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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze17.0ms (0.4%)

Memory

-12.8MiB live, 27.5MiB 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)

sample1.0s (24.4%)

Memory

15.2MiB live, 622.1MiB allocated

Samples

635.0ms	8 256×	0	valid
91.0ms	522×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 359.0ms

ival-add: 271.0ms (75.4% of total)

ival-sqrt: 78.0ms (21.7% of total)

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

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

Bogosity

explain43.0ms (1%)

Memory

3.7MiB live, 45.4MiB 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

23.0ms

512×

valid

Compiler

Compiled 28 to 16 computations (42.9% saved)

Precisions

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

ival-sqrt: 4.0ms (56.8% of total)

ival-add: 3.0ms (42.6% of total)

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

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

preprocess28.0ms (0.7%)

Memory

-23.3MiB live, 14.1MiB allocated

Algorithm

1×	egg-herbie

Rules

22×	`sub-neg`
14×	`associate--r+`
12×	`neg-mul-1`
11×	`cancel-sign-sub-inv`
11×	`+-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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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 (0.1%)

Memory

2.2MiB live, 2.2MiB 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

2×	`lower-+.f32`
1×	`lift-sqrt.f64`
1×	`lift-+.f64`
1×	`lower-+.f64`
1×	`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

localize13.0ms (0.3%)

Memory

12.4MiB live, 12.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.01171875	(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 (58.5% of total)

ival-add: 1.0ms (29.2% of total)

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

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

series5.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB 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 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 (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 (* -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 (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 (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 (* -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 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 (+.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 x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt 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 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 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>) () ())) ())

Calls

12 calls:

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

simplify533.0ms (12.7%)

Memory

-6.2MiB live, 199.3MiB allocated

Algorithm

1×	egg-herbie

Rules

14 268×	`lower-fma.f64`
14 268×	`lower-fma.f32`
2 819×	`lower-*.f64`
2 819×	`lower-*.f32`
1 416×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	630
1	454	600
2	1425	582
3	4619	570
0	8274	534

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 42

Calls

Call 1

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

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

rewrite276.0ms (6.6%)

Memory

-28.9MiB live, 213.5MiB allocated

Rules

2 564×	`lower-fma.f64`
2 564×	`lower-fma.f32`
2 146×	`lower-/.f64`
2 146×	`lower-/.f32`
1 689×	`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 (-.f64 y x) (-.f64 y x)) (.f64 y y)) (.f64 (-.f64 y x) y) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x))))) (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 (-.f64 y x) (-.f64 y x)) (.f64 y y)) (.f64 (-.f64 y x) y) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) #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 (.f64 (neg.f64 (+.f64 y x)) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 x y)))))
(.f64 (sqrt.f64 (.f64 (neg.f64 (+.f64 y x)) (-.f64 x y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 x y))))
(.f64 (sqrt.f64 (.f64 (neg.f64 (+.f64 y x)) (-.f64 x y))) (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.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))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.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 (*.f64 (neg.f64 (+.f64 y x)) (-.f64 x y)))) (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) (.f64 y y)) (.f64 y y)) (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 x x) x))) (fma.f64 (-.f64 y x) y (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (*.f64 x x) x))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 x (/.f64 x (-.f64 x y))) (.f64 x (/.f64 x (-.f64 x y))) (neg.f64 (.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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(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (-.f64 x y))) (fma.f64 (-.f64 y x) y (.f64 x x))) (/.f64 (/.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y)) (.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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(-.f64 x (neg.f64 y))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 y x))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (+.f64 y x)))
(+.f64 (/.f64 (.f64 y y) (-.f64 y x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 y x))))
(+.f64 (.f64 x (/.f64 x (-.f64 x y))) (neg.f64 (.f64 y (/.f64 y (-.f64 x y)))))
(+.f64 y x)
(+.f64 x y)

eval68.0ms (1.6%)

Memory: 10.2MiB live, 84.7MiB allocated
Compiler: Compiled 7 836 to 854 computations (89.1% saved)

prune87.0ms (2.1%)

