 y 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) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (-.f64 (hypot.f64 y x) (.f64 y 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 (-.f64 (hypot.f64 y x) (.f64 y 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 (-.f64 (hypot.f64 y x) (*.f64 y x)))) (neg.f64 (+.f64 y x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (hypot.f64 y x)) (-.f64 x y)) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (hypot.f64 y x)) (-.f64 x y)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 y y) (hypot.f64 y 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) (hypot.f64 y 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)))) (-.f64 (hypot.f64 y x) (.f64 y 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)))) (-.f64 (hypot.f64 y x) (.f64 y 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))
(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)))
(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)

eval104.0ms (2.7%)

Memory: 7.3MiB live, 138.4MiB allocated
Compiler: Compiled 5 506 to 879 computations (84% saved)

prune6.0ms (0.2%)

Memory

-16.0MiB live, 21.9MiB 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
▶	99.2%	(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	97.6%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 14 to 15 computations (-7.1% saved)

simplify4.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 y x)
cost-diff	0	(pow.f64 (+.f64 y x) #s(literal 1/4 binary64))
cost-diff	12288	(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	29
0	15	29
1	17	27
2	20	26
3	20	26
0	20	26

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
(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (+.f64 y x) #s(literal 1/4 binary64))
(+.f64 y x)
y
x
#s(literal 1/4 binary64)
#s(literal 2 binary64)

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

localize35.0ms (0.9%)

Memory

8.2MiB live, 87.9MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y x)
accuracy	0.00390625	(pow.f64 (+.f64 y x) #s(literal 1/4 binary64))
accuracy	0.49056625976844204	(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
accuracy	0	(sqrt.f64 y)
accuracy	1.5057737720553122	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Samples

27.0ms

256×

valid

Compiler

Compiled 28 to 12 computations (57.1% saved)

Precisions

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

ival-pow: 9.0ms (47.5% of total)

ival-sqrt: 4.0ms (21.1% of total)

ival-add: 3.0ms (15.8% of total)

ival-pow2: 3.0ms (15.8% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.3%)

Memory

-8.8MiB live, 30.1MiB allocated

Counts

5 → 108

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 (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())
#s(alt (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) (patch (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #<representation:binary64>) () ())
#s(alt (+.f64 y x) (patch (+.f64 y x) #<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>) () ())) ())
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#s(alt (+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (+ (* (pow (/ 1 (pow x 7)) 1/4) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (+ (* (pow (/ 1 (pow x 11)) 1/4) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3))))) (pow (* 1 x) 1/4)))) (taylor inf x) (#s(alt (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) (patch (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<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 (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 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 (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 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 (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 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 (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) (patch (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* 1/4 (/ (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))) x))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) (patch (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) x))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) (patch (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/12 (pow y 3)) (+ (* -1/384 (pow y 3)) (* 1/32 (pow y 3))))) x)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) x))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) (patch (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #<representation:binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((sqrt (+ x y)) (sqrt y) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x))
2.0ms	x	@	inf	((sqrt (+ x y)) (sqrt y) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x))
1.0ms	y	@	-inf	((sqrt (+ x y)) (sqrt y) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x))
1.0ms	y	@	0	((sqrt (+ x y)) (sqrt y) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x))
1.0ms	y	@	inf	((sqrt (+ x y)) (sqrt y) (pow (pow (+ y x) 1/4) 2) (pow (+ y x) 1/4) (+ y x))

simplify215.0ms (5.6%)

Memory

26.5MiB live, 413.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16 326×	`lower-fma.f64`
16 326×	`lower-fma.f32`
5 370×	`lower-*.f64`
5 370×	`lower-*.f32`
5 058×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	312	1970
1	907	1856
2	3483	1760
3	7504	1716
0	8223	1616

