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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze194.0ms (3.1%)

Memory

-21.3MiB live, 22.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
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)

sample553.0ms (8.9%)

Memory

4.6MiB live, 913.5MiB allocated

Samples

290.0ms	8 256×	0	valid
30.0ms	523×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 128.0ms

ival-sqrt: 61.0ms (47.5% of total)

ival-add: 59.0ms (46% of total)

ival-true: 5.0ms (3.9% of total)

ival-assert: 3.0ms (2.3% of total)

Bogosity

explain71.0ms (1.1%)

Memory

20.5MiB live, 62.8MiB 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

53.0ms

512×

valid

Compiler

Compiled 26 to 16 computations (38.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-add: 39.0ms (90.8% of total)

ival-sqrt: 4.0ms (9.3% of total)

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

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

preprocess21.0ms (0.3%)

Memory

-15.1MiB live, 22.4MiB 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

0.9MiB live, 0.9MiB 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%)

Memory

4.1MiB live, 4.1MiB 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

localize12.0ms (0.2%)

Memory

18.8MiB live, 18.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.015625	(sqrt.f64 (+.f64 x y))

Samples

8.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

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

ival-sqrt: 2.0ms (61.3% of total)

ival-add: 1.0ms (30.6% of total)

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

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

series97.0ms (1.6%)

Memory

-30.4MiB live, 6.9MiB 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
93.0ms	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))

simplify579.0ms (9.3%)

Memory

37.2MiB live, 275.6MiB 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)

rewrite421.0ms (6.8%)

Memory

-27.7MiB live, 167.2MiB 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 (fma.f64 (.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))) (-.f64 x y))))
(/.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)

eval36.0ms (0.6%)

Memory: 13.7MiB live, 51.1MiB allocated
Compiler: Compiled 5 506 to 879 computations (84% saved)

prune7.0ms (0.1%)

Memory

16.1MiB live, 16.1MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	263	5	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	263	6	269

Accuracy

100.0%

Counts

269 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 (+.f64 y x) #s(literal 1/2 binary64))
▶	52.2%	(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
▶	36.1%	(sqrt.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal -1 binary64) x y)) (.f64 (-.f64 x y) (.f64 (neg.f64 y) y))) (*.f64 (-.f64 x y) (fma.f64 #s(literal -1 binary64) x y))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	99.7%	#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)))
▶	98.8%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 122 to 86 computations (29.5% saved)

simplify326.0ms (5.2%)

Memory

-15.4MiB live, 175.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	128	(.f64 (-.f64 x y) (.f64 (neg.f64 y) y))
cost-diff	192	(fma.f64 #s(literal -1 binary64) x y)
cost-diff	512	(-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal -1 binary64) x y)) (.f64 (-.f64 x y) (.f64 (neg.f64 y) y)))
cost-diff	2560	(/.f64 (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal -1 binary64) x y)) (.f64 (-.f64 x y) (.f64 (neg.f64 y) y))) (*.f64 (-.f64 x y) (fma.f64 #s(literal -1 binary64) x y)))
cost-diff	0	(-.f64 y x)
cost-diff	0	(+.f64 y x)
cost-diff	0	(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))
cost-diff	0	(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
cost-diff	0	#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)))
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (+ x y)) (sqrt.f64 y))
cost-diff	0	(+.f64 y x)
cost-diff	5824	(pow.f64 (+.f64 y x) #s(literal 1/2 binary64))

Rules

11 438×	`lower-fma.f32`
11 434×	`lower-fma.f64`
2 734×	`lower--.f32`
2 728×	`lower--.f64`
2 706×	`lower-*.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	215
0	57	164
1	110	163
2	297	162
3	934	158
4	3219	158
5	7166	158
0	8085	158

Stop Event

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

Calls

Call 1

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

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

localize119.0ms (1.9%)

Memory

9.8MiB live, 215.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0703125	(.f64 (-.f64 x y) (.f64 (neg.f64 y) y))
accuracy	8.867087080082138	(.f64 (.f64 x x) (fma.f64 #s(literal -1 binary64) x y))
accuracy	10.253821619038447	(-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal -1 binary64) x y)) (.f64 (-.f64 x y) (.f64 (neg.f64 y) y)))
accuracy	38.81206114183477	(/.f64 (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal -1 binary64) x y)) (.f64 (-.f64 x y) (.f64 (neg.f64 y) y))) (*.f64 (-.f64 x y) (fma.f64 #s(literal -1 binary64) x y)))
accuracy	0	(*.f64 (+.f64 y x) (-.f64 y x))
accuracy	0.0078125	(sqrt.f64 (-.f64 y x))
accuracy	0.46875	(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
accuracy	29.457705952352615	(sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))
accuracy	0	(sqrt.f64 y)
accuracy	0.01171875	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
accuracy	0.11328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
accuracy	0.1782848173521826	#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y)))
accuracy	0	(sqrt.f64 y)
accuracy	0.780399464159391	#s(approx (sqrt (+ x y)) (sqrt.f64 y))
accuracy	0	(+.f64 y x)
accuracy	0.01171875	(pow.f64 (+.f64 y x) #s(literal 1/2 binary64))

Samples

91.0ms

256×

valid

Compiler

Compiled 212 to 34 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-add: 26.0ms (43.2% of total)

ival-mult: 13.0ms (21.6% of total)

ival-sqrt: 12.0ms (19.9% of total)

ival-div: 5.0ms (8.3% of total)

ival-sub: 3.0ms (5% of total)

ival-neg: 1.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series133.0ms (2.1%)

