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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze15.0ms (0.2%)

Memory

12.5MiB live, 12.5MiB 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)

sample556.0ms (8.9%)

Memory

-21.8MiB live, 1 048.8MiB allocated

Samples

332.0ms	8 256×	0	valid
22.0ms	497×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 171.0ms

ival-add: 100.0ms (58.5% of total)

ival-sqrt: 61.0ms (35.7% of total)

ival-true: 6.0ms (3.5% of total)

ival-assert: 3.0ms (1.8% of total)

Bogosity

explain132.0ms (2.1%)

Memory

8.0MiB live, 86.5MiB 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

112.0ms

512×

valid

Compiler

Compiled 28 to 16 computations (42.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 101.0ms

ival-sqrt: 98.0ms (96.6% of total)

ival-add: 3.0ms (3% of total)

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

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

preprocess17.0ms (0.3%)

Memory

-3.4MiB live, 35.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort x y)

Compiler

Compiled 6 to 4 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (0%)

Memory

6.0MiB live, 6.0MiB 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

localize20.0ms (0.3%)

Memory

-26.6MiB live, 30.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.03125	(sqrt.f64 (+.f64 x y))

Samples

9.0ms

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 (57.6% of total)

ival-add: 1.0ms (28.8% of total)

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

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

series6.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

2 → 48

Calls

Call 1

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

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

Calls

6 calls:

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

simplify232.0ms (3.7%)

Memory

13.6MiB live, 280.1MiB 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) (.f64 (.f64 x x) x))) (.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) (.f64 (.f64 x x) x))) #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) (.f64 (.f64 y y) y))) (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) (.f64 (.f64 y y) y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) x)) x (fma.f64 (.f64 (.f64 (.f64 #s(literal 1/16 binary64) x) x) x) (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) (.f64 (*.f64 y y) y))) (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) (.f64 (.f64 y y) y))) (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) (.f64 (.f64 y y) y))) (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)))) (.f64 (.f64 x x) x)) (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) (.f64 (.f64 y y) y))) (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) (.f64 (.f64 y y) y))) (.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) (.f64 (.f64 y y) y))) #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) (.f64 (.f64 x x) x))) (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) (.f64 (*.f64 x x) x))) #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 y y) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) y) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64))) (fma.f64 (.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) (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) (.f64 (.f64 x x) x))) (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) (.f64 (.f64 x x) x))) (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)))) (.f64 (.f64 y y) y)) (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) (.f64 (.f64 x x) x))) (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)

rewrite172.0ms (2.7%)