Memory

-3.0MiB live, 81.8MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Accuracy

100.0%

Counts

269 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal -1/2 binary64))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	98.1%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 20 to 14 computations (30% saved)

simplify4.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
0	15	29
1	18	29
0	18	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize113.0ms (2.7%)

Memory

22.1MiB live, 60.0MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y x)
accuracy	0.01953125	(/.f64 #s(literal 1 binary64) (+.f64 y x))
accuracy	0.17578125	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal -1/2 binary64))
accuracy	0	(sqrt.f64 y)
accuracy	1.2177815238791931	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Samples

22.0ms

256×

valid

Compiler

Compiled 28 to 12 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-pow: 5.0ms (36.1% of total)

ival-add: 3.0ms (21.7% of total)

ival-sqrt: 3.0ms (21.7% of total)

ival-div: 2.0ms (14.5% of total)

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

exact: 0.0ms (0% of total)

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

series74.0ms (1.8%)

Memory

-25.8MiB live, 11.5MiB allocated

Counts

5 → 108

Calls

Call 1

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

27 calls:

Time	Variable		Point	Expression
68.0ms	y	@	inf	(/ 1 (+ y x))
0.0ms	x	@	inf	(/ 1 (+ y x))
0.0ms	y	@	inf	(sqrt y)
0.0ms	y	@	-inf	(sqrt y)
0.0ms	x	@	0	(/ 1 (+ y x))

simplify464.0ms (11.1%)

Memory

33.1MiB live, 343.5MiB allocated

Algorithm

1×	egg-herbie

Rules

8 464×	`lower-fma.f64`
8 464×	`lower-fma.f32`
2 917×	`lower-*.f64`
2 917×	`lower-*.f32`
1 122×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	254	1590
1	738	1506
2	2188	1440
3	7230	1440
0	8175	1344

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 102

Calls

Call 1

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

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

rewrite232.0ms (5.5%)

Memory

-8.9MiB live, 230.4MiB allocated

Rules

1 731×	`lower-*.f64`
1 731×	`lower-*.f32`
1 407×	`lower-/.f32`
1 406×	`lower-/.f64`
1 161×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	24
0	15	24
1	59	21
2	349	21
3	3506	21
0	8321	21

Stop Event

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

Counts

5 → 400

Calls

Call 1

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

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

eval61.0ms (1.5%)

Memory: 13.5MiB live, 125.2MiB allocated
Compiler: Compiled 11 987 to 1 438 computations (88% saved)

prune154.0ms (3.7%)

Memory

-6.0MiB live, 245.0MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	501	1	502
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	501	4	505

Accuracy

100.0%

Counts

505 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal -1/2 binary64))
▶	73.6%	(pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ y x) (fma.f64 (/.f64 y x) x x))) #s(literal -1/2 binary64))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.1%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 33 to 22 computations (33.3% saved)

simplify215.0ms (5.1%)

Memory

9.5MiB live, 236.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ y x) (fma.f64 (/.f64 y x) x x))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)))
cost-diff	0	(pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ y x) (fma.f64 (/.f64 y x) x x))) #s(literal -1/2 binary64))
cost-diff	896	(fma.f64 (/.f64 y x) x x)

Rules

4 933×	`lower-fma.f32`
4 932×	`lower-fma.f64`
3 198×	`lower-*.f64`
3 198×	`lower-*.f32`
1 045×	`cube-prod`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	49
0	15	49
1	24	49
2	30	45
3	38	37
4	40	37
5	81	37
6	186	37
7	682	37
8	1924	37
9	2150	37
10	2357	37
11	2608	37
12	2899	37
13	3288	37
14	5224	37
15	6082	37
16	6848	37
17	6960	37
18	7047	37
19	7138	37
0	8496	37

Stop Event

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

Calls

Call 1

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

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

localize37.0ms (0.9%)

Memory

-7.7MiB live, 40.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (+ y x) (fma.f64 (/.f64 y x) x x))
accuracy	0.01953125	(/.f64 #s(literal 1 binary64) #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)))
accuracy	0.17578125	(pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ y x) (fma.f64 (/.f64 y x) x x))) #s(literal -1/2 binary64))
accuracy	16.42239359817453	(fma.f64 (/.f64 y x) x x)

