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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze17.0ms (0.3%)

Memory

11.7MiB live, 11.7MiB 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)

sample932.0ms (14.1%)

Memory

28.9MiB live, 337.2MiB allocated

Samples

663.0ms	8 256×	0	valid
14.0ms	326×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 248.0ms

ival-mult: 144.0ms (58% of total)

ival-sqrt: 57.0ms (23% of total)

ival-add: 38.0ms (15.3% of total)

ival-true: 6.0ms (2.4% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain289.0ms (4.4%)

Memory

8.4MiB live, 45.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
92	-	-	`(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	92	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	92
↳	`(*.f64 x x)`	overflow	92

Confusion

	Predicted +	Predicted -
+	92	0
-	0	164

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	92	0	0
-	0	0	164

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	164
1	92

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

254.0ms

512×

valid

Compiler

Compiled 44 to 19 computations (56.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 4.0ms (38.7% of total)

ival-sqrt: 4.0ms (38.7% of total)

ival-add: 2.0ms (19.4% of total)

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

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

preprocess53.0ms (0.8%)

Memory

-24.9MiB live, 14.7MiB allocated

Algorithm

1×	egg-herbie

Rules

64×	`sub-neg`
34×	`distribute-lft-neg-in`
34×	`associate-+l-`
32×	`associate--r+`
32×	`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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.6%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify4.0ms (0.1%)

Memory

2.1MiB live, 2.1MiB 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

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

localize17.0ms (0.2%)

Memory

13.3MiB live, 13.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(+.f64 (*.f64 x x) y)
accuracy	21.381601247503884	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

11.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (39.4% of total)

ival-sqrt: 2.0ms (39.4% of total)

ival-add: 1.0ms (19.7% of total)

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

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

series5.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB 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	y	@	inf	(sqrt (+ (* x x) y))
0.0ms	x	@	inf	(sqrt (+ (* x x) y))
0.0ms	x	@	0	(sqrt (+ (* x x) y))
0.0ms	x	@	inf	(+ (* x x) y)

simplify498.0ms (7.5%)

Memory

-19.4MiB live, 222.6MiB allocated

Algorithm

1×	egg-herbie

Rules

23 136×	`lower-fma.f64`
23 136×	`lower-fma.f32`
5 482×	`lower-*.f64`
5 482×	`lower-*.f32`
2 326×	`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 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x #s(literal 1/2 binary64))) (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 x (.f64 x (fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) (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 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #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 x (.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) (/.f64 y (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(-.f64 (/.f64 (*.f64 y #s(literal -1/2 binary64)) x) 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 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #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 x (.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) (/.f64 y (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #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 y (fma.f64 y (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 x (.f64 x (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)

rewrite477.0ms (7.2%)

Memory

17.6MiB live, 248.7MiB allocated

Rules

5 034×	`lower-fma.f64`
5 034×	`lower-fma.f32`
4 204×	`lower-/.f64`
4 204×	`lower-/.f32`
3 240×	`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 (*.f64 x x) y)
(+.f64 y (*.f64 x x))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y))))
(+.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 y (.f64 x x)))))
(exp.f64 (log.f64 (fma.f64 x x y)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 x x y))) #s(literal -1 binary64)))
(-.f64 (*.f64 x x) (neg.f64 y))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x x y)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 y (.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x (neg.f64 x) y)) (neg.f64 (fma.f64 x x y)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (/.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 y y) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (-.f64 (.f64 x x) y)) (/.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (fma.f64 (.f64 y y) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (-.f64 (.f64 x x) y)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y))) (-.f64 (.f64 x x) y)) (/.f64 (/.f64 (.f64 y (.f64 y (.f64 y y))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y))) (-.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)))) (neg.f64 (fma.f64 x x y)))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y))))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y))))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 (.f64 y y) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 (.f64 y y) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)))) (/.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 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 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)))) (fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (fma.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))))) (/.f64 (.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))) (fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (fma.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y))) (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))) (/.f64 (.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y))) (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))))
(fma.f64 x x y)
(fma.f64 x (/.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x x) y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y))))
(fma.f64 (.f64 y y) (/.f64 #s(literal 1 binary64) (-.f64 y (.f64 x x))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 y (.f64 x x)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y))))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 x (-.f64 (.f64 x x) y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y))))
(fma.f64 #s(literal -1 binary64) (neg.f64 y) (*.f64 x x))
(fma.f64 (neg.f64 (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (fma.f64 x x y) (neg.f64 (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) (fma.f64 y (fma.f64 x x y) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y))))
(neg.f64 (neg.f64 (fma.f64 x x y)))
(/.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) y))
(/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (neg.f64 (fma.f64 x x y))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
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(.f64 (pow.f64 (pow.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 y (-.f64 y (.f64 x x))) (.f64 (.f64 y (-.f64 y (.f64 x x))) (.f64 y (-.f64 y (.f64 x x)))))))) (sqrt.f64 (fma.f64 (.f64 y (-.f64 y (.f64 x x))) (-.f64 (.f64 y (-.f64 y (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y) (.f64 (.f64 x x) y))))) (sqrt.f64 (fma.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y) (.f64 (*.f64 x x) y))))
(.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y))))) (sqrt.f64 (fma.f64 y (fma.f64 x x y) (.f64 x (.f64 x (*.f64 x x))))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)

eval122.0ms (1.8%)

Memory: 3.3MiB live, 89.1MiB allocated
Compiler: Compiled 11 199 to 853 computations (92.4% saved)

prune208.0ms (3.1%)

Memory

-18.6MiB live, 102.2MiB 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
	34.6%	(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
▶	66.6%	(sqrt.f64 (fma.f64 x x y))
▶	35.5%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
▶	69.4%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x))
▶	33.9%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 134 to 60 computations (55.2% saved)

simplify75.0ms (1.1%)

Memory

6.1MiB live, 45.0MiB 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 y (/.f64 #s(literal 1/2 binary64) x) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x))

