Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze18.0ms (0.3%)

Memory

23.9MiB live, 23.9MiB 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
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.3s (25.9%)

Memory

7.7MiB live, 652.3MiB allocated

Samples

829.0ms	8 256×	0	valid
13.0ms	315×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 355.0ms

ival-mult: 174.0ms (49% of total)

ival-sqrt: 92.0ms (25.9% of total)

ival-add: 80.0ms (22.5% of total)

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

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

Bogosity

explain115.0ms (2.3%)

Memory

-12.0MiB live, 73.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
88	-	-	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
0	-	-	`(+.f64 (*.f64 x x) y)`
0	-	-	`y`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) y))`	oflow-rescue	88	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	88
↳	`(*.f64 x x)`	overflow	88

Confusion

	Predicted +	Predicted -
+	88	0
-	0	168

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	88	0	0
-	0	0	168

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	168
1	88

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

50.0ms

512×

valid

Compiler

Compiled 44 to 19 computations (56.8% saved)

Precisions

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

ival-mult: 4.0ms (37.6% of total)

ival-sqrt: 4.0ms (37.6% of total)

ival-add: 2.0ms (18.8% of total)

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

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

preprocess57.0ms (1.1%)

Memory

-13.8MiB live, 23.8MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`sub-neg`
17×	`distribute-lft-neg-in`
17×	`associate-+l-`
16×	`associate--r+`
16×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 8 to 5 computations (37.5% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.0%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 (*.f64 x x) y))
cost-diff	128	(+.f64 (*.f64 x x) y)

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	9	16
0	9	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize61.0ms (1.2%)

Memory

-8.4MiB live, 28.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (*.f64 x x) y)
accuracy	20.505867093382346	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

55.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-sqrt: 45.0ms (92.2% of total)

ival-mult: 2.0ms (4.1% of total)

ival-add: 1.0ms (2% of total)

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

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

series6.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

3 → 60

Calls

Call 1

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

Inputs

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

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

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

Outputs
#s(alt y (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (.f64 x x) y) (patch (+.f64 (.f64 x x) y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) (taylor -inf y) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) y)) (patch (sqrt.f64 (+.f64 (.f64 x x) y)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

15 calls:

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

simplify454.0ms (8.9%)

Memory

-15.6MiB live, 303.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 568×	`lower-fma.f64`
11 568×	`lower-fma.f32`
2 741×	`lower-*.f64`
2 741×	`lower-*.f32`
1 163×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	635
1	383	620
2	1206	612
3	4042	567
0	8636	515

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 55

Calls

Call 1

Inputs
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
y
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
y
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) x (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (.f64 (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y)))) x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) x) x (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 #s(literal 1/16 binary64) x)) x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) #s(literal -1/8 binary64))) (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) (.f64 x x) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 (/.f64 y x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) y #s(literal 1/2 binary64)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 (.f64 (.f64 (.f64 #s(literal 1/16 binary64) y) y) (/.f64 y (pow.f64 x #s(literal 6 binary64)))) x (fma.f64 (/.f64 y x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) y #s(literal 1/2 binary64)) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 y x) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(neg.f64 (fma.f64 (/.f64 y x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) y #s(literal 1/2 binary64)) x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(neg.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal 1/16 binary64) y) y) (/.f64 y (pow.f64 x #s(literal 6 binary64)))) x (fma.f64 (/.f64 y x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) y #s(literal 1/2 binary64)) x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) y #s(literal 1/2 binary64)) x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 y (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x))) y (/.f64 #s(literal 1/2 binary64) x)) y x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (*.f64 #s(literal 1/2 binary64) x)) x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (.f64 #s(literal 1/2 binary64) x)) x (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (*.f64 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 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) #s(literal 1/2 binary64)) x) x (fma.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (.f64 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 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) y))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) x) (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (*.f64 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 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))))) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) x) (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (.f64 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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite298.0ms (5.9%)