Memory

2.2MiB live, 75.6MiB allocated

Counts

18 → 396

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
32.0ms	y	@	-inf	((pow (+ y x) 1/2) (+ y x) (sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (- y x) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (+ (* -1 x) y) (* (- x y) (* (neg y) y)) (sqrt (- y x)) (* (+ y x) (- y x)) (* (* x x) (+ (* -1 x) y)))
6.0ms	x	@	0	((pow (+ y x) 1/2) (+ y x) (sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (- y x) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (+ (* -1 x) y) (* (- x y) (* (neg y) y)) (sqrt (- y x)) (* (+ y x) (- y x)) (* (* x x) (+ (* -1 x) y)))
4.0ms	y	@	0	((pow (+ y x) 1/2) (+ y x) (sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (- y x) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (+ (* -1 x) y) (* (- x y) (* (neg y) y)) (sqrt (- y x)) (* (+ y x) (- y x)) (* (* x x) (+ (* -1 x) y)))
4.0ms	y	@	inf	((pow (+ y x) 1/2) (+ y x) (sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (- y x) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (+ (* -1 x) y) (* (- x y) (* (neg y) y)) (sqrt (- y x)) (* (+ y x) (- y x)) (* (* x x) (+ (* -1 x) y)))
4.0ms	x	@	inf	((pow (+ y x) 1/2) (+ y x) (sqrt (+ x y)) (sqrt y) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (- y x) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (+ (* -1 x) y) (* (- x y) (* (neg y) y)) (sqrt (- y x)) (* (+ y x) (- y x)) (* (* x x) (+ (* -1 x) y)))

simplify501.0ms (8.1%)

Memory

-30.7MiB live, 351.6MiB allocated

Algorithm

1×	egg-herbie

Rules

13 598×	`lower-fma.f64`
13 598×	`lower-fma.f32`
5 812×	`lower-*.f64`
5 812×	`lower-*.f32`
4 246×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	725	5983
1	2430	5082
0	9045	4830

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 376

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

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 x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) y (sqrt.f64 x))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
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(* (pow x 2) (- (+ (* -1 (/ y x)) (/ y x)) 1))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (+ (* -1 (/ y x)) (+ (/ y x) (/ (pow y 2) (pow x 2)))) 1))
(.f64 (.f64 (-.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 0 binary64)) #s(literal 1 binary64)) x) x)
(* (pow x 2) (- (+ (* -1 (/ y x)) (+ (/ y x) (/ (pow y 2) (pow x 2)))) 1))
(.f64 (.f64 (-.f64 (fma.f64 (/.f64 y x) (/.f64 y x) #s(literal 0 binary64)) #s(literal 1 binary64)) x) x)
(* -1 (pow x 3))
(neg.f64 (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (/ y x) 1))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (/ y x) 1))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (/ y x) 1))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (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)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 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 -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 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 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (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)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 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 -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 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 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (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)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 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 -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 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 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 (sqrt.f64 y) (neg.f64 x))) (neg.f64 x))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 (sqrt.f64 y) (neg.f64 x))) (neg.f64 x))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 (sqrt.f64 y) (neg.f64 x))) (neg.f64 x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (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)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 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 -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 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 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 y y) x) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 (*.f64 y y) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x)) x)) (neg.f64 x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 x))
x
(* -1 (* x (- (/ y x) (+ 1 (* 2 (/ y x))))))
(fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x)
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (- y (* 2 y))) (* -1 (/ (pow y 2) x))) (+ (* 2 (/ (* y (- y (* 2 y))) x)) (/ (pow y 2) x))) x)) 1)))
(fma.f64 (/.f64 (fma.f64 y (/.f64 (neg.f64 y) x) (-.f64 y (fma.f64 (.f64 y (/.f64 (neg.f64 y) x)) #s(literal 2 binary64) (/.f64 (.f64 y y) x)))) (neg.f64 x)) (neg.f64 x) x)
(* -1 (* x (- (* -1 (/ (+ (* -1 (- y (* 2 y))) (* -1 (/ (- (+ (* -1 (- (* -1 (pow y 2)) (+ (* 2 (* y (- y (* 2 y)))) (pow y 2)))) (* -1 (/ (pow y 3) x))) (+ (* 2 (/ (* y (- (* -1 (pow y 2)) (+ (* 2 (* y (- y (* 2 y)))) (pow y 2)))) x)) (/ (* (pow y 2) (- y (* 2 y))) x))) x))) x)) 1)))
(fma.f64 (/.f64 (-.f64 y (/.f64 (-.f64 (-.f64 (fma.f64 (neg.f64 y) y (*.f64 y y)) (/.f64 (pow.f64 y #s(literal 3 binary64)) x)) (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) x) #s(literal -1 binary64) #s(literal 0 binary64))) x)) (neg.f64 x)) (neg.f64 x) x)
(* -1 (pow x 3))
(neg.f64 (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ (+ y (/ (pow y 2) x)) x)))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 y y) x) y) x)) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ (+ y (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x))) x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (/.f64 (fma.f64 (neg.f64 y) y (/.f64 (pow.f64 y #s(literal 3 binary64)) x)) x)) x)) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 x))
(* -1 (* x (pow y 2)))
(.f64 (.f64 (neg.f64 y) x) y)
(* -1 (* x (+ (* -1 (/ (pow y 3) x)) (pow y 2))))
(*.f64 (fma.f64 y y (/.f64 (pow.f64 y #s(literal 3 binary64)) (neg.f64 x))) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (pow y 3) x)) (pow y 2))))
(*.f64 (fma.f64 y y (/.f64 (pow.f64 y #s(literal 3 binary64)) (neg.f64 x))) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (pow y 3) x)) (pow y 2))))
(*.f64 (fma.f64 y y (/.f64 (pow.f64 y #s(literal 3 binary64)) (neg.f64 x))) (neg.f64 x))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* -1 (/ (+ y (* -1 y)) x)) 1))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1))
(.f64 (.f64 (fma.f64 (/.f64 (*.f64 y (/.f64 (neg.f64 y) x)) x) #s(literal -1 binary64) #s(literal -1 binary64)) x) x)
(* (pow x 2) (- (* -1 (/ (+ y (+ (* -1 y) (* -1 (/ (pow y 2) x)))) x)) 1))
(.f64 (.f64 (fma.f64 (/.f64 (*.f64 y (/.f64 (neg.f64 y) x)) x) #s(literal -1 binary64) #s(literal -1 binary64)) x) x)
(* -1 (pow x 3))
(neg.f64 (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(* -1 (* (pow x 3) (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 (pow.f64 x #s(literal 3 binary64))))