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 102

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)))))))
(pow (* 1 x) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4))
(+ (* y (+ (* -3/32 (* (pow (/ 1 (pow x 7)) 1/4) y)) (* 1/4 (pow (/ 1 (pow x 3)) 1/4)))) (pow (* 1 x) 1/4))
(+ (* y (+ (* 1/4 (pow (/ 1 (pow x 3)) 1/4)) (* y (+ (* -3/32 (pow (/ 1 (pow x 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow x 11)) 1/4) y)))))) (pow (* 1 x) 1/4))
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)))))))))
(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)))))))))
(pow (* 1 y) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (pow (* 1 y) 1/4))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (pow (* 1 y) 1/4)))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (+ (* (pow (/ 1 (pow y 11)) 1/4) (+ (* -1/32 (pow x 3)) (+ (* 1/384 (pow x 3)) (* 1/12 (pow x 3))))) (pow (* 1 y) 1/4))))
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)))))))
(* -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)))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* 1/4 (/ (* x (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))) y)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) y)) (* -1/4 (* x (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/12 (pow x 3)) (+ (* -1/384 (pow x 3)) (* 1/32 (pow x 3))))) y)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2))))) y)) (* -1/4 (* x (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y)))
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))))))))))
(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))))))))))
(pow (* 1 y) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (pow (* 1 y) 1/4))
(+ (* x (+ (* -3/32 (* (pow (/ 1 (pow y 7)) 1/4) x)) (* 1/4 (pow (/ 1 (pow y 3)) 1/4)))) (pow (* 1 y) 1/4))
(+ (* x (+ (* 1/4 (pow (/ 1 (pow y 3)) 1/4)) (* x (+ (* -3/32 (pow (/ 1 (pow y 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow y 11)) 1/4) x)))))) (pow (* 1 y) 1/4))
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))))))
(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)
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (+ (* (pow (/ 1 (pow x 7)) 1/4) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (pow (* 1 x) 1/4)))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (+ (* (pow (/ 1 (pow x 7)) 1/4) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (+ (* (pow (/ 1 (pow x 11)) 1/4) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3))))) (pow (* 1 x) 1/4))))
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)))))))
(* -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)))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* 1/4 (/ (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))) x)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) x)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/12 (pow y 3)) (+ (* -1/384 (pow y 3)) (* 1/32 (pow y 3))))) x)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) x)))
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 #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 #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 #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 #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))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4))
(fma.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) y) #s(literal 1/4 binary64) (pow.f64 x #s(literal 1/4 binary64)))
(+ (* y (+ (* -3/32 (* (pow (/ 1 (pow x 7)) 1/4) y)) (* 1/4 (pow (/ 1 (pow x 3)) 1/4)))) (pow (* 1 x) 1/4))
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(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (+ (* (pow (/ 1 (pow x 7)) 1/4) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (pow (* 1 x) 1/4)))
(fma.f64 (.f64 y #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (*.f64 y y) #s(literal -3/32 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (+ (* (pow (/ 1 (pow x 7)) 1/4) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (+ (* (pow (/ 1 (pow x 11)) 1/4) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3))))) (pow (* 1 x) 1/4))))
(fma.f64 (.f64 y #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 7/128 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (.f64 y y) #s(literal -3/32 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))))
x
(* x (+ 1 (/ y x)))
(fma.f64 (/.f64 y x) x x)
(* x (+ 1 (/ y x)))
(fma.f64 (/.f64 y x) x x)
(* x (+ 1 (/ y x)))
(fma.f64 (/.f64 y x) x 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 (.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal 1/8 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 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (.f64 (.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal 1/8 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 (* (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 (.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal 1/8 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 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (.f64 (.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal 1/8 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)))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/4 binary64))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* 1/4 (/ (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))) x)))
(fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) y) x) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/4 binary64)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) x)))
(-.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/4 binary64)) (/.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/4 binary64)) (fma.f64 #s(literal -1/4 binary64) y (.f64 (*.f64 (/.f64 y x) y) #s(literal 3/32 binary64)))) x))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/12 (pow y 3)) (+ (* -1/384 (pow y 3)) (* 1/32 (pow y 3))))) x)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) x)))
(-.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) y) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/4 binary64)) (/.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/4 binary64)) (fma.f64 (.f64 y y) #s(literal -3/32 binary64) (/.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -7/128 binary64)) (neg.f64 x)))) (neg.f64 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 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)

rewrite188.0ms (4.9%)

Memory

-2.0MiB live, 366.7MiB allocated

Rules

3 638×	`lower-*.f64`
3 638×	`lower-*.f32`
2 412×	`lower-pow.f32`
2 408×	`lower-pow.f64`
2 118×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
0	15	21
1	57	21
2	317	21
3	3247	21
0	8348	21