Rules

384×	`lower-fma.f32`
380×	`lower-fma.f64`
264×	`lower-*.f32`
262×	`lower-*.f64`
162×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	78
0	27	78
1	36	78
2	40	78
3	44	78
4	47	78
5	51	78
6	66	78
7	103	78
8	133	78
9	242	78
10	391	78
11	684	78
12	968	78
13	1026	78
14	1040	78
15	1052	78
0	1052	78

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize195.0ms (2.9%)

Memory

10.1MiB live, 85.5MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x y)
accuracy	9.774814332869333	(sqrt.f64 (fma.f64 x x y))
accuracy	0	(*.f64 x x)
accuracy	9.774814332869333	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
accuracy	20.039338286626652	#s(approx (+ (* x x) y) (*.f64 x x))
accuracy	0	(sqrt.f64 y)
accuracy	19.79502095944033	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0	(neg.f64 x)
accuracy	40.919881603472625	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.06640625	(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
accuracy	19.596285540672493	#s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x))

Samples

116.0ms	166×	0	valid
8.0ms	90×	0	invalid

Compiler

Compiled 67 to 13 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 4.0ms (32.6% of total)

ival-sqrt: 3.0ms (24.5% of total)

ival-div: 2.0ms (16.3% of total)

ival-add: 2.0ms (16.3% of total)

ival-neg: 1.0ms (8.2% 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

12.9MiB live, 12.9MiB allocated

Counts

12 → 240

Calls

Call 1

Inputs
#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())
#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<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 #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<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 #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<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 #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<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 #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<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 #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<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 #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) (patch #s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ y x)) (taylor inf y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (/ 1 x)) (/ x y))) (taylor inf y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (/ 1 x)) (/ x y))) (taylor inf y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (/ 1 x)) (/ x y))) (taylor inf y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ y x)) (taylor -inf y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x))))) (taylor -inf y) (#s(alt (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) (patch (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x) #<representation binary64>) () ())) ())
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#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	y	@	0	(+ (* y (/ 1/2 x)) x)
0.0ms	y	@	-inf	(sqrt y)
0.0ms	y	@	inf	(+ (* y (/ 1/2 x)) x)
0.0ms	x	@	inf	(+ (* y (/ 1/2 x)) x)
0.0ms	x	@	0	(+ (* y (/ 1/2 x)) x)

simplify394.0ms (6%)

Memory

2.3MiB live, 480.2MiB allocated

Algorithm

1×	egg-herbie

Rules

23 474×	`lower-fma.f64`
23 474×	`lower-fma.f32`
5 372×	`lower-*.f64`
5 372×	`lower-*.f32`
2 410×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	2989
1	425	2914
2	1317	2874
3	4474	2654
0	8662	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)))))))
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 (/ 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)))
(/ 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 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) 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 x x) (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (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 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/16 binary64))))))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 x (/.f64 (.f64 y (.f64 y #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 x (fma.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 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (*.f64 y (/.f64 #s(literal 1/2 binary64) x)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(fma.f64 y (/.f64 #s(literal -1/2 binary64) x) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 x (fma.f64 (/.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/8 binary64) #s(literal -1 binary64)) (*.f64 y (/.f64 #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))))))))
(fma.f64 (neg.f64 x) (fma.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 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (*.f64 y (/.f64 #s(literal -1/2 binary64) x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
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(* -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 y (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (*.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) 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 x x) (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (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 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/16 binary64))))))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 x (/.f64 (.f64 y (.f64 y #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 x (fma.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 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (*.f64 y (/.f64 #s(literal 1/2 binary64) x)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(fma.f64 y (/.f64 #s(literal -1/2 binary64) x) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 x (fma.f64 (/.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/8 binary64) #s(literal -1 binary64)) (*.f64 y (/.f64 #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))))))))
(fma.f64 (neg.f64 x) (fma.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 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (*.f64 y (/.f64 #s(literal -1/2 binary64) x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #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 y (fma.f64 y (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 (*.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 (+ (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 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (*.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (*.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)
(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)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) 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 x x) (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (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 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/16 binary64))))))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 x (/.f64 (.f64 y (.f64 y #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 x (fma.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 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (*.f64 y (/.f64 #s(literal 1/2 binary64) x)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(fma.f64 y (/.f64 #s(literal -1/2 binary64) x) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(fma.f64 x (fma.f64 (/.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/8 binary64) #s(literal -1 binary64)) (*.f64 y (/.f64 #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))))))))
(fma.f64 (neg.f64 x) (fma.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 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (*.f64 y (/.f64 #s(literal -1/2 binary64) x)))
x
(+ x (* 1/2 (/ y x)))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 y x) (fma.f64 y (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #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 y (fma.f64 y (fma.f64 y (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) x)
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(.f64 y (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 (*.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 (+ (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 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/8 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (*.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (*.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 y (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x (.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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)

rewrite298.0ms (4.5%)