rewrite329.0ms (5.3%)

Memory

-7.2MiB live, 435.2MiB allocated

Rules

4 670×	`lower-/.f32`
4 664×	`lower-/.f64`
4 170×	`lower-fma.f32`
4 166×	`lower-fma.f64`
3 876×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	147
0	55	132
1	213	127
2	1831	127
0	8559	123

Stop Event

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

Counts

18 → 1 110

Calls

Call 1

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

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

eval385.0ms (6.2%)

Memory: 40.3MiB live, 631.6MiB allocated
Compiler: Compiled 49 903 to 5 256 computations (89.5% saved)

prune41.0ms (0.7%)

Memory

-19.0MiB live, 142.2MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1 726	3	1 729
Fresh	0	0	0
Picked	3	2	5
Done	0	1	1
Total	1 729	6	1 735

Accuracy

100.0%

Counts

1 735 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.2%	(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
▶	99.0%	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	74.1%	(sqrt.f64 #s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x)))
▶	99.7%	#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))
✓	98.8%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 46 to 37 computations (19.6% saved)

simplify153.0ms (2.5%)

Memory

5.2MiB live, 277.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 y x)
cost-diff	0	(sqrt.f64 (-.f64 y x))
cost-diff	0	#s(approx (sqrt (* (+ y x) (- y x))) y)
cost-diff	0	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x)))
cost-diff	0	(/.f64 (neg.f64 y) x)
cost-diff	0	#s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x)))
cost-diff	1152	(fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x)
cost-diff	0	(sqrt.f64 y)
cost-diff	0	(/.f64 x (sqrt.f64 y))
cost-diff	0	(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))
cost-diff	0	#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))

Rules

12 718×	`lower-fma.f32`
12 714×	`lower-fma.f64`
2 946×	`lower-*.f64`
2 946×	`lower-*.f32`
1 682×	`lower-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	157
0	48	149
1	110	147
2	333	122
3	1216	108
4	4849	92
0	8318	92

Stop Event

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

Calls

Call 1

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

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

localize85.0ms (1.4%)

Memory

9.7MiB live, 126.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 y x)
accuracy	0.0078125	(sqrt.f64 (-.f64 y x))
accuracy	0.2010214485041775	#s(approx (sqrt (* (+ y x) (- y x))) y)
accuracy	0.46875	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) (sqrt.f64 (-.f64 y x)))
accuracy	0	(neg.f64 x)
accuracy	0	#s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x))
accuracy	0.015625	(sqrt.f64 #s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x)))
accuracy	16.175730836997854	(fma.f64 (/.f64 (neg.f64 y) x) (neg.f64 x) x)
accuracy	0	(sqrt.f64 y)
accuracy	0.01171875	(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y))
accuracy	0.17578125	(/.f64 x (sqrt.f64 y))
accuracy	0.1782848173521826	#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))

Samples

69.0ms

256×

valid

Compiler

Compiled 130 to 34 computations (73.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-mult: 13.0ms (33.1% of total)

ival-sqrt: 8.0ms (20.4% of total)

ival-div: 7.0ms (17.8% of total)

ival-add: 7.0ms (17.8% of total)

ival-sub: 3.0ms (7.6% of total)

ival-neg: 2.0ms (5.1% of total)

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

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

exact: 0.0ms (0% of total)

series60.0ms (1%)

Memory

-1.8MiB live, 53.5MiB allocated

Counts

13 → 288

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
39.0ms	x	@	-inf	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ (neg y) x) (neg x)) x) (sqrt (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y)))) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (/ (neg y) x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x) (neg x))
3.0ms	y	@	-inf	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ (neg y) x) (neg x)) x) (sqrt (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y)))) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (/ (neg y) x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x) (neg x))
2.0ms	x	@	inf	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ (neg y) x) (neg x)) x) (sqrt (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y)))) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (/ (neg y) x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x) (neg x))
2.0ms	y	@	inf	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ (neg y) x) (neg x)) x) (sqrt (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y)))) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (/ (neg y) x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x) (neg x))
2.0ms	y	@	0	((sqrt (+ x y)) (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) (/ x (sqrt y)) (sqrt y) (+ (* (/ (neg y) x) (neg x)) x) (sqrt (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y)))) (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) (/ (neg y) x) (/ (sqrt (* (+ y x) (- y x))) (sqrt (- y x))) (sqrt (* (+ y x) (- y x))) (sqrt (- y x)) (- y x) (neg x))

simplify234.0ms (3.8%)