Stop Event

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

Counts

5 → 339

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 y #s(literal 1/2 binary64))
(sqrt.f64 y)
(exp.f64 (fma.f64 (log.f64 y) #s(literal 1/4 binary64) (*.f64 (log.f64 y) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 y #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (-.f64 y x) (+.f64 y x)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (hypot.f64 y x) (*.f64 y x))))
(.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 (+.f64 (hypot.f64 y x) (*.f64 y x))))
(.f64 (sqrt.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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) (-.f64 (.f64 (-.f64 y x) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (*.f64 (-.f64 x y) (+.f64 y x)))) (sqrt.f64 (+.f64 y x)))
(.f64 (sqrt.f64 (/.f64 (.f64 (-.f64 y x) (+.f64 y x)) (*.f64 (-.f64 y x) (+.f64 y x)))) (sqrt.f64 (+.f64 y x)))
(.f64 (pow.f64 (.f64 (+.f64 y x) (*.f64 (-.f64 y x) (+.f64 y x))) #s(literal 1/4 binary64)) (pow.f64 (-.f64 y x) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (.f64 (+.f64 y x) (*.f64 (-.f64 x y) (+.f64 y x))) #s(literal 1/4 binary64)) (pow.f64 (-.f64 x y) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (.f64 (+.f64 y x) (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -2 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (-.f64 y x) (+.f64 y x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (-.f64 x y) #s(literal -2 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (-.f64 y x) (+.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 (-.f64 y x) #s(literal -1/8 binary64)) #s(literal 4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal 1/8 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 (-.f64 x y) #s(literal -1/8 binary64)) #s(literal 4 binary64)))
(.f64 (pow.f64 (pow.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1/8 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1/8 binary64)) #s(literal 4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (-.f64 y x) (+.f64 y x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 y x) #s(literal -1/4 binary64)) #s(literal 2 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 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 y x) (+.f64 y x)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (hypot.f64 y x) (*.f64 y x))))
(.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 (+.f64 (hypot.f64 y x) (*.f64 y x))))
(.f64 (pow.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 x y) x) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 y y) (.f64 (-.f64 x y) x))))
(.f64 (pow.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 x y) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/2 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 (pow.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 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) (-.f64 (.f64 (-.f64 y x) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 y x) (+.f64 y x)) (*.f64 (-.f64 y x) (+.f64 y x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 y x)))
(*.f64 (pow.f64 (pow.f64 (+.f64 y x) #s(literal 7/16 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 y x) #s(literal 1/16 binary64)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (-.f64 y x) (+.f64 y x))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 y x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (-.f64 x y) (+.f64 y x))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (sqrt.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (*.f64 (-.f64 x y) (+.f64 y x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 y x)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 y x)))
(*.f64 (pow.f64 (+.f64 y x) #s(literal 7/16 binary64)) (pow.f64 (+.f64 y x) #s(literal 1/16 binary64)))
(.f64 (sqrt.f64 (neg.f64 (.f64 (-.f64 y x) (+.f64 y x)))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 y x)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (.f64 (-.f64 y x) (+.f64 y x)))) (pow.f64 (pow.f64 (neg.f64 (-.f64 y x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x)))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 x y)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x)))) (pow.f64 (pow.f64 (neg.f64 (-.f64 x y)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (-.f64 (hypot.f64 y x) (.f64 y x))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (pow.f64 (pow.f64 (neg.f64 (-.f64 (hypot.f64 y x) (.f64 y x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 y x) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (-.f64 y x) (+.f64 y x))))
(.f64 (pow.f64 (-.f64 x y) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (-.f64 x y) (+.f64 y x))))
(.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1/2 binary64)) (sqrt.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(.f64 (pow.f64 (.f64 (-.f64 y x) (+.f64 y x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)) (+.f64 y x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (+.f64 y x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 (pow.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)) #s(literal -1 binary64)) (+.f64 y x)) #s(literal 1/4 binary64)))
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(/.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))) (fma.f64 (.f64 x x) (hypot.f64 y x) (pow.f64 y #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (hypot.f64 y x))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (fma.f64 (.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9/2 binary64))) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64))) (-.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9/2 binary64))) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64))) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))))
(/.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))) (fma.f64 y (/.f64 y (-.f64 y x)) (*.f64 x (/.f64 x (-.f64 y x)))))
(/.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))) (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y)))))
(/.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)))) (+.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 (-.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 (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 (neg.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x)))) (neg.f64 (neg.f64 (-.f64 y x))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x)))) (neg.f64 (neg.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 (-.f64 (hypot.f64 y x) (*.f64 y x)))))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (hypot.f64 y x) (-.f64 y x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (hypot.f64 y x) (-.f64 x y)))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (*.f64 x x) (hypot.f64 y x) (pow.f64 y #s(literal 4 binary64))) (-.f64 y x)))
(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (*.f64 y x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (*.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))) (-.f64 x y)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (*.f64 y x))))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9/2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (.f64 y x))))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9/2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (.f64 y x))))
(/.f64 (.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) (-.f64 (hypot.f64 y x) (.f64 y x)))
(/.f64 (-.f64 (.f64 (.f64 y y) (-.f64 y x)) (.f64 (-.f64 y x) (.f64 x x))) (pow.f64 (-.f64 y x) #s(literal 2 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) (hypot.f64 y x)))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 y x) (hypot.f64 y x)))
(/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (-.f64 y x) (fma.f64 (.f64 x x) (hypot.f64 y x) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.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) (hypot.f64 y 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 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9/2 binary64))) (.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9/2 binary64))) (.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))) (neg.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 (-.f64 (hypot.f64 y x) (*.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 y x) (+.f64 y x)) (-.f64 y x))
(/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 x y))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (hypot.f64 y x) (*.f64 y x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))) (-.f64 y x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))) (-.f64 x y)))
(neg.f64 (/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (hypot.f64 y x) (*.f64 y x))))
(neg.f64 (/.f64 (*.f64 (-.f64 y x) (+.f64 y x)) (neg.f64 (-.f64 y x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (neg.f64 (-.f64 x y))))
(neg.f64 (/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (+.f64 (hypot.f64 y x) (.f64 y 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 (/.f64 (.f64 y y) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (+.f64 (hypot.f64 y x) (.f64 y x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (/.f64 (.f64 y y) (.f64 (-.f64 y x) (+.f64 y x))) (+.f64 y x) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 (.f64 y y) (pow.f64 (-.f64 y x) #s(literal -1 binary64)) (neg.f64 (.f64 x (/.f64 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 y (/.f64 y (-.f64 y x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 y x)))))
(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(-.f64 (.f64 y (/.f64 y (-.f64 y x))) (.f64 x (/.f64 x (-.f64 y x))))
(-.f64 (.f64 x (/.f64 x (-.f64 x y))) (.f64 y (/.f64 y (-.f64 x y))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 y x))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (+.f64 y x)))
(+.f64 (.f64 y (/.f64 y (-.f64 y x))) (neg.f64 (.f64 x (/.f64 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)