Memory

5.5MiB live, 479.6MiB allocated

Rules

5 804×	`lower-fma.f32`
5 800×	`lower-fma.f64`
4 018×	`lower-*.f32`
4 016×	`lower-*.f64`
1 914×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	70
0	27	70
1	73	70
2	405	70
3	4465	70
0	8326	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 y (/.f64 #s(literal 1/2 binary64) x) x))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) x) 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 y (/.f64 #s(literal 1/2 binary64) x) x))
(+.f64 x (*.f64 y (/.f64 #s(literal 1/2 binary64) x)))
(+.f64 (*.f64 y (/.f64 #s(literal 1/2 binary64) x)) x)
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) y))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (neg.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (fma.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x))))) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x))) (-.f64 y (*.f64 x x)))
(/.f64 (.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (*.f64 y y)))))
(/.f64 (.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (.f64 y y) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 y y))))))
(/.f64 (.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)) (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 y y))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 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 (.f64 (fma.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (.f64 y y) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)))) (-.f64 (.f64 x x) y)))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)) (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)) (-.f64 (.f64 x x) y)))
(/.f64 (neg.f64 (neg.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(/.f64 (neg.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)))) (neg.f64 (neg.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x)))) (neg.f64 (-.f64 y (*.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y))) (.f64 (.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y))) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))) (fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (fma.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y))) (.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))) (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y))))
(/.f64 (.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))
(/.f64 (.f64 (fma.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (fma.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (*.f64 y y))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (.f64 y y) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 y y)))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y y)) (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 y y)))
(/.f64 (exp.f64 (log.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (exp.f64 (log.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(/.f64 (exp.f64 (log.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)))) (exp.f64 (log.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))))) (exp.f64 (log.f64 (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))))) (exp.f64 (log.f64 (neg.f64 (-.f64 (*.f64 x x) y)))))
(/.f64 (exp.f64 (log.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x))))) (exp.f64 (log.f64 (-.f64 y (*.f64 x x)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 y (.f64 x x)) (.f64 (fma.f64 x x y) (-.f64 y (*.f64 x x)))) #s(literal -1 binary64))
(.f64 (fma.f64 x x y) (.f64 (-.f64 (.f64 x x) y) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))))
(.f64 (fma.f64 x x y) (/.f64 (-.f64 (.f64 x x) y) (-.f64 (*.f64 x x) y)))
(.f64 (.f64 (fma.f64 x x y) (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))))
(.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (.f64 (fma.f64 x x y) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))))
(.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(*.f64 #s(literal 1 binary64) (fma.f64 x x y))
(.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)))
(.f64 (neg.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))))
(.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 x x) y))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)))
(.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 y (.f64 x x))))
(.f64 (/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (.f64 (fma.f64 x x y) (-.f64 (*.f64 x x) y))) (fma.f64 x x y))
(.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 y (-.f64 y (.f64 x x))) (.f64 (.f64 y (-.f64 y (.f64 x x))) (.f64 y (-.f64 y (.f64 x x))))))) (fma.f64 (.f64 y (-.f64 y (.f64 x x))) (-.f64 (.f64 y (-.f64 y (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y) (.f64 y (.f64 x x))))) (fma.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y) (.f64 y (*.f64 x x))))
(.f64 (/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 y (fma.f64 x x y))))
(.f64 (exp.f64 (log.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))))
(.f64 (exp.f64 (log.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)))) (exp.f64 (neg.f64 (log.f64 (-.f64 (.f64 x x) y)))))

eval89.0ms (1.3%)

Memory: -27.2MiB live, 131.6MiB allocated
Compiler: Compiled 9 934 to 857 computations (91.4% saved)

prune49.0ms (0.7%)

Memory

1.6MiB live, 123.4MiB 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
▶	34.6%	(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
✓	66.6%	(sqrt.f64 (fma.f64 x x y))
✓	35.5%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	69.4%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x))
✓	33.9%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 67 to 30 computations (55.2% saved)

simplify97.0ms (1.5%)

Memory

7.5MiB live, 104.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))
cost-diff	0	(sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
cost-diff	0	(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))

Rules

1 224×	`lower-fma.f32`
1 220×	`lower-fma.f64`
572×	`lower-*.f32`
566×	`lower-*.f64`
338×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	109
0	21	109
1	29	109
2	48	109
3	97	109
4	165	103
5	261	103
6	440	103
7	725	103
8	958	103
9	1178	103
10	1814	103
11	1971	103
12	2043	103
13	2072	103
14	2085	103
15	2085	103
0	2085	97

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))
(*.f64 x x)
x
(-.f64 (*.f64 x x) y)
y
(*.f64 y y)
(sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(fma.f64 x x y)

Outputs
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))
(*.f64 x x)
x
(-.f64 (*.f64 x x) y)
y
(*.f64 y y)
(sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(fma.f64 x x y)

localize57.0ms (0.9%)

Memory

-15.7MiB live, 97.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	17.509374049379666	(sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
accuracy	20.769910911873385	(sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
accuracy	21.561288747503884	(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
accuracy	40.21911823609832	(/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))

Samples

38.0ms

256×

valid

Compiler

Compiled 121 to 14 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-add: 18.0ms (60.5% of total)

ival-mult: 6.0ms (20.2% of total)

ival-sqrt: 3.0ms (10.1% of total)

ival-sub: 1.0ms (3.4% of total)

ival-div: 1.0ms (3.4% of total)

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

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

series18.0ms (0.3%)

Memory

-2.0MiB live, 43.6MiB allocated

Counts

6 → 132

Calls

Call 1

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

Outputs
#s(alt (sqrt y) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* 1/2 (/ y x))) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 y) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ y (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ y (* (pow x 2) (- (* 3/8 (/ (pow x 2) y)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ y (* (pow x 2) (- (* (pow x 2) (+ (* 3/16 (/ (pow x 2) (pow y 2))) (* 3/8 (/ 1 y)))) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1/2 (/ y (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4)))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* 1/4 (/ (* y (- (pow y 2) (* 1/4 (pow y 2)))) (pow x 6))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4))))))) (taylor inf x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1/2 (/ y (pow x 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* 1/4 (/ (* y (- (pow y 2) (* 1/4 (pow y 2)))) (pow x 6))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 y) (pow x 2)) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (- (* 3/8 (/ y (pow x 2))) 1/2)) (pow x 2)) (taylor 0 y) (#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())) ())
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#s(alt (+ (sqrt (/ 1 y)) (* (pow x 2) (+ (sqrt (/ 1 (pow y 3))) (* (pow x 4) (+ (* -1/2 (sqrt (/ 1 (pow y 7)))) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 9)))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
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#s(alt (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ (- y (* -1 y)) (pow x 2))))) x) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (- y (* -1 y)))) (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y))))) (pow x 6))) (* 1/2 (/ (- y (* -1 y)) (pow x 2)))))) x) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* 1/2 (/ (- y (* -1 y)) (pow x 2)))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ (- y (* -1 y)) (pow x 2))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (- y (* -1 y)))) (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y))))) (pow x 6))) (* 1/2 (/ (- y (* -1 y)) (pow x 2)))))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ 1 x) (/ y (pow x 3))) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/2 (/ (pow y 2) (pow x 7))) (/ 1 (pow x 3)))) (/ 1 x)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* (pow y 2) (- (* -1/2 (/ y (pow x 9))) (* 1/2 (/ 1 (pow x 7))))) (/ 1 (pow x 3)))) (/ 1 x)) (taylor 0 y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 y)) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2)))))) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))))) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* y (pow (- (pow x 2) (* -1 (pow x 2))) 2))) (+ (* (pow x 2) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2)))))))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2)))))))) (taylor inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) (taylor -inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) (taylor -inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1/2 (* (sqrt y) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1 (* (pow x 2) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (+ (* -1/4 (/ (* y (pow (- (pow x 2) (* -1 (pow x 2))) 2)) (pow (sqrt -1) 2))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2))))))))) (pow y 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) (taylor -inf y) (#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())) ())