Memory

-5.8MiB live, 257.4MiB allocated

Algorithm

1×	egg-herbie

Rules

14 174×	`lower-fma.f64`
14 174×	`lower-fma.f32`
6 352×	`lower-*.f64`
6 352×	`lower-*.f32`
4 486×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	698	4743
1	2339	3945
0	9250	3718

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 271

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

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))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)
(/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x (sqrt.f64 (pow.f64 y #s(literal 3 binary64)))) y)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(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)
(* -1 (/ y x))
(/.f64 (neg.f64 y) x)
(* -1 (/ y x))
(/.f64 (neg.f64 y) x)
(* -1 (/ y x))
(/.f64 (neg.f64 y) x)
(* -1 (/ y x))
(/.f64 (neg.f64 y) x)
(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 (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (fma.f64 (.f64 y #s(literal 1/2 binary64)) (/.f64 (+.f64 y (.f64 (/.f64 #s(literal 0 binary64) (.f64 x x)) y)) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (/.f64 (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) y (/.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) y (.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) y (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(* -1 x)
(neg.f64 x)
(- y x)
(-.f64 y x)
(- y x)
(-.f64 y x)
(- y x)
(-.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 #s(literal -1/8 binary64) (.f64 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 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.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 #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)
(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)) (* 1/2 (* 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)) (* 1/2 (* 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)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 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)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 x) (* -2 x))))))
(.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)
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(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 y y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 y y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))))) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ y x) 1))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(* x (- (/ y x) 1))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(* x (- (/ y x) 1))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 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 -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 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 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* 1/2 (* x (sqrt (/ 1 y))))
(.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 (sqrt.f64 y) (neg.f64 x))) (neg.f64 x))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 (sqrt.f64 y) (neg.f64 x))) (neg.f64 x))
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 (sqrt.f64 y) (neg.f64 x))) (neg.f64 x))
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
(* x (sqrt (/ 1 y)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 (neg.f64 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)))) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (* -1 (/ (+ (* 1/2 (* (sqrt x) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (* (pow y 2) (pow (sqrt -1) 2)))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (fma.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal -1/2 binary64) (.f64 (.f64 (neg.f64 y) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))) x)) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (* (pow y 2) (pow (sqrt -1) 2)))) (* -1 (* (sqrt (/ 1 x)) (* (pow y 3) (pow (sqrt -1) 2))))) x)) (+ (* 1/2 (* (sqrt x) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (* (pow y 2) (pow (sqrt -1) 2))))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal -1/2 binary64) (.f64 (.f64 (neg.f64 y) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 (fma.f64 (neg.f64 (neg.f64 (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (*.f64 (sqrt.f64 x) y) y)) x)) x)) x)) (neg.f64 x))
x
(* -1 (* x (- (/ y x) (+ 1 (* 2 (/ y x))))))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (- y (* 2 y))) (* -1 (/ (pow y 2) x))) (+ (* 2 (/ (* y (- y (* 2 y))) x)) (/ (pow y 2) x))) x)) 1)))
(neg.f64 (fma.f64 (/.f64 (fma.f64 y (/.f64 (neg.f64 y) x) (-.f64 y (fma.f64 (/.f64 (.f64 (neg.f64 y) y) x) #s(literal 2 binary64) (/.f64 (.f64 y y) x)))) (neg.f64 x)) x (neg.f64 x)))
(* -1 (* x (- (* -1 (/ (+ (* -1 (- y (* 2 y))) (* -1 (/ (- (+ (* -1 (- (* -1 (pow y 2)) (+ (* 2 (* y (- y (* 2 y)))) (pow y 2)))) (* -1 (/ (pow y 3) x))) (+ (* 2 (/ (* y (- (* -1 (pow y 2)) (+ (* 2 (* y (- y (* 2 y)))) (pow y 2)))) x)) (/ (* (pow y 2) (- y (* 2 y))) x))) x))) x)) 1)))
(neg.f64 (fma.f64 (/.f64 (-.f64 y (/.f64 (-.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) y) y) (/.f64 (pow.f64 y #s(literal 3 binary64)) x)) (fma.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) x) #s(literal 2 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (neg.f64 x)))) x)) (neg.f64 x)) x (neg.f64 x)))
(* -1 (/ y x))
(/.f64 (neg.f64 y) x)
(* -1 (/ y x))
(/.f64 (neg.f64 y) x)
(* -1 (/ y x))
(/.f64 (neg.f64 y) x)
(* -1 (/ y x))
(/.f64 (neg.f64 y) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 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 -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 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 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 y y #s(literal 0 binary64)) x) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 (/.f64 (fma.f64 y y #s(literal 0 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))))) x)) x)) (neg.f64 x))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) (neg.f64 x))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)

rewrite240.0ms (3.8%)

Memory

38.2MiB live, 186.0MiB allocated

Rules

5 336×	`lower-fma.f32`
5 332×	`lower-fma.f64`
4 140×	`lower-/.f32`
4 134×	`lower-/.f64`
3 878×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	148
0	48	140
1	223	138
2	2041	130
0	8645	128