eval264.0ms (6.9%)

Memory: -23.6MiB live, 130.9MiB allocated
Compiler: Compiled 8 643 to 1 457 computations (83.1% saved)

prune8.0ms (0.2%)

Memory

29.0MiB live, 29.0MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	440	1	441
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	441	3	444

Accuracy

100.0%

Counts

444 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	97.6%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 14 to 15 computations (-7.1% saved)

simplify7.0ms (0.2%)

Memory

-30.6MiB live, 8.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 y x)
cost-diff	0	(sqrt.f64 (+.f64 y x))
cost-diff	0	(sqrt.f64 (sqrt.f64 (+.f64 y x)))
cost-diff	7104	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64))

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	22
0	11	25
1	13	19
2	13	19
3	14	19
0	14	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64))
(sqrt.f64 (sqrt.f64 (+.f64 y x)))
(sqrt.f64 (+.f64 y x))
(+.f64 y x)
y
x
#s(literal 2 binary64)

Outputs
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64))
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (sqrt.f64 (+.f64 y x)))
(sqrt.f64 (sqrt.f64 (+.f64 x y)))
(sqrt.f64 (+.f64 y x))
(sqrt.f64 (+.f64 x y))
(+.f64 y x)
(+.f64 x y)
y
x
#s(literal 2 binary64)

localize22.0ms (0.6%)

Memory

3.9MiB live, 42.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y x)
accuracy	0.00390625	(sqrt.f64 (+.f64 y x))
accuracy	0.125	(sqrt.f64 (sqrt.f64 (+.f64 y x)))
accuracy	0.49056625976844204	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64))

Samples

17.0ms

256×

valid

Compiler

Compiled 24 to 9 computations (62.5% saved)