Calls

33 calls:

Time	Variable		Point	Expression
4.0ms	y	@	-inf	(sqrt (/ (+ (* x x) y) (+ (* (* x x) (- (* x x) y)) (* y y))))
1.0ms	x	@	inf	(sqrt (+ (* (* x x) (- (* x x) y)) (* y y)))
1.0ms	y	@	inf	(sqrt (/ (+ (* x x) y) (+ (* (* x x) (- (* x x) y)) (* y y))))
1.0ms	x	@	inf	(sqrt (/ (+ (* x x) y) (+ (* (* x x) (- (* x x) y)) (* y y))))
1.0ms	y	@	-inf	(sqrt (+ (* (* x x) (- (* x x) y)) (* y y)))

simplify273.0ms (4.1%)

Memory

21.9MiB live, 605.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 934×	`lower-fma.f64`
9 934×	`lower-fma.f32`
5 922×	`lower-*.f64`
5 922×	`lower-*.f32`
3 936×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	457	2766
1	1426	2453
2	4640	2406
0	8609	2254

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 128

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)))))))
y
(+ y (* -1/2 (pow x 2)))
(+ y (* (pow x 2) (- (* 3/8 (/ (pow x 2) y)) 1/2)))
(+ y (* (pow x 2) (- (* (pow x 2) (+ (* 3/16 (/ (pow x 2) (pow y 2))) (* 3/8 (/ 1 y)))) 1/2)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4))))))
(* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* 1/4 (/ (* y (- (pow y 2) (* 1/4 (pow y 2)))) (pow x 6))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4))))))
(* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* 1/4 (/ (* y (- (pow y 2) (* 1/4 (pow y 2)))) (pow x 6))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4)))))))
(pow x 2)
(+ (* -1/2 y) (pow x 2))
(+ (* y (- (* 3/8 (/ y (pow x 2))) 1/2)) (pow x 2))
(+ (* y (- (* y (+ (* 3/16 (/ y (pow x 4))) (* 3/8 (/ 1 (pow x 2))))) 1/2)) (pow x 2))
y
(* y (+ 1 (* -1/2 (/ (pow x 2) y))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) y)) (* 1/2 (/ (- (pow x 4) (* 1/4 (pow x 4))) (pow y 2))))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) y)) (+ (* 1/4 (/ (* (pow x 2) (- (pow x 4) (* 1/4 (pow x 4)))) (pow y 3))) (* 1/2 (/ (- (pow x 4) (* 1/4 (pow x 4))) (pow y 2)))))))
(* -1 y)
(* -1 (* y (+ 1 (* -1/2 (/ (pow x 2) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1/2 (/ (- (pow x 4) (* 1/4 (pow x 4))) y)) (* 1/2 (pow x 2))) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (pow x 2) (- (pow x 4) (* 1/4 (pow x 4)))) y)) (* 1/2 (- (pow x 4) (* 1/4 (pow x 4))))) y)) (* 1/2 (pow x 2))) y)))))
(pow y 2)
(+ (* -1 (* (pow x 2) y)) (pow y 2))
(+ (* (pow x 2) (+ (* -1 y) (pow x 2))) (pow y 2))
(+ (* (pow x 2) (+ (* -1 y) (pow x 2))) (pow y 2))
(pow x 4)
(* (pow x 4) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 4) (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))))
(* (pow x 4) (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))))
(pow x 4)
(* (pow x 4) (+ 1 (* -1 (/ y (pow x 2)))))
(* (pow x 4) (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))))
(* (pow x 4) (- (+ 1 (/ (pow y 2) (pow x 4))) (/ y (pow x 2))))
(pow x 4)
(+ (* -1 (* (pow x 2) y)) (pow x 4))
(+ (* y (+ y (* -1 (pow x 2)))) (pow x 4))
(+ (* y (+ y (* -1 (pow x 2)))) (pow x 4))
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) y))))
(* (pow y 2) (+ 1 (+ (* -1 (/ (pow x 2) y)) (/ (pow x 4) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* -1 (/ (pow x 2) y)) (/ (pow x 4) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (/ (pow x 4) y)) (pow x 2)) y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (/ (pow x 4) y)) (pow x 2)) y))))
(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)
(/ 1 y)
(+ (* 2 (/ (pow x 2) (pow y 2))) (/ 1 y))
(+ (* (pow x 2) (+ (* 2 (/ 1 (pow y 2))) (/ (pow x 2) (pow y 3)))) (/ 1 y))
(+ (* (pow x 2) (+ (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (* 2 (/ 1 (pow y 2))))) (/ 1 y))
(/ 1 (pow x 2))
(/ (- (+ 1 (/ y (pow x 2))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (+ (* -1 (/ (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)) (pow x 4))) (/ y (pow x 2)))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (+ (* -1 (/ (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y)))) (pow x 6))) (/ y (pow x 2)))) (+ (* -1 (/ y (pow x 2))) (+ (* -1 (/ (* y (- y (* -1 y))) (pow x 4))) (/ (pow y 2) (pow x 4))))) (pow x 2))
(/ 1 (pow x 2))
(/ (- (+ 1 (/ y (pow x 2))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (+ (* -1 (/ (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)) (pow x 4))) (/ y (pow x 2)))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (+ (* -1 (/ (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y)))) (pow x 6))) (/ y (pow x 2)))) (+ (* -1 (/ y (pow x 2))) (+ (* -1 (/ (* y (- y (* -1 y))) (pow x 4))) (/ (pow y 2) (pow x 4))))) (pow x 2))
(/ 1 (pow x 2))
(+ (* 2 (/ y (pow x 4))) (/ 1 (pow x 2)))
(+ (* y (+ (* 2 (/ 1 (pow x 4))) (/ y (pow x 6)))) (/ 1 (pow x 2)))
(+ (* y (+ (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))
(/ 1 y)
(/ (- (+ 1 (/ (pow x 2) y)) (* -1 (/ (pow x 2) y))) y)
(/ (- (+ 1 (+ (* -1 (/ (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)) (pow y 2))) (/ (pow x 2) y))) (* -1 (/ (pow x 2) y))) y)
(/ (- (+ 1 (+ (* -1 (/ (+ (* (pow x 2) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2))))) (pow y 3))) (/ (pow x 2) y))) (+ (* -1 (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) (pow y 2))) (+ (* -1 (/ (pow x 2) y)) (/ (pow x 4) (pow y 2))))) y)
(/ 1 y)
(* -1 (/ (- (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow x 4) y)) (+ (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) y) (pow x 2))) (* -1 (pow x 2))) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (pow x 2) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))))) y)) (/ (* (pow x 4) (- (pow x 2) (* -1 (pow x 2)))) y)) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))))) y)) (pow x 2)) (* -1 (pow x 2))) y)) 1) y))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* (pow x 2) (sqrt (/ 1 (pow y 3)))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (sqrt (/ 1 (pow y 3))) (* -1/2 (* (pow x 4) (sqrt (/ 1 (pow y 7))))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (sqrt (/ 1 (pow y 3))) (* (pow x 4) (+ (* -1/2 (sqrt (/ 1 (pow y 7)))) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 9))))))))))
(/ 1 x)
(/ (+ 1 (* 1/2 (/ (- y (* -1 y)) (pow x 2)))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ (- y (* -1 y)) (pow x 2))))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (- y (* -1 y)))) (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y))))) (pow x 6))) (* 1/2 (/ (- y (* -1 y)) (pow x 2)))))) x)
(/ -1 x)
(* -1 (/ (+ 1 (* 1/2 (/ (- y (* -1 y)) (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ (- y (* -1 y)) (pow x 2))))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (- y (* -1 y)))) (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y))))) (pow x 6))) (* 1/2 (/ (- y (* -1 y)) (pow x 2)))))) x))
(/ 1 x)
(+ (/ 1 x) (/ y (pow x 3)))
(+ (* y (+ (* -1/2 (/ (pow y 2) (pow x 7))) (/ 1 (pow x 3)))) (/ 1 x))
(+ (* y (+ (* (pow y 2) (- (* -1/2 (/ y (pow x 9))) (* 1/2 (/ 1 (pow x 7))))) (/ 1 (pow x 3)))) (/ 1 x))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2)))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* y (pow (- (pow x 2) (* -1 (pow x 2))) 2))) (+ (* (pow x 2) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2)))))))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (sqrt y) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1 (* (pow x 2) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (+ (* -1/4 (/ (* y (pow (- (pow x 2) (* -1 (pow x 2))) 2)) (pow (sqrt -1) 2))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2))))))))) (pow y 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))