Stop Event

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

Counts

13 → 303

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ x y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (sqrt.f64 y)))
(.f64 (-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) y) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 y) (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y)) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))) (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) y)) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (sqrt.f64 y) (-.f64 (sqrt.f64 y) (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -3 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) #s(literal 3 binary64)) (pow.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (fma.f64 (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (.f64 (/.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y)))) (/.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))))))))
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(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) y) y))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 y)) (neg.f64 (sqrt.f64 y))))))
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(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x)))) (neg.f64 (neg.f64 (+.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 (neg.f64 x) y)) (.f64 (-.f64 (neg.f64 x) y) (.f64 y y))) (*.f64 (-.f64 (neg.f64 x) y) (-.f64 (neg.f64 x) y)))
(/.f64 (-.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) (+.f64 (hypot.f64 y x) (.f64 y x))) (.f64 (+.f64 (hypot.f64 y x) (.f64 y x)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (+.f64 (hypot.f64 y x) (.f64 y x)) (+.f64 (hypot.f64 y x) (*.f64 y x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (neg.f64 (+.f64 (hypot.f64 x y) (*.f64 y x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (+.f64 (hypot.f64 x y) (*.f64 y x)))
(/.f64 (neg.f64 (fma.f64 x x (*.f64 (neg.f64 y) y))) (neg.f64 (neg.f64 (+.f64 y x))))
(/.f64 (neg.f64 (fma.f64 x x (*.f64 (neg.f64 y) y))) (neg.f64 (-.f64 (neg.f64 x) y)))
(/.f64 (neg.f64 (fma.f64 x x (*.f64 (neg.f64 y) y))) (+.f64 y x))
(/.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))) (neg.f64 (+.f64 y x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 y y (-.f64 (.f64 x x) (.f64 (neg.f64 x) y)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (hypot.f64 x y) (*.f64 y x))))
(/.f64 (neg.f64 (-.f64 (pow.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 y x) (+.f64 y x)) (+.f64 y x))
(/.f64 (fma.f64 x x (*.f64 (neg.f64 y) y)) (neg.f64 (+.f64 y x)))
(/.f64 (fma.f64 x x (*.f64 (neg.f64 y) y)) (-.f64 (neg.f64 x) y))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y x) (*.f64 (-.f64 y x) (+.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (neg.f64 x) y) (fma.f64 x x (*.f64 (neg.f64 y) y))))
(/.f64 #s(literal 1 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 #s(literal 1 binary64) (/.f64 (+.f64 (hypot.f64 x y) (*.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 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (+.f64 (hypot.f64 x y) (*.f64 y x))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y y (-.f64 (.f64 x x) (.f64 (neg.f64 x) y))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (hypot.f64 x y) (*.f64 y x)))
(/.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 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 y x) (*.f64 (-.f64 y x) (+.f64 y x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (neg.f64 x) y) (fma.f64 x x (*.f64 (neg.f64 y) y)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.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 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (hypot.f64 x y) (*.f64 y x)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(neg.f64 (-.f64 x y))
(fma.f64 #s(literal 1 binary64) y (neg.f64 x))
(fma.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 y) #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) (neg.f64 y) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) x y)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (neg.f64 x))
(fma.f64 x #s(literal -1 binary64) y)
(-.f64 (/.f64 (.f64 x x) (neg.f64 (+.f64 y x))) (/.f64 (.f64 y y) (neg.f64 (+.f64 y x))))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (.f64 x x) (.f64 (neg.f64 x) y)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (-.f64 (.f64 x x) (.f64 (neg.f64 x) y)))))
(-.f64 (+.f64 y #s(literal 0 binary64)) x)
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (+.f64 (hypot.f64 x y) (.f64 y x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (hypot.f64 x y) (.f64 y x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (hypot.f64 x y) (.f64 y x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (neg.f64 (+.f64 (hypot.f64 x y) (.f64 y x)))))
(-.f64 (/.f64 (.f64 y y) (+.f64 y x)) (/.f64 (.f64 x x) (+.f64 y x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 (neg.f64 x) y)) (/.f64 (.f64 y y) (-.f64 (neg.f64 x) y)))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (+.f64 (hypot.f64 y x) (.f64 y x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (hypot.f64 y x) (.f64 y x))))
(-.f64 #s(literal 0 binary64) (-.f64 x y))
(-.f64 y x)
(+.f64 (neg.f64 x) y)
(+.f64 y (neg.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 #s(literal 0 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))) (neg.f64 (+.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal 0 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))))
(neg.f64 x)
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x)))))
(-.f64 #s(literal 0 binary64) x)
(+.f64 #s(literal 0 binary64) (neg.f64 x))

eval350.0ms (5.6%)

Memory: -47.2MiB live, 211.3MiB allocated
Compiler: Compiled 10 709 to 1 860 computations (82.6% saved)

prune33.0ms (0.5%)

Memory

7.0MiB live, 45.8MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	597	2	599
Fresh	0	0	0
Picked	2	1	3
Done	0	3	3
Total	599	6	605

Accuracy

100.0%

Counts

605 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.2%	(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
▶	98.1%	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	74.1%	(sqrt.f64 #s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) #s(approx (+ (* (/ (neg y) x) (neg x)) x) (fma.f64 (/.f64 y x) x x))))
✓	99.7%	#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))
✓	98.8%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 44 to 36 computations (18.2% saved)

simplify254.0ms (4.1%)