Memory

25.4MiB live, 226.0MiB allocated

Rules

2 517×	`lower-fma.f64`
2 517×	`lower-fma.f32`
2 102×	`lower-/.f64`
2 102×	`lower-/.f32`
1 620×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12

Stop Event

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

Counts

3 → 228

Calls

Call 1

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

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

eval45.0ms (0.9%)

Memory: 6.6MiB live, 43.5MiB allocated
Compiler: Compiled 11 199 to 856 computations (92.4% saved)

prune87.0ms (1.7%)

Memory

-3.7MiB live, 72.1MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	277	6	283
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	278	6	284

Accuracy

100.0%

Counts

284 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	67.5%	(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
▶	68.0%	(sqrt.f64 (fma.f64 x x y))
▶	39.7%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
▶	72.3%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
▶	30.3%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 86 to 52 computations (39.5% saved)

simplify93.0ms (1.8%)

Memory

-31.1MiB live, 65.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

192×	`lower-fma.f32`
190×	`lower-fma.f64`
132×	`lower-*.f32`
131×	`lower-*.f64`
81×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	78
0	27	78
1	36	78
2	42	78
3	45	78
4	47	78
5	51	78
6	66	78
7	103	78
8	133	78
9	242	78
10	391	78
11	676	78
12	957	78
13	1013	78
14	1027	78
15	1039	78
0	1039	78

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize73.0ms (1.4%)

Memory

-6.5MiB live, 70.5MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x y)
accuracy	11.403286120303502	(sqrt.f64 (fma.f64 x x y))
accuracy	0	(*.f64 x x)
accuracy	11.403286120303502	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
accuracy	17.87204529730713	#s(approx (+ (* x x) y) (*.f64 x x))
accuracy	0	(sqrt.f64 y)
accuracy	23.580479723946283	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0	(neg.f64 x)
accuracy	42.412543439952735	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.07421875	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
accuracy	17.61305718867234	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))

Samples

47.0ms	172×	0	valid
8.0ms	84×	0	invalid

Compiler

Compiled 67 to 13 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-sqrt: 35.0ms (79.5% of total)

ival-mult: 3.0ms (6.8% of total)

ival-div: 2.0ms (4.5% of total)

ival-add: 2.0ms (4.5% of total)

ival-neg: 1.0ms (2.3% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.2%)

Memory

18.7MiB live, 18.7MiB allocated

Counts

12 → 240

Calls

Call 1

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

Outputs
#s(alt (sqrt y) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) #<representation binary64>) () ())) ())
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#s(alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) (taylor -inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) (taylor -inf y) (#s(alt (sqrt.f64 (fma.f64 x x y)) (patch (sqrt.f64 (fma.f64 x x y)) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())

Calls

60 calls:

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

simplify356.0ms (7%)

Memory

11.4MiB live, 317.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 737×	`lower-fma.f64`
11 737×	`lower-fma.f32`
2 686×	`lower-*.f64`
2 686×	`lower-*.f32`
1 205×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	2989
1	425	2914
2	1316	2874
3	4488	2654
0	8689	2430