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

rewrite326.0ms (4.9%)

Memory

2.3MiB live, 575.5MiB allocated

Rules

6 268×	`lower-fma.f32`
6 264×	`lower-fma.f64`
4 972×	`lower-*.f32`
4 966×	`lower-*.f64`
3 668×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	95
0	21	94
1	75	94
2	582	64
3	7688	64
0	8749	60

Stop Event

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

Counts

6 → 415

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))
(*.f64 x x)
(/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))

Outputs
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/2 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))))
(hypot.f64 x (pow.f64 y #s(literal 1/2 binary64)))
(hypot.f64 (exp.f64 (log.f64 x)) (pow.f64 y #s(literal 1/2 binary64)))
(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) x)
(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (exp.f64 (log.f64 x)))
(sqrt.f64 (fma.f64 x x y))
(/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) y)) (sqrt.f64 (.f64 (-.f64 (*.f64 x x) y) (fma.f64 x x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)) (fma.f64 x x y)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 (.f64 x x) (.f64 (.f64 x x) (-.f64 (.f64 x x) y)))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 (.f64 x x) (.f64 (.f64 x x) (-.f64 (.f64 x x) y)))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (fma.f64 x x y))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y))))) (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 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (sqrt.f64 (neg.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)))) (sqrt.f64 (neg.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y))) (.f64 y (.f64 y (.f64 y y)))))) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y))) (.f64 y (.f64 y (*.f64 y y))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y))))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y (neg.f64 y)))))
(/.f64 (sqrt.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(/.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 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 (.f64 x x) (.f64 (.f64 x x) (-.f64 (.f64 x x) y)))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))))) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 (.f64 x x) (.f64 (.f64 x x) (-.f64 (.f64 x x) y)))) (.f64 (.f64 y y) (.f64 y (.f64 y (*.f64 y y)))))))
(/.f64 (sqrt.f64 (neg.f64 (.f64 (fma.f64 x x y) (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 (.f64 x x) (.f64 (.f64 x x) (-.f64 (.f64 x x) y)))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 (.f64 x x) (.f64 (.f64 x x) (-.f64 (.f64 x x) y)))) (.f64 (.f64 y y) (.f64 y (.f64 y (*.f64 y y))))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y)))))) (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y (neg.f64 y))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y))) (neg.f64 (fma.f64 x x y))))) (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (-.f64 (.f64 x x) y) (.f64 x (neg.f64 x)) (*.f64 y y)))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)) (fma.f64 x x y))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (neg.f64 (fma.f64 x x y)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (neg.f64 (sqrt.f64 (fma.f64 x x y)))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 (.f64 x x) (.f64 (.f64 x x) (-.f64 (.f64 x x) y)))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))))) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y))) (.f64 y (.f64 y (.f64 y y))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y)))))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y)))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 (.f64 x x) (.f64 (.f64 x x) (-.f64 (.f64 x x) y)))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y))) (.f64 y (.f64 y (.f64 y y))))))
(/.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y))))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y (neg.f64 y)))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (sqrt.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)) (fma.f64 x x y))))
(/.f64 (.f64 (sqrt.f64 (neg.f64 (fma.f64 x x y))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(/.f64 (.f64 (neg.f64 (sqrt.f64 (fma.f64 x x y))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(/.f64 (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y))) (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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)))
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(.f64 (sqrt.f64 (fma.f64 x x y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))))
(.f64 (sqrt.f64 (fma.f64 x x y)) (/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y)))
(.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))))
(.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (.f64 x x) y))))
(.f64 (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(.f64 (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))))
(.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))))
(.f64 (pow.f64 (.f64 (/.f64 (fma.f64 x x y) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y)))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x y)))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 (fma.f64 x x y) (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y)))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (fma.f64 x x y)))))
(.f64 (/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (fma.f64 x x y)) (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (fma.f64 x x y)) (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1/4 binary64))))
(.f64 (.f64 (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #s(literal 1/4 binary64))) (.f64 (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))) #s(literal 1/4 binary64))))
(.f64 (.f64 (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y 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 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))) #s(literal 1/4 binary64)))
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eval111.0ms (1.7%)