Memory

-0.3MiB live, 272.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (- y x)) (sqrt.f64 y))
cost-diff	0	#s(approx (sqrt (* (+ y x) (- y x))) y)
cost-diff	0	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y)))
cost-diff	0	#s(approx (+ (* (/ (neg y) x) (neg x)) x) (fma.f64 (/.f64 y x) x x))
cost-diff	0	#s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) #s(approx (+ (* (/ (neg y) x) (neg x)) x) (fma.f64 (/.f64 y x) x x)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) #s(approx (+ (* (/ (neg y) x) (neg x)) x) (fma.f64 (/.f64 y x) x x))))
cost-diff	896	(fma.f64 (/.f64 y x) x x)

Rules

12 922×	`lower-fma.f32`
12 920×	`lower-fma.f64`
2 928×	`lower-*.f64`
2 928×	`lower-*.f32`
2 480×	`lower--.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	156
0	38	148
1	102	143
2	330	94
3	1182	92
4	4030	76
0	8256	76

Stop Event

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

Calls

Call 1

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

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

localize111.0ms (1.8%)

Memory

26.0MiB live, 64.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 y)
accuracy	0.2010214485041775	#s(approx (sqrt (* (+ y x) (- y x))) y)
accuracy	0.46875	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y)))
accuracy	0.776328975969621	#s(approx (sqrt (- y x)) (sqrt.f64 y))
accuracy	0	#s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) #s(approx (+ (* (/ (neg y) x) (neg x)) x) (fma.f64 (/.f64 y x) x x)))
accuracy	0	#s(approx (+ (* (/ (neg y) x) (neg x)) x) (fma.f64 (/.f64 y x) x x))
accuracy	0.015625	(sqrt.f64 #s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) #s(approx (+ (* (/ (neg y) x) (neg x)) x) (fma.f64 (/.f64 y x) x x))))
accuracy	16.175730836997854	(fma.f64 (/.f64 y x) x x)

Samples

98.0ms

256×

valid

Compiler

Compiled 108 to 31 computations (71.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 13.0ms (36.6% of total)

ival-div: 7.0ms (19.7% of total)

ival-sqrt: 6.0ms (16.9% of total)

ival-add: 4.0ms (11.3% of total)

ival-sub: 3.0ms (8.4% of total)

ival-neg: 2.0ms (5.6% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory

-21.3MiB live, 16.2MiB allocated

Counts

8 → 180

Calls

Call 1

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

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

Calls

6 calls:

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

simplify218.0ms (3.5%)

Memory

4.0MiB live, 291.1MiB allocated

Algorithm

1×	egg-herbie

Rules

15 066×	`lower-fma.f64`
15 066×	`lower-fma.f32`
6 358×	`lower-*.f64`
6 358×	`lower-*.f32`
4 386×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	673	3641
1	2258	2863
0	9188	2676