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 221

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* 1/2 (/ y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
x
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(+ x (* 1/2 (/ y x)))
(* 1/2 (/ y x))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* 1/2 (/ y x))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (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 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) x (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y)))) x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) (.f64 x x) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (fma.f64 (.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) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) x) x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) (.f64 x x) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 y y) (.f64 (.f64 (*.f64 x x) x) x)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 (.f64 (.f64 y y) (fma.f64 (/.f64 y (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (*.f64 x x) x) x)))) x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) y (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) y) (/.f64 y (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) x (*.f64 (/.f64 #s(literal -1/2 binary64) x) y))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(neg.f64 (fma.f64 (.f64 (.f64 y y) (fma.f64 (/.f64 y (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (*.f64 x x) x) x)))) x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) y #s(literal 1/2 binary64)) x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x))) y (/.f64 #s(literal 1/2 binary64) x)) y x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (*.f64 x #s(literal 1/2 binary64))) x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (.f64 x #s(literal 1/2 binary64))) x (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (*.f64 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 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (.f64 x #s(literal 1/2 binary64))) x (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) y))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (*.f64 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 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (.f64 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)
(* 1/2 (/ y x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) y (*.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) y (*.f64 x x)) x)
(/ (+ (* 1/2 y) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) y (*.f64 x x)) x)
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
x
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
x
(+ x (* 1/2 (/ y x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(+ x (* 1/2 (/ y x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(+ x (* 1/2 (/ y x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* 1/2 (/ y x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* 1/2 (/ y x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) y)
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) x (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y)))) x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) (.f64 x x) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (fma.f64 (.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) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) x) x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) (.f64 x x) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 y y) (.f64 (.f64 (*.f64 x x) x) x)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 (.f64 (.f64 y y) (fma.f64 (/.f64 y (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (*.f64 x x) x) x)))) x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) y (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) y) (/.f64 y (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) x (*.f64 (/.f64 #s(literal -1/2 binary64) x) y))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(neg.f64 (fma.f64 (.f64 (.f64 y y) (fma.f64 (/.f64 y (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (*.f64 x x) x) x)))) x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) y #s(literal 1/2 binary64)) x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x))) y (/.f64 #s(literal 1/2 binary64) x)) y x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (*.f64 x #s(literal 1/2 binary64))) x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (.f64 x #s(literal 1/2 binary64))) x (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (*.f64 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 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (.f64 x #s(literal 1/2 binary64))) x (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) y))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
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(fma.f64 (/.f64 #s(literal -1/2 binary64) x) y (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) y) (/.f64 y (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) x (*.f64 (/.f64 #s(literal -1/2 binary64) x) y))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(neg.f64 (fma.f64 (.f64 (.f64 y y) (fma.f64 (/.f64 y (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (*.f64 x x) x) x)))) x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) y #s(literal 1/2 binary64)) x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x))) y (/.f64 #s(literal 1/2 binary64) x)) y x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (*.f64 x #s(literal 1/2 binary64))) x (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (.f64 x #s(literal 1/2 binary64))) x (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (*.f64 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 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (.f64 x #s(literal 1/2 binary64))) x (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) y))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) y)
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (*.f64 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 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (fma.f64 (.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) x) (.f64 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
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
y
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)

rewrite389.0ms (7.6%)

Memory

-12.2MiB live, 237.8MiB allocated

Rules

2 902×	`lower-fma.f32`
2 900×	`lower-fma.f64`
2 009×	`lower-*.f32`
2 008×	`lower-*.f64`
958×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	70
0	27	70
1	73	70
2	408	70
3	4497	70
0	8364	70