Memory: -15.3MiB live, 294.2MiB allocated
Compiler: Compiled 43 338 to 2 485 computations (94.3% saved)

prune107.0ms (1.6%)

Memory

-22.1MiB live, 310.1MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	771	1	772
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	772	6	778

Accuracy

100.0%

Counts

778 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	16.9%	(.f64 #s(approx (sqrt (+ ( (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
✓	66.6%	(sqrt.f64 (fma.f64 x x y))
✓	35.5%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	69.4%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x))
✓	33.9%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 68 to 35 computations (48.5% saved)

simplify308.0ms (4.6%)

Memory

13.9MiB live, 211.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)
cost-diff	0	#s(approx (sqrt (+ (* (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y))
cost-diff	0	(.f64 #s(approx (sqrt (+ ( (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))

Rules

3 400×	`lower-fma.f32`
3 392×	`lower-fma.f64`
2 326×	`unsub-neg`
1 740×	`lower-*.f32`
1 732×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	173
0	39	173
1	63	173
2	125	173
3	240	173
4	336	167
5	527	167
6	790	167
7	1288	167
8	2407	167
9	4453	167
10	5163	167
11	5774	167
12	5785	167
13	5792	167
14	6174	167
15	6424	167
16	6430	167
17	6430	167
18	6430	167
19	6502	167
20	6514	167
21	6514	167
22	6650	167
23	7605	167
0	7605	161

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 #s(approx (sqrt (+ ( (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
#s(approx (sqrt (+ (* (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)
x
(.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))
(*.f64 x x)
(/.f64 #s(literal 3/8 binary64) y)
#s(literal 3/8 binary64)
y
#s(literal -1/2 binary64)
(sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (fma.f64 x x y) (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))
(-.f64 (*.f64 x x) y)
(*.f64 y y)

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

localize80.0ms (1.2%)

Memory

11.6MiB live, 131.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	20.769910911873385	(sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
accuracy	21.561288747503884	(.f64 #s(approx (sqrt (+ ( (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
accuracy	32.044076679570935	#s(approx (sqrt (+ (* (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y))
accuracy	40.21911823609832	(/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))

Samples

61.0ms

256×

valid

Compiler

Compiled 161 to 22 computations (86.3% saved)

Precisions

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

ival-add: 29.0ms (59.7% of total)

ival-mult: 10.0ms (20.6% of total)

ival-div: 4.0ms (8.2% of total)

ival-sqrt: 3.0ms (6.2% of total)

ival-sub: 1.0ms (2.1% of total)

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

exact: 0.0ms (0% of total)

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

series15.0ms (0.2%)

Memory

2.0MiB live, 40.5MiB allocated

Counts

6 → 144

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx (sqrt (+ ( (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))) (patch (.f64 #s(approx (sqrt (+ (* (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (patch #s(approx (sqrt (+ (* (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y) (patch (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (patch (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (patch (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #<representation binary64>) () ())

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

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(+ (* x (* x (+ (* (* x x) (/ 3/8 y)) -1/2))) y)
2.0ms	y	@	0	(* x (+ (* (* x x) (/ 3/8 y)) -1/2))
1.0ms	x	@	0	(+ (* x (* x (+ (* (* x x) (/ 3/8 y)) -1/2))) y)
1.0ms	x	@	inf	(* x (+ (* (* x x) (/ 3/8 y)) -1/2))
0.0ms	x	@	0	(* x (+ (* (* x x) (/ 3/8 y)) -1/2))

simplify302.0ms (4.6%)

Memory

-0.6MiB live, 510.0MiB allocated

Algorithm

1×	egg-herbie

Rules

9 808×	`lower-fma.f64`
9 808×	`lower-fma.f32`
6 052×	`lower-*.f64`
6 052×	`lower-*.f32`
4 018×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	476	3001
1	1460	2736
2	4712	2661
0	8762	2491