Memory

3.5MiB live, 203.3MiB 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 (fma.f64 y (+.f64 y x) (.f64 x x)) (-.f64 x y)))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (-.f64 (.f64 x x) (.f64 (-.f64 y x) y))))) (sqrt.f64 (-.f64 (.f64 x x) (.f64 (-.f64 y x) y))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (.f64 (-.f64 y x) y) (.f64 (-.f64 y x) y)) (.f64 (-.f64 y x) y))))) (sqrt.f64 (fma.f64 (.f64 (-.f64 y x) y) (fma.f64 (-.f64 y x) y (neg.f64 (.f64 x x))) (.f64 (.f64 x x) (.f64 x x)))))
(.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 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (-.f64 x y))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (-.f64 (.f64 x x) (.f64 (-.f64 y x) y)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 x x) (.f64 (-.f64 y x) y))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (.f64 (-.f64 y x) y) (.f64 (-.f64 y x) y)) (.f64 (-.f64 y x) y)))) #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))) (.f64 (.f64 x x) (.f64 x x)))))
(*.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 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 y x) y (*.f64 x x))))))
(.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 y x))))
(.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))))
(.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 y x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 x y)))))
(.f64 (sqrt.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
(.f64 (sqrt.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x)))) (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x))))))
(.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 y x) y (*.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 x y))) (sqrt.f64 (.f64 (-.f64 x y) (+.f64 y x))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 y x) y (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 y y) y (.f64 (*.f64 x x) x))))
(*.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))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 x y))))
(.f64 (sqrt.f64 (fma.f64 (-.f64 y x) y (.f64 x x))) (sqrt.f64 (/.f64 (+.f64 y x) (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(.f64 (sqrt.f64 (fma.f64 (-.f64 y x) y (.f64 x x))) (pow.f64 (/.f64 (+.f64 y x) (fma.f64 (-.f64 y x) y (*.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(*.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 (*.f64 (+.f64 y x) (+.f64 y x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #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 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (-.f64 y x) y (.f64 x x))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x)))) (neg.f64 (sqrt.f64 (-.f64 y x))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))))) (neg.f64 (sqrt.f64 (neg.f64 (-.f64 x y)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))))) (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 (-.f64 y x) y (.f64 x x))))))
(/.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 y y (.f64 x x)) (.f64 (-.f64 x y) (+.f64 y x))) (-.f64 x y))) (sqrt.f64 (fma.f64 y y (.f64 x x))))
(/.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (-.f64 x y))) (-.f64 x y))) (sqrt.f64 (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))))
(/.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (-.f64 x y))) (fma.f64 (-.f64 y x) y (.f64 x x)))) (sqrt.f64 (.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)) (-.f64 x y))))
(/.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)) (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) (fma.f64 (-.f64 y x) y (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x (/.f64 x (-.f64 x y))) (.f64 x (/.f64 x (-.f64 x y)))) (.f64 (.f64 y (/.f64 y (-.f64 x y))) (.f64 y (/.f64 y (-.f64 x y)))))) (sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 (.f64 x (/.f64 x (-.f64 x y))) (.f64 x (/.f64 x (-.f64 x y)))) (.f64 x (/.f64 x (-.f64 x y)))) (.f64 (.f64 (.f64 y (/.f64 y (-.f64 x y))) (.f64 y (/.f64 y (-.f64 x y)))) (.f64 y (/.f64 y (-.f64 x y)))))) (sqrt.f64 (fma.f64 (.f64 x (/.f64 x (-.f64 x y))) (.f64 x (/.f64 x (-.f64 x y))) (fma.f64 (.f64 y (/.f64 y (-.f64 x y))) (.f64 y (/.f64 y (-.f64 x y))) (.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 (*.f64 (-.f64 x y) (-.f64 x y))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))) (neg.f64 (sqrt.f64 (-.f64 x y))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 y x) y (.f64 x x)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 y y (.f64 x x)) (.f64 (-.f64 x y) (+.f64 y x)))) (sqrt.f64 (.f64 (fma.f64 y y (*.f64 x x)) (-.f64 x y))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 y y (.f64 x x)) (.f64 (-.f64 x y) (+.f64 y x)))) (sqrt.f64 (.f64 (-.f64 x y) (fma.f64 y y (*.f64 x x)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (-.f64 x y)))) (sqrt.f64 (.f64 (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 x y))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (-.f64 x y)))) (sqrt.f64 (.f64 (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (-.f64 x y)) (fma.f64 (-.f64 y x) y (.f64 x x)))))
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eval32.0ms (0.5%)

Memory: 19.9MiB live, 54.3MiB allocated
Compiler: Compiled 7 836 to 851 computations (89.1% saved)

prune85.0ms (1.4%)

Memory

-16.3MiB live, 112.5MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	261	7	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	261	8	269

Accuracy

100.0%

Counts

269 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	49.8%	(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
▶	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 y x))))
▶	100.0%	(sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))))
▶	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	99.0%	#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)))
▶	96.9%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 166 to 104 computations (37.3% saved)

simplify157.0ms (2.5%)

Memory

19.2MiB live, 126.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
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	(+.f64 y x)
cost-diff	0	(sqrt.f64 (+.f64 y x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 y x)))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 y x))))
cost-diff	0	(+.f64 y x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 y x))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x)))
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (+ x y)) (sqrt.f64 y))
cost-diff	0	(/.f64 x (-.f64 x y))
cost-diff	0	(sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))))
cost-diff	128	(neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))
cost-diff	2304	(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))

Rules

4 088×	`lower-fma.f32`
4 084×	`lower-fma.f64`
2 608×	`lower-*.f32`
2 604×	`lower-*.f64`
2 184×	`lower-+.f32`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	27	162
0	48	222
1	76	222
2	121	222
3	165	213
4	301	213
5	648	205
6	1046	189
7	1207	189
8	1709	125
9	2190	125
10	2710	125
11	3882	125
12	4766	125
13	5213	125
14	7408	125
15	7517	125
0	8468	125

Stop Event

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

Calls

Call 1

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

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

localize98.0ms (1.6%)