Stop Event

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

Counts

12 → 282

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
(.f64 (/.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y (.f64 (neg.f64 x) x)) (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 y y) y) (.f64 (.f64 (neg.f64 x) x) x))) (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y (fma.f64 #s(literal 1/2 binary64) y (*.f64 x x))))
(.f64 (/.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x)) (.f64 y y)) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x)) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y) (fma.f64 #s(literal -1/2 binary64) y (.f64 x x))))) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y) (fma.f64 #s(literal -1/2 binary64) y (*.f64 x x))))
(.f64 (/.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x)) (.f64 y y)) y (.f64 (.f64 x x) x)) (fma.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) y (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) y (.f64 x x))) (fma.f64 #s(literal -1/2 binary64) y (.f64 x x)) (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y))) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) y (.f64 x x)) (-.f64 (fma.f64 #s(literal -1/2 binary64) y (.f64 x x)) (.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y)) (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 (*.f64 x x) x) x))))
(.f64 (/.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y (.f64 (neg.f64 x) x)) (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y (*.f64 (neg.f64 x) x))) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
(.f64 (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y)) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 (/.f64 y x) #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)) (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y (.f64 (neg.f64 x) x)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x))) (fma.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x)) (.f64 y y)) y (.f64 (.f64 x x) x)))
(.f64 (neg.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y (.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)))
(.f64 (neg.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x)) (.f64 y y)) y (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x)))))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y (.f64 (neg.f64 x) x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)))
(*.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
(.f64 (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x)) (/.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x) (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (*.f64 x x))))
(.f64 (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x)) (.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x)))))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x)) (.f64 y y)) y (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x))))
(*.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x) (/.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x))))
(.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x) (.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))))
(pow.f64 (/.f64 (-.f64 x (.f64 (/.f64 y x) #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) y) y))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))) (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y (*.f64 x x)))
(/.f64 (.f64 (-.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y))) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))) (+.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 (*.f64 x x) x) x))))
(/.f64 (.f64 (-.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y))) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x)))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 y y) y) (.f64 (.f64 (neg.f64 x) x) x)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x) (/.f64 (.f64 #s(literal 1/512 binary64) (.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y)) (.f64 (.f64 y y) y))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x)))) (-.f64 (+.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y))) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)) (.f64 #s(literal 1/8 binary64) (.f64 (*.f64 y y) y))))
(/.f64 (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x)) (.f64 y y)) y (.f64 (.f64 x x) x)) #s(literal 1 binary64)) (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x)) (.f64 x x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x)) (.f64 x x)))) (.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x)) (.f64 x x))) (/.f64 (*.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x)) (.f64 x x))) #s(literal 3 binary64)) (.f64 (.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)))) (fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x)) (.f64 x x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x)) (.f64 x x))) (fma.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) (neg.f64 x)) (.f64 x x))) (/.f64 (*.f64 (neg.f64 x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y))) (neg.f64 (-.f64 x (*.f64 (/.f64 y x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) y (*.f64 (neg.f64 x) x)))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x)) (.f64 y y)) y (.f64 (.f64 x x) x)))) (neg.f64 (neg.f64 (fma.f64 y (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) y) #s(literal 1/2 binary64)) (*.f64 x x)))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (.f64 x x)) (.f64 (fma.f64 x x y) (-.f64 y (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))
(/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(neg.f64 (/.f64 (.f64 (fma.f64 x x y) (neg.f64 (-.f64 (.f64 x x) y))) (-.f64 (*.f64 x x) y)))
(neg.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (neg.f64 (fma.f64 x x y))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(neg.f64 (/.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) (neg.f64 (-.f64 (*.f64 x x) y))))
(neg.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x) (.f64 (.f64 y y) y))) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (fma.f64 x x y))) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (fma.f64 x x y) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 #s(literal 1 binary64) y (*.f64 x x))
(fma.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 y #s(literal 1 binary64) (*.f64 x x))
(fma.f64 x (/.f64 (.f64 (.f64 x x) x) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 x x y)
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 y (.f64 x x))))
(-.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y))) (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 x x y))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (fma.f64 x x y)))
(+.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y))) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
(+.f64 (*.f64 x x) y)
(+.f64 y (*.f64 x x))

eval97.0ms (1.9%)

Memory: 24.5MiB live, 94.8MiB allocated
Compiler: Compiled 9 934 to 858 computations (91.4% saved)

prune90.0ms (1.8%)

Memory

-15.3MiB live, 104.2MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	503	0	503
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	503	6	509

Accuracy

100.0%

Counts

509 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.5%	(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	68.0%	(sqrt.f64 (fma.f64 x x y))
✓	39.7%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	72.3%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	30.3%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 43 to 26 computations (39.5% saved)

simplify4.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

3×	`lower-pow.f32`
2×	`lower-*.f64`
2×	`lower-+.f64`
2×	`lift-pow.f64`
2×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	22
0	11	22
1	13	20
2	16	19
3	17	19
0	17	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize38.0ms (0.7%)