Precisions

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

ival-sqrt: 3.0ms (37.6% of total)

ival-pow2: 3.0ms (37.6% of total)

ival-add: 1.0ms (12.5% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

4 → 96

Calls

Call 1

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

Outputs
#s(alt (sqrt x) (taylor 0 y) (#s(alt (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 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 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 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 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow (* 1 x) 1/4) (taylor 0 y) (#s(alt (sqrt.f64 (sqrt.f64 (+.f64 y x))) (patch (sqrt.f64 (sqrt.f64 (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4)) (taylor 0 y) (#s(alt (sqrt.f64 (sqrt.f64 (+.f64 y x))) (patch (sqrt.f64 (sqrt.f64 (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (+ (* y (+ (* -3/32 (* (pow (/ 1 (pow x 7)) 1/4) y)) (* 1/4 (pow (/ 1 (pow x 3)) 1/4)))) (pow (* 1 x) 1/4)) (taylor 0 y) (#s(alt (sqrt.f64 (sqrt.f64 (+.f64 y x))) (patch (sqrt.f64 (sqrt.f64 (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (+ (* y (+ (* 1/4 (pow (/ 1 (pow x 3)) 1/4)) (* y (+ (* -3/32 (pow (/ 1 (pow x 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow x 11)) 1/4) y)))))) (pow (* 1 x) 1/4)) (taylor 0 y) (#s(alt (sqrt.f64 (sqrt.f64 (+.f64 y x))) (patch (sqrt.f64 (sqrt.f64 (+.f64 y x))) #<representation:binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation:binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y 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 (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y 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 (sqrt.f64 (+.f64 y x)) (patch (sqrt.f64 (+.f64 y x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation:binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 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 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) (patch (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
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Calls

6 calls:

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

simplify257.0ms (6.7%)

Memory

11.4MiB live, 334.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16 326×	`lower-fma.f64`
16 326×	`lower-fma.f32`
5 370×	`lower-*.f64`
5 370×	`lower-*.f32`
5 058×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	312	1946
1	907	1832
2	3484	1736
3	7510	1692
0	8229	1592

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 90

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)))))))
(pow (* 1 x) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4))
(+ (* y (+ (* -3/32 (* (pow (/ 1 (pow x 7)) 1/4) y)) (* 1/4 (pow (/ 1 (pow x 3)) 1/4)))) (pow (* 1 x) 1/4))
(+ (* y (+ (* 1/4 (pow (/ 1 (pow x 3)) 1/4)) (* y (+ (* -3/32 (pow (/ 1 (pow x 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow x 11)) 1/4) y)))))) (pow (* 1 x) 1/4))
(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)))))))))
(pow (* 1 y) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (pow (* 1 y) 1/4))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (pow (* 1 y) 1/4)))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (+ (* (pow (/ 1 (pow y 11)) 1/4) (+ (* -1/32 (pow x 3)) (+ (* 1/384 (pow x 3)) (* 1/12 (pow x 3))))) (pow (* 1 y) 1/4))))
(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)))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* 1/4 (/ (* x (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))) y)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) y)) (* -1/4 (* x (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/12 (pow x 3)) (+ (* -1/384 (pow x 3)) (* 1/32 (pow x 3))))) y)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2))))) y)) (* -1/4 (* x (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) 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))))))))))
(pow (* 1 y) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (pow (* 1 y) 1/4))
(+ (* x (+ (* -3/32 (* (pow (/ 1 (pow y 7)) 1/4) x)) (* 1/4 (pow (/ 1 (pow y 3)) 1/4)))) (pow (* 1 y) 1/4))
(+ (* x (+ (* 1/4 (pow (/ 1 (pow y 3)) 1/4)) (* x (+ (* -3/32 (pow (/ 1 (pow y 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow y 11)) 1/4) x)))))) (pow (* 1 y) 1/4))
(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))))))
(pow (* 1 x) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (+ (* (pow (/ 1 (pow x 7)) 1/4) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (pow (* 1 x) 1/4)))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (+ (* (pow (/ 1 (pow x 7)) 1/4) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (+ (* (pow (/ 1 (pow x 11)) 1/4) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3))))) (pow (* 1 x) 1/4))))
(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)))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* 1/4 (/ (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))) x)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) x)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/12 (pow y 3)) (+ (* -1/384 (pow y 3)) (* 1/32 (pow y 3))))) x)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))) x)) (* -1/4 (* y (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))))) 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 #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 #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))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(+ (* 1/4 (* (pow (/ 1 (pow x 3)) 1/4) y)) (pow (* 1 x) 1/4))
(fma.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) y) #s(literal 1/4 binary64) (pow.f64 x #s(literal 1/4 binary64)))
(+ (* y (+ (* -3/32 (* (pow (/ 1 (pow x 7)) 1/4) y)) (* 1/4 (pow (/ 1 (pow x 3)) 1/4)))) (pow (* 1 x) 1/4))
(fma.f64 (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) y) #s(literal -3/32 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) y (pow.f64 x #s(literal 1/4 binary64)))
(+ (* y (+ (* 1/4 (pow (/ 1 (pow x 3)) 1/4)) (* y (+ (* -3/32 (pow (/ 1 (pow x 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow x 11)) 1/4) y)))))) (pow (* 1 x) 1/4))
(fma.f64 (fma.f64 (fma.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64))) #s(literal 1/4 binary64)) y) #s(literal 7/128 binary64) (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64))) y (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) y (pow.f64 x #s(literal 1/4 binary64)))
(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 #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 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 (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 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))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (pow (* 1 y) 1/4))
(fma.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64)) x) #s(literal 1/4 binary64) (pow.f64 y #s(literal 1/4 binary64)))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (pow (* 1 y) 1/4)))
(fma.f64 (.f64 #s(literal 1/4 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (*.f64 x x) #s(literal -3/32 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))) #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64))))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) x)) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 2)) (* 1/32 (pow x 2)))) (+ (* (pow (/ 1 (pow y 11)) 1/4) (+ (* -1/32 (pow x 3)) (+ (* 1/384 (pow x 3)) (* 1/12 (pow x 3))))) (pow (* 1 y) 1/4))))
(fma.f64 (.f64 #s(literal 1/4 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 7/128 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 11 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (.f64 x x) #s(literal -3/32 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))) #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))))
(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 (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 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
(* 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)
(* -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 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))))))
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(fma.f64 (/.f64 y x) x x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 y x) x x)