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 160

Calls

Call 1

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

Outputs
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(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)
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(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 (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* 1/2 (/ (* y (+ x (* -1 x))) (* x (sqrt -1)))) (* x (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2)))))) (* x (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))))))
(fma.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 0 binary64) x) x)) (/.f64 y (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(+ (* x (sqrt -1)) (* y (+ (* 1/2 (/ (+ x (* -1 x)) (* x (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ x (* -1 x)) (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))))) (* (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ x (* -1 x)) 2) (* (pow x 2) (pow (sqrt -1) 2))))) (* x (sqrt -1)))))))))
(fma.f64 (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 0 binary64) x) x)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y x)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 0 binary64) x) x)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 y (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) y (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 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)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 x) (* -2 x))))))
(.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)) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 x) (* -2 x)))) (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (* -1 (pow x 2)) (+ (* -2 (* x (- (* -1 x) (* -2 x)))) (pow x 2))))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (hypot.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) 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)))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 x) (* -2 x)))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (- (* -1 (pow x 2)) (+ (* -2 (* x (- (* -1 x) (* -2 x)))) (pow x 2))))) (* 1/2 (* (sqrt (/ 1 (pow y 7))) (- (pow x 3) (+ (* -2 (* x (- (* -1 (pow x 2)) (+ (* -2 (* x (- (* -1 x) (* -2 x)))) (pow x 2))))) (+ (* 1/4 (* y (pow (- (* -1 x) (* -2 x)) 2))) (* (pow x 2) (- (* -1 x) (* -2 x))))))))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) x (fma.f64 (hypot.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 (*.f64 x x) y) #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
y
(* y (- (+ 1 (* -1 (/ x y))) (* -2 (/ x y))))
(fma.f64 (/.f64 x y) y y)
(* y (- (+ 1 (+ (* -1 (/ x y)) (* -1 (/ (pow x 2) (pow y 2))))) (+ (* -2 (/ x y)) (+ (* -2 (/ (* x (- (* -1 x) (* -2 x))) (pow y 2))) (/ (pow x 2) (pow y 2))))))
(.f64 (-.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 x y)) #s(literal 1 binary64)) (fma.f64 #s(literal -2 binary64) (+.f64 (/.f64 x y) (.f64 (/.f64 x y) (/.f64 x y))) (*.f64 (/.f64 x y) (/.f64 x y)))) y)
(* y (- (+ 1 (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ (pow x 3) (pow y 3))))) (+ (* -2 (/ x y)) (+ (* -2 (/ (* x (- (* -1 x) (* -2 x))) (pow y 2))) (+ (* -2 (/ (* x (- (* -1 (pow x 2)) (+ (* -2 (* x (- (* -1 x) (* -2 x)))) (pow x 2)))) (pow y 3))) (+ (/ (* (pow x 2) (- (* -1 x) (* -2 x))) (pow y 3)) (/ (pow x 2) (pow y 2))))))))
(.f64 (-.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 x y)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) #s(literal 1 binary64)) (fma.f64 #s(literal -2 binary64) (/.f64 x y) (fma.f64 #s(literal -2 binary64) (fma.f64 (/.f64 x y) (/.f64 x y) (.f64 (hypot.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (/.f64 x (pow.f64 y #s(literal 3 binary64))))) (fma.f64 (/.f64 x y) (/.f64 x y) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))))) 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)
(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 #s(literal -1/8 binary64) (.f64 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 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.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 #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 (* 1/2 (/ (+ x (* -1 x)) y))))
(+.f64 (/.f64 #s(literal 0 binary64) y) y)
(* y (+ 1 (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) y) (/.f64 #s(literal 0 binary64) y)) y y)
(* y (+ 1 (+ (* -1/4 (/ (* (+ x (* -1 x)) (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ x (* -1 x)) y)) (* 1/2 (/ (- (* -1 (pow x 2)) (* 1/4 (pow (+ x (* -1 x)) 2))) (pow y 2)))))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) y) (/.f64 #s(literal 0 binary64) y))) y y)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 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)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7)))))))))
(.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.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)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 (neg.f64 y) (/.f64 (neg.f64 x) y) y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 (neg.f64 y) (/.f64 (neg.f64 x) y) y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 (neg.f64 y) (/.f64 (neg.f64 x) y) y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 y) #s(literal 1 binary64))
(* -1 (* y (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 x) (* -2 x)))) (* (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)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64))))
(* -1 (* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (- (pow x 2) (+ (* -1 (pow x 2)) (* 2 (* x (- (* -1 x) (* -2 x)))))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 x) (* -2 x)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (neg.f64 y) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (hypot.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 y)) (- (pow x 3) (+ (* -1/4 (/ (* y (pow (- (* -1 x) (* -2 x)) 2)) (pow (sqrt -1) 2))) (+ (* 2 (* x (- (pow x 2) (+ (* -1 (pow x 2)) (* 2 (* x (- (* -1 x) (* -2 x)))))))) (* (pow x 2) (- (* -1 x) (* -2 x)))))))) (* 1/2 (* (sqrt y) (- (pow x 2) (+ (* -1 (pow x 2)) (* 2 (* x (- (* -1 x) (* -2 x))))))))) (pow y 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (* -1 x) (* -2 x)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))) x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (.f64 (.f64 x x) y) #s(literal -1 binary64)) #s(literal -1/4 binary64) (fma.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (sqrt.f64 y))) (neg.f64 (pow.f64 y #s(literal 3 binary64)))))))
y
(* -1 (* y (- (* -1 (/ (- (* -1 x) (* -2 x)) y)) 1)))
(fma.f64 (neg.f64 y) (/.f64 (neg.f64 x) y) y)
(* -1 (* y (- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (pow x 2) (+ (* -1 (pow x 2)) (* 2 (* x (- (* -1 x) (* -2 x)))))) y))) (* -2 x)) y)) 1)))
(fma.f64 (neg.f64 y) (/.f64 (fma.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) y) #s(literal -1 binary64) x) (neg.f64 y)) y)
(* -1 (* y (- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (+ (* -1 (/ (- (pow x 3) (+ (* 2 (* x (- (pow x 2) (+ (* -1 (pow x 2)) (* 2 (* x (- (* -1 x) (* -2 x)))))))) (* (pow x 2) (- (* -1 x) (* -2 x))))) y)) (pow x 2)) (+ (* -1 (pow x 2)) (* 2 (* x (- (* -1 x) (* -2 x)))))) y))) (* -2 x)) y)) 1)))
(fma.f64 (neg.f64 y) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 y)) (hypot.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (neg.f64 y)) x) (neg.f64 y)) y)
y
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(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (* y (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 (neg.f64 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)))) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (* -1 (/ (+ (* 1/2 (* (sqrt x) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (* (pow y 2) (pow (sqrt -1) 2)))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y (/.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal -1/2 binary64) (.f64 (.f64 (neg.f64 y) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))) x)) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (* (pow y 2) (pow (sqrt -1) 2)))) (* -1 (* (sqrt (/ 1 x)) (* (pow y 3) (pow (sqrt -1) 2))))) x)) (+ (* 1/2 (* (sqrt x) (* y (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (* (pow y 2) (pow (sqrt -1) 2))))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y) (/.f64 (-.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal -1/2 binary64) (.f64 (.f64 (neg.f64 y) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 (fma.f64 (neg.f64 (neg.f64 (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (*.f64 (sqrt.f64 x) y) y)) x)) x)) x)) (neg.f64 x))
x
(* -1 (* x (- (/ y x) (+ 1 (* 2 (/ y x))))))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (- y (* 2 y))) (* -1 (/ (pow y 2) x))) (+ (* 2 (/ (* y (- y (* 2 y))) x)) (/ (pow y 2) x))) x)) 1)))
(neg.f64 (fma.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 y) (/.f64 y x) y) (fma.f64 y (/.f64 y x) (/.f64 (.f64 (.f64 #s(literal -2 binary64) y) y) x))) (neg.f64 x)) x (neg.f64 x)))
(* -1 (* x (- (* -1 (/ (+ (* -1 (- y (* 2 y))) (* -1 (/ (- (+ (* -1 (- (* -1 (pow y 2)) (+ (* 2 (* y (- y (* 2 y)))) (pow y 2)))) (* -1 (/ (pow y 3) x))) (+ (* 2 (/ (* y (- (* -1 (pow y 2)) (+ (* 2 (* y (- y (* 2 y)))) (pow y 2)))) x)) (/ (* (pow y 2) (- y (* 2 y))) x))) x))) x)) 1)))
(neg.f64 (fma.f64 (/.f64 (-.f64 y (/.f64 (-.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) y) y) (/.f64 (pow.f64 y #s(literal 3 binary64)) x)) (fma.f64 (/.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64))) x) #s(literal 2 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (neg.f64 x)))) x)) (neg.f64 x)) x (neg.f64 x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 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 -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 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 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (+ y (* -1 y)) (* x (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* x (sqrt -1)))) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 y y #s(literal 0 binary64)) x) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) (neg.f64 x))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* x (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) x)) (* 1/2 (/ (+ y (* -1 y)) (sqrt -1)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 (/.f64 (fma.f64 y y #s(literal 0 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x)) x)) (neg.f64 x))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))