Memory

-13.3MiB live, 66.2MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x y)
accuracy	0.47265625	(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
accuracy	21.089907805729066	(pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))

Samples

25.0ms

256×

valid

Compiler

Compiled 27 to 10 computations (63% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-pow: 12.0ms (66.6% of total)

ival-pow2: 3.0ms (16.6% of total)

ival-mult: 2.0ms (11.1% of total)

ival-add: 1.0ms (5.5% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

22.7MiB live, 22.7MiB allocated

Counts

3 → 72

Calls

Call 1

Inputs

#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())

#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())

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

Outputs
#s(alt (sqrt y) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))) (taylor inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))) (taylor inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))) (taylor inf y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) (taylor inf y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) (taylor -inf y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) (taylor -inf y) (#s(alt (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 y) 1/4) (taylor 0 x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (pow (* 1 y) 1/4)) (taylor 0 x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (+ (* -3/32 (* (pow (/ 1 (pow y 7)) 1/4) (pow x 2))) (* 1/4 (pow (/ 1 (pow y 3)) 1/4)))) (pow (* 1 y) 1/4)) (taylor 0 x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (+ (* 1/4 (pow (/ 1 (pow y 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ 1 (pow y 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow y 11)) 1/4) (pow x 2))))))) (pow (* 1 y) 1/4)) (taylor 0 x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* 1/4 (* (sqrt (/ 1 (pow x 3))) y))) (taylor inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))))) (taylor inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3)))))))) (taylor inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))))) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3))))))))) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow 1 1/4) (sqrt x)) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* (pow 1 1/4) (* (sqrt (/ 1 (pow x 3))) y))) (* (pow 1 1/4) (sqrt x))) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -3/32 (* (pow 1 1/4) (* (sqrt (/ 1 (pow x 7))) y))) (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x))) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* y (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* 7/128 (* (pow 1 1/4) (* (sqrt (/ 1 (pow x 11))) y))))))) (* (pow 1 1/4) (sqrt x))) (taylor 0 y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 y) 1/4) (taylor inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (pow (* 1 y) 1/4)) (taylor inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow (* 1 y) 1/4))) (taylor inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (+ (* (pow (/ 1 (pow y 11)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6))))) (pow (* 1 y) 1/4)))) (taylor inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (taylor -inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* 1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))) y))) (taylor -inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) y)) (* -1/4 (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y))) (taylor -inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) y)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) y)) (* -1/4 (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y))) (taylor -inf y) (#s(alt (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (patch (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ y (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (+ y (pow x 2)) (taylor 0 y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ (pow x 2) y))) (taylor inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))) (taylor -inf y) (#s(alt (fma.f64 x x y) (patch (fma.f64 x x y) #<representation binary64>) () ())) ())

Calls

18 calls:

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

simplify407.0ms (8%)

Memory

-25.2MiB live, 377.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8 568×	`lower-fma.f64`
8 568×	`lower-fma.f32`
2 586×	`lower-*.f64`
2 586×	`lower-*.f32`
2 285×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	280	1246
1	821	1188
2	2857	1138
3	6428	1095
0	8252	1009