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 137

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)))))))
y
(+ y (* -1/2 (pow x 2)))
(+ y (* (pow x 2) (- (* 3/8 (/ (pow x 2) y)) 1/2)))
(+ y (* (pow x 2) (- (* (pow x 2) (+ (* 3/16 (/ (pow x 2) (pow y 2))) (* 3/8 (/ 1 y)))) 1/2)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4))))))
(* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* 1/4 (/ (* y (- (pow y 2) (* 1/4 (pow y 2)))) (pow x 6))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4))))))
(* (pow x 2) (+ 1 (+ (* -1/2 (/ y (pow x 2))) (+ (* 1/4 (/ (* y (- (pow y 2) (* 1/4 (pow y 2)))) (pow x 6))) (* 1/2 (/ (- (pow y 2) (* 1/4 (pow y 2))) (pow x 4)))))))
(pow x 2)
(+ (* -1/2 y) (pow x 2))
(+ (* y (- (* 3/8 (/ y (pow x 2))) 1/2)) (pow x 2))
(+ (* y (- (* y (+ (* 3/16 (/ y (pow x 4))) (* 3/8 (/ 1 (pow x 2))))) 1/2)) (pow x 2))
y
(* y (+ 1 (* -1/2 (/ (pow x 2) y))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) y)) (* 1/2 (/ (- (pow x 4) (* 1/4 (pow x 4))) (pow y 2))))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) y)) (+ (* 1/4 (/ (* (pow x 2) (- (pow x 4) (* 1/4 (pow x 4)))) (pow y 3))) (* 1/2 (/ (- (pow x 4) (* 1/4 (pow x 4))) (pow y 2)))))))
(* -1 y)
(* -1 (* y (+ 1 (* -1/2 (/ (pow x 2) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1/2 (/ (- (pow x 4) (* 1/4 (pow x 4))) y)) (* 1/2 (pow x 2))) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (pow x 2) (- (pow x 4) (* 1/4 (pow x 4)))) y)) (* 1/2 (- (pow x 4) (* 1/4 (pow x 4))))) y)) (* 1/2 (pow x 2))) y)))))
y
(+ y (* -1/2 (pow x 2)))
(+ y (* (pow x 2) (- (* 3/8 (/ (pow x 2) y)) 1/2)))
(+ y (* (pow x 2) (- (* 3/8 (/ (pow x 2) y)) 1/2)))
(* 3/8 (/ (pow x 4) y))
(* (pow x 4) (- (* 3/8 (/ 1 y)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ (* 3/8 (/ 1 y)) (/ y (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ (* 3/8 (/ 1 y)) (/ y (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 3/8 (/ (pow x 4) y))
(* (pow x 4) (- (* 3/8 (/ 1 y)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ (* 3/8 (/ 1 y)) (/ y (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ (* 3/8 (/ 1 y)) (/ y (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 3/8 (/ (pow x 4) y))
(/ (+ (* -1/2 (* (pow x 2) y)) (* 3/8 (pow x 4))) y)
(/ (+ (* 3/8 (pow x 4)) (* y (+ y (* -1/2 (pow x 2))))) y)
(/ (+ (* 3/8 (pow x 4)) (* y (+ y (* -1/2 (pow x 2))))) y)
y
(* y (+ 1 (* -1/2 (/ (pow x 2) y))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) y)) (* 3/8 (/ (pow x 4) (pow y 2))))))
(* y (+ 1 (+ (* -1/2 (/ (pow x 2) y)) (* 3/8 (/ (pow x 4) (pow y 2))))))
y
(* -1 (* y (- (* 1/2 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ (* -1/2 (pow x 2)) (* 3/8 (/ (pow x 4) y))) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ (* -1/2 (pow x 2)) (* 3/8 (/ (pow x 4) y))) y)) 1)))
(* -1/2 x)
(* x (- (* 3/8 (/ (pow x 2) y)) 1/2))
(* x (- (* 3/8 (/ (pow x 2) y)) 1/2))
(* x (- (* 3/8 (/ (pow x 2) y)) 1/2))
(* 3/8 (/ (pow x 3) y))
(* (pow x 3) (- (* 3/8 (/ 1 y)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (* 3/8 (/ 1 y)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (* 3/8 (/ 1 y)) (* 1/2 (/ 1 (pow x 2)))))
(* 3/8 (/ (pow x 3) y))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 3/8 (/ 1 y)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 3/8 (/ 1 y)))))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 3/8 (/ 1 y)))))
(* 3/8 (/ (pow x 3) y))
(/ (+ (* -1/2 (* x y)) (* 3/8 (pow x 3))) y)
(/ (+ (* -1/2 (* x y)) (* 3/8 (pow x 3))) y)
(/ (+ (* -1/2 (* x y)) (* 3/8 (pow x 3))) y)
(* -1/2 x)
(+ (* -1/2 x) (* 3/8 (/ (pow x 3) y)))
(+ (* -1/2 x) (* 3/8 (/ (pow x 3) y)))
(+ (* -1/2 x) (* 3/8 (/ (pow x 3) y)))
(* -1/2 x)
(+ (* -1/2 x) (* 3/8 (/ (pow x 3) y)))
(+ (* -1/2 x) (* 3/8 (/ (pow x 3) y)))
(+ (* -1/2 x) (* 3/8 (/ (pow x 3) y)))
(/ 1 y)
(+ (* 2 (/ (pow x 2) (pow y 2))) (/ 1 y))
(+ (* (pow x 2) (+ (* 2 (/ 1 (pow y 2))) (/ (pow x 2) (pow y 3)))) (/ 1 y))
(+ (* (pow x 2) (+ (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (* 2 (/ 1 (pow y 2))))) (/ 1 y))
(/ 1 (pow x 2))
(/ (- (+ 1 (/ y (pow x 2))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (+ (* -1 (/ (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)) (pow x 4))) (/ y (pow x 2)))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (+ (* -1 (/ (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y)))) (pow x 6))) (/ y (pow x 2)))) (+ (* -1 (/ y (pow x 2))) (+ (* -1 (/ (* y (- y (* -1 y))) (pow x 4))) (/ (pow y 2) (pow x 4))))) (pow x 2))
(/ 1 (pow x 2))
(/ (- (+ 1 (/ y (pow x 2))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (+ (* -1 (/ (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)) (pow x 4))) (/ y (pow x 2)))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/ (- (+ 1 (+ (* -1 (/ (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y)))) (pow x 6))) (/ y (pow x 2)))) (+ (* -1 (/ y (pow x 2))) (+ (* -1 (/ (* y (- y (* -1 y))) (pow x 4))) (/ (pow y 2) (pow x 4))))) (pow x 2))
(/ 1 (pow x 2))
(+ (* 2 (/ y (pow x 4))) (/ 1 (pow x 2)))
(+ (* y (+ (* 2 (/ 1 (pow x 4))) (/ y (pow x 6)))) (/ 1 (pow x 2)))
(+ (* y (+ (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))
(/ 1 y)
(/ (- (+ 1 (/ (pow x 2) y)) (* -1 (/ (pow x 2) y))) y)
(/ (- (+ 1 (+ (* -1 (/ (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)) (pow y 2))) (/ (pow x 2) y))) (* -1 (/ (pow x 2) y))) y)
(/ (- (+ 1 (+ (* -1 (/ (+ (* (pow x 2) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2))))) (pow y 3))) (/ (pow x 2) y))) (+ (* -1 (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) (pow y 2))) (+ (* -1 (/ (pow x 2) y)) (/ (pow x 4) (pow y 2))))) y)
(/ 1 y)
(* -1 (/ (- (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow x 4) y)) (+ (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) y) (pow x 2))) (* -1 (pow x 2))) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (pow x 2) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))))) y)) (/ (* (pow x 4) (- (pow x 2) (* -1 (pow x 2)))) y)) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))))) y)) (pow x 2)) (* -1 (pow x 2))) y)) 1) y))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* (pow x 2) (sqrt (/ 1 (pow y 3)))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (sqrt (/ 1 (pow y 3))) (* -1/2 (* (pow x 4) (sqrt (/ 1 (pow y 7))))))))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (sqrt (/ 1 (pow y 3))) (* (pow x 4) (+ (* -1/2 (sqrt (/ 1 (pow y 7)))) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 9))))))))))
(/ 1 x)
(/ (+ 1 (* 1/2 (/ (- y (* -1 y)) (pow x 2)))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ (- y (* -1 y)) (pow x 2))))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (- y (* -1 y)))) (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y))))) (pow x 6))) (* 1/2 (/ (- y (* -1 y)) (pow x 2)))))) x)
(/ -1 x)
(* -1 (/ (+ 1 (* 1/2 (/ (- y (* -1 y)) (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ (- y (* -1 y)) (pow x 2))))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (- y (* -1 y)))) (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y))))) (pow x 6))) (* 1/2 (/ (- y (* -1 y)) (pow x 2)))))) x))
(/ 1 x)
(+ (/ 1 x) (/ y (pow x 3)))
(+ (* y (+ (* -1/2 (/ (pow y 2) (pow x 7))) (/ 1 (pow x 3)))) (/ 1 x))
(+ (* y (+ (* (pow y 2) (- (* -1/2 (/ y (pow x 9))) (* 1/2 (/ 1 (pow x 7))))) (/ 1 (pow x 3)))) (/ 1 x))
(sqrt (/ 1 y))
(+ (sqrt (/ 1 y)) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2)))))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* y (pow (- (pow x 2) (* -1 (pow x 2))) 2))) (+ (* (pow x 2) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2)))))))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (sqrt y) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1 (* (pow x 2) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (+ (* -1/4 (/ (* y (pow (- (pow x 2) (* -1 (pow x 2))) 2)) (pow (sqrt -1) 2))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2))))))))) (pow y 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))