rewrite194.0ms (3.1%)

Memory

-1.3MiB live, 272.8MiB allocated

Rules

4 994×	`lower-fma.f32`
4 992×	`lower-fma.f64`
4 850×	`lower-/.f32`
4 846×	`lower-/.f64`
3 818×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	150
0	38	142
1	199	131
2	1889	122
0	8587	113

Stop Event

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

Counts

8 → 96

Calls

Call 1

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

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

eval32.0ms (0.5%)

Memory: 5.7MiB live, 80.6MiB allocated
Compiler: Compiled 4 464 to 966 computations (78.4% saved)

prune9.0ms (0.1%)

Memory

-17.1MiB live, 28.7MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	0	0	0
Picked	0	2	2
Done	1	3	4
Total	256	6	262

Accuracy

100.0%

Counts

262 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.1%	(/.f64 #s(approx (sqrt (* (+ y x) (- y x))) y) #s(approx (sqrt (- y x)) (sqrt.f64 y)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	74.1%	(sqrt.f64 #s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) #s(approx (+ (* (/ (neg y) x) (neg x)) x) (fma.f64 (/.f64 y x) x x))))
	79.2%	(sqrt.f64 #s(approx (/ (- (* (* x x) (+ (* -1 x) y)) (* (- x y) (* (neg y) y))) (* (- x y) (+ (* -1 x) y))) #s(approx (+ (* (/ (neg y) x) (neg x)) x) (fma.f64 (*.f64 (neg.f64 y) x) (/.f64 #s(literal -1 binary64) x) x))))
✓	99.7%	#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))
✓	98.8%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 159 to 93 computations (41.5% saved)

regimes16.0ms (0.3%)

Memory

36.6MiB live, 36.6MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

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)

regimes29.0ms (0.5%)

Memory

-10.8MiB live, 28.4MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

4 calls:

17.0ms	(+.f64 x y)
4.0ms	(sqrt.f64 (+.f64 x y))
4.0ms	y
4.0ms	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

11.5MiB live, 11.5MiB 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	(sqrt.f64 (+.f64 x y))
1.0ms	(+.f64 x y)
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`y`
98.8%	1	`(sqrt.f64 (+.f64 x y))`
98.8%	1	`(+.f64 x y)`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify34.0ms (0.5%)

Memory

-9.8MiB live, 67.9MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	12	16

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness294.0ms (4.7%)

Memory

-23.6MiB live, 219.5MiB allocated

Rules

27 648×	`lower-fma.f64`
27 648×	`lower-fma.f32`
5 638×	`lower-*.f64`
5 638×	`lower-*.f32`
5 128×	`lower-fma.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
0	156	630
1	454	600
2	1426	582
3	4628	570
0	8167	534

Stop Event

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

Compiler

Compiled 28 to 19 computations (32.1% saved)

preprocess29.0ms (0.5%)

Memory: 9.4MiB live, 85.6MiB allocated
Remove: (sort x y)
Compiler: Compiled 62 to 54 computations (12.9% 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%)

analyze194.0ms (3.1%)

sample553.0ms (8.9%)

explain71.0ms (1.1%)

preprocess21.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize12.0ms (0.2%)

series97.0ms (1.6%)

simplify579.0ms (9.3%)

rewrite421.0ms (6.8%)

eval36.0ms (0.6%)

prune7.0ms (0.1%)

simplify326.0ms (5.2%)

localize119.0ms (1.9%)

series133.0ms (2.1%)

simplify501.0ms (8.1%)

rewrite329.0ms (5.3%)

eval385.0ms (6.2%)

prune41.0ms (0.7%)

simplify153.0ms (2.5%)

localize85.0ms (1.4%)

series60.0ms (1%)

simplify234.0ms (3.8%)

rewrite240.0ms (3.8%)

eval350.0ms (5.6%)

prune33.0ms (0.5%)

simplify254.0ms (4.1%)

localize111.0ms (1.8%)

series14.0ms (0.2%)

simplify218.0ms (3.5%)

rewrite194.0ms (3.1%)

eval32.0ms (0.5%)

prune9.0ms (0.1%)

regimes16.0ms (0.3%)

regimes29.0ms (0.5%)

regimes5.0ms (0.1%)

simplify34.0ms (0.5%)

soundness294.0ms (4.7%)

preprocess29.0ms (0.5%)

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