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 67

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
x
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(pow (* 1 y) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (pow (* 1 y) 1/4))
(+ (* (pow x 2) (+ (* -3/32 (* (pow (/ 1 (pow y 7)) 1/4) (pow x 2))) (* 1/4 (pow (/ 1 (pow y 3)) 1/4)))) (pow (* 1 y) 1/4))
(+ (* (pow x 2) (+ (* 1/4 (pow (/ 1 (pow y 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ 1 (pow y 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow y 11)) 1/4) (pow x 2))))))) (pow (* 1 y) 1/4))
(sqrt x)
(+ (sqrt x) (* 1/4 (* (sqrt (/ 1 (pow x 3))) y)))
(+ (sqrt x) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))))
(+ (sqrt x) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3))))))))
(* (sqrt x) (sqrt -1))
(+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))))))
(+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3)))))))))
(* (pow 1 1/4) (sqrt x))
(+ (* 1/4 (* (pow 1 1/4) (* (sqrt (/ 1 (pow x 3))) y))) (* (pow 1 1/4) (sqrt x)))
(+ (* y (+ (* -3/32 (* (pow 1 1/4) (* (sqrt (/ 1 (pow x 7))) y))) (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* y (+ (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* y (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* 7/128 (* (pow 1 1/4) (* (sqrt (/ 1 (pow x 11))) y))))))) (* (pow 1 1/4) (sqrt x)))
(pow (* 1 y) 1/4)
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (pow (* 1 y) 1/4))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow (* 1 y) 1/4)))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (+ (* (pow (/ 1 (pow y 11)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6))))) (pow (* 1 y) 1/4))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* 1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))) y)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) y)) (* -1/4 (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) y)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) y)) (* -1/4 (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y)))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 x 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))) (.f64 x x) (sqrt.f64 y))
(+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 x 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))) (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64))) (.f64 x x) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 (.f64 (/.f64 (.f64 y y) (.f64 (.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64)) x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 y (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64))) x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(neg.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(neg.f64 (fma.f64 (.f64 (/.f64 (.f64 y y) (.f64 (.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64)) x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 y (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64))) x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) y (/.f64 #s(literal 1/2 binary64) x)) y x)
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 y (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x))) y (/.f64 #s(literal 1/2 binary64) x)) y x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) 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 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) 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 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) 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 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) 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 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) 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 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (.f64 (.f64 x x) (.f64 x x)) (fma.f64 #s(literal -1/16 binary64) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))))) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) y)
(pow (* 1 y) 1/4)
(pow.f64 y #s(literal 1/4 binary64))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (pow (* 1 y) 1/4))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y)) #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -3/32 (* (pow (/ 1 (pow y 7)) 1/4) (pow x 2))) (* 1/4 (pow (/ 1 (pow y 3)) 1/4)))) (pow (* 1 y) 1/4))
(fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal -3/32 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y)) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (.f64 x x) (pow.f64 y #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* 1/4 (pow (/ 1 (pow y 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ 1 (pow y 7)) 1/4)) (* 7/128 (* (pow (/ 1 (pow y 11)) 1/4) (pow x 2))))))) (pow (* 1 y) 1/4))
(fma.f64 (fma.f64 (fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64) (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 11 binary64))) #s(literal 1/4 binary64)))) (.f64 x x) (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y)) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (.f64 x x) (pow.f64 y #s(literal 1/4 binary64)))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/4 (* (sqrt (/ 1 (pow x 3))) y)))
(fma.f64 (.f64 y #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) (sqrt.f64 x))
(+ (sqrt x) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))))
(fma.f64 (.f64 y #s(literal 1/4 binary64)) (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 7 binary64))))) #s(literal -3/32 binary64) (sqrt.f64 x)))
(+ (sqrt x) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3))))))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (.f64 (.f64 y y) y)) #s(literal 7/128 binary64) (fma.f64 (.f64 y #s(literal 1/4 binary64)) (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 7 binary64))))) #s(literal -3/32 binary64) (sqrt.f64 x))))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 y #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))
(+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2)))))))
(fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1 binary64))) y (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (*.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) #s(literal -3/32 binary64) (sqrt.f64 x))))
(+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow y 2)) (* 1/32 (pow y 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/32 (pow y 3)) (+ (* 1/384 (pow y 3)) (* 1/12 (pow y 3)))))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) #s(literal -3/32 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 y y) y) #s(literal 7/128 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (.f64 (.f64 y #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))))))
(* (pow 1 1/4) (sqrt x))
(sqrt.f64 x)
(+ (* 1/4 (* (pow 1 1/4) (* (sqrt (/ 1 (pow x 3))) y))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 (.f64 y #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) (sqrt.f64 x))
(+ (* y (+ (* -3/32 (* (pow 1 1/4) (* (sqrt (/ 1 (pow x 7))) y))) (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 (fma.f64 (.f64 #s(literal -3/32 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/4 binary64))) y (sqrt.f64 x))
(+ (* y (+ (* 1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* y (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* 7/128 (* (pow 1 1/4) (* (sqrt (/ 1 (pow x 11))) y))))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 7/128 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -3/32 binary64))) y (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/4 binary64))) y (sqrt.f64 x))
(pow (* 1 y) 1/4)
(pow.f64 y #s(literal 1/4 binary64))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (pow (* 1 y) 1/4))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y)) #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow (* 1 y) 1/4)))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y)) #s(literal 1/4 binary64)) (fma.f64 (.f64 #s(literal -3/32 binary64) (.f64 (.f64 x x) (.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))) #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64))))
(+ (* 1/4 (* (pow (/ 1 (pow y 3)) 1/4) (pow x 2))) (+ (* (pow (/ 1 (pow y 7)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (+ (* (pow (/ 1 (pow y 11)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6))))) (pow (* 1 y) 1/4))))
(fma.f64 (.f64 #s(literal -3/32 binary64) (.f64 (.f64 x x) (.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/128 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 11 binary64))) #s(literal 1/4 binary64)) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) y)) #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))
(pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/4 binary64))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* 1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))) y)))
(fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) y) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/4 binary64)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) y)) (* -1/4 (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y)))
(-.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/4 binary64)) (/.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/4 binary64)) (fma.f64 (.f64 #s(literal -1/4 binary64) x) x (.f64 #s(literal 3/32 binary64) (/.f64 (.f64 (.f64 x x) (.f64 x x)) y)))) y))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) y)) (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) y)) (* -1/4 (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 y))))))))) y)))
(+.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/4 binary64)) (/.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/4 binary64)) (fma.f64 #s(literal -3/32 binary64) (.f64 (.f64 x x) (.f64 x x)) (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) y) #s(literal 7/128 binary64)))) y)) y) (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) #s(literal 1/4 binary64)))
y
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(fma.f64 x x y)
(pow x 2)
(*.f64 x x)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
(+ y (pow x 2))
(fma.f64 x x y)
y
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
(* y (+ 1 (/ (pow x 2) y)))
(fma.f64 x x y)
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(fma.f64 x x y)