Memory

2.2MiB live, 154.8MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 y)
accuracy	0.0234375	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
accuracy	0.10546875	(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
accuracy	0.47984263801214766	#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	(+.f64 y x)
accuracy	0.02734375	(sqrt.f64 (+.f64 y x))
accuracy	0.26953125	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 y x))))
accuracy	0.28515625	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 y x)))
accuracy	0	(+.f64 y x)
accuracy	0.01953125	(/.f64 #s(literal 1 binary64) (+.f64 y x))
accuracy	0.02734375	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x))))
accuracy	0.15625	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x)))
accuracy	0	(sqrt.f64 y)
accuracy	1.7877051856462651	#s(approx (sqrt (+ x y)) (sqrt.f64 y))
accuracy	0.015625	(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
accuracy	0.015625	(/.f64 x (-.f64 x y))
accuracy	0.02734375	(sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y))))))
accuracy	0.0390625	(*.f64 y (/.f64 y (-.f64 x y)))

Samples

80.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 153 to 29 computations (81% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-div: 15.0ms (33% of total)

ival-add: 11.0ms (24.2% of total)

ival-sqrt: 9.0ms (19.8% of total)

ival-mult: 6.0ms (13.2% of total)

ival-neg: 1.0ms (2.2% of total)

ival-sub: 1.0ms (2.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series47.0ms (0.7%)

Memory

6.2MiB live, 85.4MiB allocated

Counts

18 → 396

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	y	@	-inf	((+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (sqrt (+ x y)) (sqrt y) (/ 1 (/ 1 (+ y x))) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (+ y x)) (+ y x) (/ 1 (/ 1 (sqrt (+ y x)))) (/ 1 (sqrt (+ y x))) (sqrt (+ y x)) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (* y (/ y (- x y))))
5.0ms	x	@	inf	((+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (sqrt (+ x y)) (sqrt y) (/ 1 (/ 1 (+ y x))) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (+ y x)) (+ y x) (/ 1 (/ 1 (sqrt (+ y x)))) (/ 1 (sqrt (+ y x))) (sqrt (+ y x)) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (* y (/ y (- x y))))
4.0ms	x	@	-inf	((+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (sqrt (+ x y)) (sqrt y) (/ 1 (/ 1 (+ y x))) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (+ y x)) (+ y x) (/ 1 (/ 1 (sqrt (+ y x)))) (/ 1 (sqrt (+ y x))) (sqrt (+ y x)) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (* y (/ y (- x y))))
4.0ms	y	@	0	((+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (sqrt (+ x y)) (sqrt y) (/ 1 (/ 1 (+ y x))) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (+ y x)) (+ y x) (/ 1 (/ 1 (sqrt (+ y x)))) (/ 1 (sqrt (+ y x))) (sqrt (+ y x)) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (* y (/ y (- x y))))
4.0ms	x	@	0	((+ (* x (/ x (- x y))) (neg (* y (/ y (- x y))))) (neg (* y (/ y (- x y)))) (sqrt (+ (* x (/ x (- x y))) (neg (* y (/ y (- x y)))))) (/ x (- x y)) (sqrt (+ x y)) (sqrt y) (/ 1 (/ 1 (+ y x))) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (+ y x)) (+ y x) (/ 1 (/ 1 (sqrt (+ y x)))) (/ 1 (sqrt (+ y x))) (sqrt (+ y x)) (sqrt (+ x y)) (+ (* (* 1/2 x) (sqrt (/ 1 y))) (sqrt y)) (* 1/2 x) (sqrt (/ 1 y)) (* y (/ y (- x y))))

simplify365.0ms (5.8%)

Memory

-30.0MiB live, 306.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10 370×	`lower-fma.f64`
10 370×	`lower-fma.f32`
4 510×	`lower-*.f64`
4 510×	`lower-*.f32`
3 998×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	640	6133
1	2042	5743
2	6506	5558
0	8244	5220

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 375

Calls

Call 1

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

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

rewrite385.0ms (6.1%)

Memory

2.8MiB live, 274.5MiB allocated

Rules

8 336×	`lower-fma.f32`
8 332×	`lower-fma.f64`
3 922×	`lower-/.f32`
3 908×	`lower-/.f64`
3 888×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	133
0	48	181
1	175	93
2	1143	93
0	8573	91

Stop Event

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

Counts

18 → 1 700

Calls

Call 1

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

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

eval422.0ms (6.7%)