rewrite175.0ms (4.5%)

Memory

12.3MiB live, 206.9MiB allocated

Rules

4 224×	`lower-/.f64`
4 224×	`lower-/.f32`
3 480×	`lower-fma.f64`
3 480×	`lower-fma.f32`
3 270×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	19
0	11	20
1	37	16
2	186	16
3	1567	16
0	8290	16

Stop Event

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

Counts

4 → 509

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64))
(sqrt.f64 (sqrt.f64 (+.f64 y x)))
(sqrt.f64 (+.f64 y x))
(+.f64 y x)

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

eval139.0ms (3.6%)

Memory: -24.0MiB live, 220.4MiB allocated
Compiler: Compiled 12 876 to 2 235 computations (82.6% saved)

prune11.0ms (0.3%)

Memory

6.8MiB live, 45.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	599	0	599
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	599	3	602

Accuracy

100.0%

Counts

602 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 y x))) #s(literal 2 binary64))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	97.6%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 35 to 29 computations (17.1% saved)

regimes10.0ms (0.3%)

Memory

-10.1MiB live, 28.3MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

14.9MiB live, 14.9MiB 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	(+.f64 x y)
1.0ms	(sqrt.f64 (+.f64 x y))
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`y`
97.6%	1	`(sqrt.f64 (+.f64 x y))`
97.6%	1	`(+.f64 x y)`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify29.0ms (0.8%)

Memory

-20.4MiB live, 61.8MiB 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 (5.2%)

Memory

2.5MiB live, 115.0MiB 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)

preprocess22.0ms (0.6%)

Memory: 17.9MiB live, 55.5MiB 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%)

analyze129.0ms (3.4%)

sample861.0ms (22.4%)

explain94.0ms (2.4%)

preprocess16.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize57.0ms (1.5%)

series6.0ms (0.1%)

simplify623.0ms (16.2%)

rewrite332.0ms (8.6%)

eval104.0ms (2.7%)

prune6.0ms (0.2%)

simplify4.0ms (0.1%)

localize35.0ms (0.9%)

series12.0ms (0.3%)

simplify215.0ms (5.6%)

rewrite188.0ms (4.9%)

eval264.0ms (6.9%)

prune8.0ms (0.2%)

simplify7.0ms (0.2%)

localize22.0ms (0.6%)

series4.0ms (0.1%)

simplify257.0ms (6.7%)

rewrite175.0ms (4.5%)

eval139.0ms (3.6%)

prune11.0ms (0.3%)

regimes10.0ms (0.3%)

regimes5.0ms (0.1%)

simplify29.0ms (0.8%)

soundness201.0ms (5.2%)

preprocess22.0ms (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