rewrite193.0ms (3.8%)

Memory

5.0MiB live, 279.7MiB allocated

Rules

2 312×	`lower-fma.f32`
2 311×	`lower-fma.f64`
1 803×	`lower-*.f64`
1 803×	`lower-*.f32`
1 555×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	18
0	11	16
1	44	15
2	229	15
3	1951	15
0	8690	15

Stop Event

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

Counts

3 → 292

Calls

Call 1

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

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

eval46.0ms (0.9%)

Memory: 19.2MiB live, 94.3MiB allocated
Compiler: Compiled 12 587 to 1 278 computations (89.8% saved)

prune102.0ms (2%)

Memory

1.3MiB live, 123.2MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	359	0	359
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	359	6	365

Accuracy

100.0%

Counts

365 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	67.5%	(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	68.0%	(sqrt.f64 (fma.f64 x x y))
✓	39.7%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	72.3%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	30.3%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 82 to 43 computations (47.6% saved)

regimes17.0ms (0.3%)

Memory

2.4MiB live, 41.1MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	(+.f64 (*.f64 x x) y)
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
3.0ms	y
3.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
84.1%	2	`y`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes34.0ms (0.7%)

Memory

-15.1MiB live, 73.3MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

24.0ms	(+.f64 (*.f64 x x) y)
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	x
2.0ms	y
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
68.0%	1	`y`
68.0%	1	`x`
68.0%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
68.0%	1	`(+.f64 (*.f64 x x) y)`
68.0%	1	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes11.0ms (0.2%)