Memory: 61.6MiB live, 547.0MiB allocated
Compiler: Compiled 68 213 to 4 875 computations (92.9% saved)

prune619.0ms (9.8%)

Memory

-31.8MiB live, 557.8MiB allocated

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	2 454	4	2 458
Fresh	2	0	2
Picked	3	2	5
Done	0	1	1
Total	2 459	7	2 466

Accuracy

100.0%

Counts

2 466 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
▶	100.0%	(sqrt.f64 (fma.f64 (sqrt.f64 y) (sqrt.f64 y) x))
✓	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	74.8%	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 y x) x x)))
▶	100.0%	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 x y) y y)))
✓	96.9%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 60 to 36 computations (40% saved)

simplify122.0ms (1.9%)

Memory

-8.7MiB live, 105.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 y x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 y x))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
cost-diff	0	(sqrt.f64 y)
cost-diff	0	(sqrt.f64 (fma.f64 (sqrt.f64 y) (sqrt.f64 y) x))
cost-diff	1472	(fma.f64 (sqrt.f64 y) (sqrt.f64 y) x)
cost-diff	0	(/.f64 y x)
cost-diff	0	#s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 y x) x x))
cost-diff	0	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 y x) x x)))
cost-diff	896	(fma.f64 (/.f64 y x) x x)
cost-diff	0	(/.f64 x y)
cost-diff	0	#s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 x y) y y))
cost-diff	0	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 x y) y y)))
cost-diff	896	(fma.f64 (/.f64 x y) y y)

Rules

5 344×	`lower-*.f64`
5 344×	`lower-*.f32`
4 178×	`lower-/.f32`
4 170×	`lower-/.f64`
2 598×	`cube-div`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	122
0	37	106
1	58	106
2	98	82
3	153	82
4	1375	82
5	2255	82
6	3199	82
7	5576	82
8	6281	82
9	6357	82
10	6357	82
11	6357	82
0	8187	82

Stop Event

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

Calls

Call 1

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

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

localize67.0ms (1.1%)

Memory

-1.8MiB live, 79.2MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y x)
accuracy	0.01953125	(/.f64 #s(literal 1 binary64) (+.f64 y x))
accuracy	0.1171875	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)))
accuracy	0.26953125	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
accuracy	0	(sqrt.f64 y)
accuracy	0.02734375	(sqrt.f64 (fma.f64 (sqrt.f64 y) (sqrt.f64 y) x))
accuracy	0.46875	(fma.f64 (sqrt.f64 y) (sqrt.f64 y) x)
accuracy	0	(/.f64 y x)
accuracy	0	#s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 y x) x x))
accuracy	0.02734375	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 y x) x x)))
accuracy	15.737843891777931	(fma.f64 (/.f64 y x) x x)
accuracy	0	(fma.f64 (/.f64 x y) y y)
accuracy	0	(/.f64 x y)
accuracy	0	#s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 x y) y y))
accuracy	0.02734375	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 x y) y y)))

Samples

47.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 100 to 21 computations (79% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-div: 9.0ms (35.1% of total)

ival-sqrt: 7.0ms (27.3% of total)

ival-add: 5.0ms (19.5% of total)

ival-mult: 4.0ms (15.6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory

21.4MiB live, 21.4MiB allocated

Counts

15 → 348

Calls

Call 1

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

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

Calls

6 calls:

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

simplify190.0ms (3%)

Memory

6.3MiB live, 236.0MiB allocated

Algorithm

1×	egg-herbie

Rules

13 796×	`lower-fma.f64`
13 796×	`lower-fma.f32`
5 032×	`lower-*.f64`
5 032×	`lower-*.f32`
3 920×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	344	4010
1	1028	3828
2	3128	3704
0	8209	3438

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 313

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

rewrite280.0ms (4.5%)

Memory

7.6MiB live, 202.1MiB allocated

Rules

8 464×	`lower-fma.f32`
8 458×	`lower-fma.f64`
3 904×	`lower-*.f64`
3 904×	`lower-*.f32`
2 486×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	113
0	37	93
1	132	92
2	795	68
0	9622	68

Stop Event

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

Counts

15 → 1 151

Calls

Call 1

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

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

eval396.0ms (6.3%)

Memory: -16.0MiB live, 294.2MiB allocated
Compiler: Compiled 24 559 to 2 411 computations (90.2% saved)

prune257.0ms (4.1%)