Samples

27.0ms

256×

valid

Compiler

Compiled 31 to 12 computations (61.3% saved)

Precisions

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

ival-div: 9.0ms (46.5% of total)

ival-pow: 6.0ms (31% of total)

ival-add: 3.0ms (15.5% of total)

ival-mult: 2.0ms (10.3% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

4 → 96

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (fma.f64 (/.f64 y x) x x) (patch (fma.f64 (/.f64 y x) x x) #<representation binary64>) () ())) ())
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#s(alt y (taylor inf y) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ 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 (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ 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 (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ 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 (+ y x) (fma.f64 (/.f64 y x) x x)) (patch #s(approx (+ y x) (fma.f64 (/.f64 y x) x x)) #<representation binary64>) () ())) ())

Calls

24 calls:

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

simplify237.0ms (5.7%)

Memory

-15.2MiB live, 257.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8 464×	`lower-fma.f64`
8 464×	`lower-fma.f32`
2 917×	`lower-*.f64`
2 917×	`lower-*.f32`
1 122×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	254	1104
1	738	1050
2	2182	1002
3	7234	1002
0	8181	930

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 84

Calls

Call 1

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

rewrite154.0ms (3.7%)

Memory

20.7MiB live, 216.5MiB allocated

Rules

2 584×	`lower-fma.f32`
2 583×	`lower-fma.f64`
1 620×	`lower-*.f64`
1 620×	`lower-*.f32`
931×	`lower-pow.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	42
0	15	42
1	69	40
2	410	27
3	4968	27
0	8193	27

Stop Event

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

Counts

4 → 192

Calls

Call 1

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

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

eval39.0ms (0.9%)

Memory: 10.4MiB live, 80.1MiB allocated
Compiler: Compiled 4 986 to 831 computations (83.3% saved)

prune40.0ms (1%)

Memory

-8.5MiB live, 78.4MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	276	4	280

Accuracy

100.0%

Counts

280 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal -1/2 binary64))
✓	73.6%	(pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ y x) (fma.f64 (/.f64 y x) x x))) #s(literal -1/2 binary64))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.1%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 60 to 36 computations (40% saved)

regimes10.0ms (0.2%)

Memory

-19.4MiB live, 19.3MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

13.4MiB live, 13.4MiB 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	x
1.0ms	y

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`y`
98.1%	1	`(sqrt.f64 (+.f64 x y))`
98.1%	1	`(+.f64 x y)`

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify5.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness224.0ms (5.3%)

Memory

-39.4MiB live, 133.0MiB allocated

Rules

14 268×	`lower-fma.f64`
14 268×	`lower-fma.f32`
2 819×	`lower-*.f64`
2 819×	`lower-*.f32`
1 416×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	630
1	454	600
2	1425	582
3	4619	570
0	8274	534

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

preprocess21.0ms (0.5%)

Memory: 34.3MiB live, 73.3MiB allocated
Remove: (sort x y)
Compiler: Compiled 54 to 34 computations (37% 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%)

analyze17.0ms (0.4%)

sample1.0s (24.4%)

explain43.0ms (1%)

preprocess28.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize13.0ms (0.3%)

series5.0ms (0.1%)

simplify533.0ms (12.7%)

rewrite276.0ms (6.6%)

eval68.0ms (1.6%)

prune87.0ms (2.1%)

simplify4.0ms (0.1%)

localize113.0ms (2.7%)

series74.0ms (1.8%)

simplify464.0ms (11.1%)

rewrite232.0ms (5.5%)

eval61.0ms (1.5%)

prune154.0ms (3.7%)

simplify215.0ms (5.1%)

localize37.0ms (0.9%)

series4.0ms (0.1%)

simplify237.0ms (5.7%)

rewrite154.0ms (3.7%)

eval39.0ms (0.9%)

prune40.0ms (1%)

regimes10.0ms (0.2%)

regimes5.0ms (0.1%)

simplify5.0ms (0.1%)

soundness224.0ms (5.3%)

preprocess21.0ms (0.5%)

end0.0ms (0%)

Profiling

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