Memory

-15.7MiB live, 23.4MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
58.1%	2	`x`
53.1%	2	`y`
43.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
43.0%	2	`(+.f64 (*.f64 x x) y)`
58.1%	2	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes8.0ms (0.2%)

Memory

18.9MiB live, 18.9MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
30.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
30.3%	1	`(+.f64 (*.f64 x x) y)`
30.3%	1	`y`
30.3%	1	`(*.f64 x x)`
30.3%	1	`x`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes8.0ms (0.2%)

Memory

-20.1MiB live, 18.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	x
1.0ms	y
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
1.2%	1	`x`
1.2%	1	`y`
1.2%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.2%	1	`(+.f64 (*.f64 x x) y)`
1.2%	1	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.0679685116305256e+246	1.2133933491383052e+251

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch13.0ms (0.2%)

Memory

28.1MiB live, 28.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	1.8521784409803978e-97	1.0881925230461485e-94

Samples

5.0ms	128×	0	valid
1.0ms	32×	0	invalid

Compiler

Compiled 123 to 82 computations (33.3% saved)

Precisions

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

ival-add: 1.0ms (31.9% of total)

ival-mult: 1.0ms (31.9% of total)

ival-sqrt: 1.0ms (31.9% of total)

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

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

simplify10.0ms (0.2%)

Memory

-20.9MiB live, 18.0MiB allocated

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	70
1	28	70
2	30	70
3	31	70

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) #s(literal 4000000000000000274344207407128205986828376693251859946763293583032077279495508851011551677505358463377940987332918550789499579195624344458912919864732385398286165882478020041602539077783111773557029874084212885869852527834136514200640825480708096 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 x #s(literal 126821299469787/1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192384351515967488 binary64)) #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Outputs
(if (<=.f64 (.f64 x x) #s(literal 4000000000000000274344207407128205986828376693251859946763293583032077279495508851011551677505358463377940987332918550789499579195624344458912919864732385398286165882478020041602539077783111773557029874084212885869852527834136514200640825480708096 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 x #s(literal 126821299469787/1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192384351515967488 binary64)) #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

soundness572.0ms (11.2%)

Memory

15.7MiB live, 277.5MiB allocated

Rules

11 568×	`lower-fma.f64`
11 568×	`lower-fma.f32`
2 741×	`lower-*.f64`
2 741×	`lower-*.f32`
2 517×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12
0	133	635
1	383	620
2	1206	612
3	4042	567
0	8636	515

Stop Event

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

Compiler

Compiled 95 to 49 computations (48.4% saved)

preprocess50.0ms (1%)

Memory: 21.7MiB live, 103.2MiB allocated
Compiler: Compiled 204 to 98 computations (52% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

start0.0ms (0%)

analyze18.0ms (0.3%)

sample1.3s (25.9%)

explain115.0ms (2.3%)

preprocess57.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize61.0ms (1.2%)

series6.0ms (0.1%)

simplify454.0ms (8.9%)

rewrite298.0ms (5.9%)

eval45.0ms (0.9%)

prune87.0ms (1.7%)

simplify93.0ms (1.8%)

localize73.0ms (1.4%)

series11.0ms (0.2%)

simplify356.0ms (7%)

rewrite389.0ms (7.6%)

eval97.0ms (1.9%)

prune90.0ms (1.8%)

simplify4.0ms (0.1%)

localize38.0ms (0.7%)

series9.0ms (0.2%)

simplify407.0ms (8%)

rewrite193.0ms (3.8%)

eval46.0ms (0.9%)

prune102.0ms (2%)

regimes17.0ms (0.3%)

regimes34.0ms (0.7%)

regimes11.0ms (0.2%)

regimes8.0ms (0.2%)

regimes8.0ms (0.2%)

bsearch0.0ms (0%)

bsearch13.0ms (0.2%)

simplify10.0ms (0.2%)

soundness572.0ms (11.2%)

preprocess50.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5