Memory

-19.7MiB live, 270.6MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	1 496	2	1 498
Fresh	0	0	0
Picked	0	4	4
Done	0	3	3
Total	1 496	9	1 505

Accuracy

100.0%

Counts

1 505 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
✓	100.0%	(sqrt.f64 (fma.f64 (sqrt.f64 y) (sqrt.f64 y) x))
✓	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	99.9%	(sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))
✓	74.8%	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 y x) x x)))
✓	100.0%	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 x y) y y)))
▶	74.7%	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y) x x)))
✓	96.9%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 82 to 50 computations (39% saved)

simplify324.0ms (5.2%)

Memory

27.6MiB live, 148.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 x y)
cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 x y))
cost-diff	0	(sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))
cost-diff	1024	(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y)
cost-diff	0	#s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y) x x))
cost-diff	0	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y) x x)))
cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) x) y)
cost-diff	896	(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y) x x)

Rules

6 298×	`lower-*.f32`
6 294×	`lower-*.f64`
3 626×	`lower-/.f32`
3 622×	`lower-/.f64`
3 114×	`cube-div`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	78
0	24	71
1	42	61
2	81	49
3	109	49
4	258	45
5	1457	45
6	2207	45
7	2673	45
8	3594	45
9	5181	45
10	5796	45
11	6078	45
12	6291	45
13	6489	45
14	6573	45
15	6594	45
16	6713	45
17	6772	45
18	6786	45
19	6914	45
20	7105	45
21	7316	45
22	7528	45
23	7740	45
24	7973	45
0	8015	45

Stop Event

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

Calls

Call 1

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

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

localize84.0ms (1.3%)

Memory

-4.1MiB live, 72.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 x y)
accuracy	0	(+.f64 #s(literal 1 binary64) (/.f64 x y))
accuracy	0.02734375	(sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))
accuracy	0.03125	(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y)
accuracy	0	#s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y) x x))
accuracy	0.02734375	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y) x x)))
accuracy	0.171875	(*.f64 (/.f64 #s(literal 1 binary64) x) y)
accuracy	15.737843891777931	(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y) x x)

Samples

74.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 63 to 17 computations (73% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-add: 51.0ms (77.4% of total)

ival-div: 7.0ms (10.6% of total)

ival-mult: 5.0ms (7.6% of total)

ival-sqrt: 3.0ms (4.6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series22.0ms (0.3%)

Memory

-8.5MiB live, 34.9MiB allocated

Counts

8 → 192

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	x	@	-inf	((+ (* (* (/ 1 x) y) x) x) (* (/ 1 x) y) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (/ 1 (+ y x))) (* (+ 1 (/ x y)) y) (sqrt (* (+ 1 (/ x y)) y)) (+ 1 (/ x y)) (/ x y))
2.0ms	y	@	-inf	((+ (* (* (/ 1 x) y) x) x) (* (/ 1 x) y) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (/ 1 (+ y x))) (* (+ 1 (/ x y)) y) (sqrt (* (+ 1 (/ x y)) y)) (+ 1 (/ x y)) (/ x y))
1.0ms	y	@	inf	((+ (* (* (/ 1 x) y) x) x) (* (/ 1 x) y) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (/ 1 (+ y x))) (* (+ 1 (/ x y)) y) (sqrt (* (+ 1 (/ x y)) y)) (+ 1 (/ x y)) (/ x y))
1.0ms	y	@	0	((+ (* (* (/ 1 x) y) x) x) (* (/ 1 x) y) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (/ 1 (+ y x))) (* (+ 1 (/ x y)) y) (sqrt (* (+ 1 (/ x y)) y)) (+ 1 (/ x y)) (/ x y))
1.0ms	x	@	inf	((+ (* (* (/ 1 x) y) x) x) (* (/ 1 x) y) (sqrt (/ 1 (/ 1 (+ y x)))) (/ 1 (/ 1 (+ y x))) (* (+ 1 (/ x y)) y) (sqrt (* (+ 1 (/ x y)) y)) (+ 1 (/ x y)) (/ x y))

simplify302.0ms (4.8%)

Memory

12.8MiB live, 235.6MiB allocated

Algorithm

1×	egg-herbie

Rules

18 680×	`lower-fma.f64`
18 680×	`lower-fma.f32`
4 458×	`lower-*.f64`
4 458×	`lower-*.f32`
3 146×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	182	1571
1	544	1499
2	1842	1465
3	4031	1441
0	8573	1369

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 174

Calls

Call 1

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

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

rewrite154.0ms (2.5%)

Memory

-12.1MiB live, 194.6MiB allocated

Rules

5 350×	`lower-fma.f32`
5 348×	`lower-fma.f64`
3 494×	`lower-*.f32`
3 490×	`lower-*.f64`
2 716×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	69
0	24	61
1	107	53
2	687	44
0	9161	42

Stop Event

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

Counts

8 → 339

Calls

Call 1

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

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

eval63.0ms (1%)

Memory: 7.6MiB live, 163.5MiB allocated
Compiler: Compiled 8 806 to 1 259 computations (85.7% saved)

prune93.0ms (1.5%)

Memory

-1.8MiB live, 199.6MiB allocated

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	513	0	513
Fresh	0	0	0
Picked	0	2	2
Done	0	7	7
Total	513	9	522

Accuracy

100.0%

Counts

522 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
✓	100.0%	(sqrt.f64 (fma.f64 (sqrt.f64 y) (sqrt.f64 y) x))
✓	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	99.9%	(sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) y))
✓	74.8%	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 y x) x x)))
✓	100.0%	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (/.f64 x y) y y)))
✓	74.7%	(sqrt.f64 #s(approx (/ 1 (/ 1 (+ y x))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) y) x x)))
✓	96.9%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 203 to 101 computations (50.2% saved)

regimes47.0ms (0.7%)

Memory

11.4MiB live, 49.5MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

4 calls:

32.0ms	y
5.0ms	(sqrt.f64 (+.f64 x y))
5.0ms	(+.f64 x 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 17 to 11 computations (35.3% saved)

regimes9.0ms (0.1%)

Memory

-15.1MiB live, 22.4MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	x
2.0ms	(sqrt.f64 (+.f64 x y))
2.0ms	(+.f64 x y)
2.0ms	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 17 to 11 computations (35.3% saved)

regimes5.0ms (0.1%)

Memory

19.2MiB live, 19.2MiB 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
96.9%	1	`x`
96.9%	1	`y`
96.9%	1	`(sqrt.f64 (+.f64 x y))`
96.9%	1	`(+.f64 x y)`

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify5.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	20	26

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness426.0ms (6.8%)

Memory

-36.6MiB live, 330.8MiB allocated

Rules

27 648×	`lower-fma.f64`
27 648×	`lower-fma.f32`
10 370×	`lower-fma.f64`
10 370×	`lower-fma.f32`
5 638×	`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
0	156	630
1	454	600
2	1426	582
3	4628	570
0	8167	534
0	640	6133
1	2042	5743
2	6506	5558
0	8244	5220

Stop Event

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

Compiler

Compiled 52 to 28 computations (46.2% saved)

preprocess56.0ms (0.9%)

Memory: -3.6MiB live, 156.7MiB allocated
Compiler: Compiled 86 to 44 computations (48.8% 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%)

analyze15.0ms (0.2%)

sample556.0ms (8.9%)

explain132.0ms (2.1%)

preprocess17.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize20.0ms (0.3%)

series6.0ms (0.1%)

simplify232.0ms (3.7%)

rewrite172.0ms (2.7%)

eval32.0ms (0.5%)

prune85.0ms (1.4%)

simplify157.0ms (2.5%)

localize98.0ms (1.6%)

series47.0ms (0.7%)

simplify365.0ms (5.8%)

rewrite385.0ms (6.1%)

eval422.0ms (6.7%)

prune619.0ms (9.8%)

simplify122.0ms (1.9%)

localize67.0ms (1.1%)

series15.0ms (0.2%)

simplify190.0ms (3%)

rewrite280.0ms (4.5%)

eval396.0ms (6.3%)

prune257.0ms (4.1%)

simplify324.0ms (5.2%)

localize84.0ms (1.3%)

series22.0ms (0.3%)

simplify302.0ms (4.8%)

rewrite154.0ms (2.5%)

eval63.0ms (1%)

prune93.0ms (1.5%)

regimes47.0ms (0.7%)

regimes9.0ms (0.1%)

regimes5.0ms (0.1%)

simplify5.0ms (0.1%)

soundness426.0ms (6.8%)

preprocess56.0ms (0.9%)

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