Outputs
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 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 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 x x) #s(literal -1/8 binary64)))) (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 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) (sqrt.f64 y))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(fma.f64 x (.f64 #s(literal 1/2 binary64) (/.f64 y (.f64 x x))) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 y (.f64 x x)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 y y)) (.f64 (.f64 x x) (.f64 x x)))) 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)))))))
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(/.f64 #s(literal 1 binary64) y)
(+ (* 2 (/ (pow x 2) (pow y 2))) (/ 1 y))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) y)) y)
(+ (* (pow x 2) (+ (* 2 (/ 1 (pow y 2))) (/ (pow x 2) (pow y 3)))) (/ 1 y))
(fma.f64 x (.f64 x (fma.f64 x (/.f64 x (.f64 y (.f64 y y))) (/.f64 #s(literal 2 binary64) (.f64 y y)))) (/.f64 #s(literal 1 binary64) y))
(+ (* (pow x 2) (+ (* (pow x 2) (+ (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (* 2 (/ 1 (pow y 2))))) (/ 1 y))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))) (/.f64 (.f64 x x) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 2 binary64) (.f64 y y)))) (/.f64 #s(literal 1 binary64) y))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- (+ 1 (/ y (pow x 2))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (+ (* -1 (/ (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)) (pow x 4))) (/ y (pow x 2)))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (fma.f64 y (+.f64 y y) (.f64 y (neg.f64 y))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (+.f64 y y) (.f64 x x)))) (.f64 x x))
(/ (- (+ 1 (+ (* -1 (/ (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y)))) (pow x 6))) (/ y (pow x 2)))) (+ (* -1 (/ y (pow x 2))) (+ (* -1 (/ (* y (- y (* -1 y))) (pow x 4))) (/ (pow y 2) (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (.f64 y (+.f64 y y)) (.f64 y (-.f64 (.f64 y y) (.f64 y (+.f64 y y))))) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (/.f64 (fma.f64 y (+.f64 y y) (.f64 y (neg.f64 y))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (+.f64 y y) (.f64 x x)))) (.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- (+ 1 (/ y (pow x 2))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (+ (* -1 (/ (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)) (pow x 4))) (/ y (pow x 2)))) (* -1 (/ y (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (fma.f64 y (+.f64 y y) (.f64 y (neg.f64 y))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (+.f64 y y) (.f64 x x)))) (.f64 x x))
(/ (- (+ 1 (+ (* -1 (/ (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y)))) (pow x 6))) (/ y (pow x 2)))) (+ (* -1 (/ y (pow x 2))) (+ (* -1 (/ (* y (- y (* -1 y))) (pow x 4))) (/ (pow y 2) (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (.f64 y (+.f64 y y)) (.f64 y (-.f64 (.f64 y y) (.f64 y (+.f64 y y))))) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (/.f64 (fma.f64 y (+.f64 y y) (.f64 y (neg.f64 y))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (+.f64 y y) (.f64 x x)))) (.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(+ (* 2 (/ y (pow x 4))) (/ 1 (pow x 2)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (+.f64 y y) (.f64 (.f64 x x) (.f64 x x))))
(+ (* y (+ (* 2 (/ 1 (pow x 4))) (/ y (pow x 6)))) (/ 1 (pow x 2)))
(fma.f64 y (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 y (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(+ (* y (+ (* y (+ (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))
(fma.f64 y (fma.f64 y (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 y (pow.f64 x #s(literal 8 binary64)))) (/.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (- (+ 1 (/ (pow x 2) y)) (* -1 (/ (pow x 2) y))) y)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) y)) y)
(/ (- (+ 1 (+ (* -1 (/ (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)) (pow y 2))) (/ (pow x 2) y))) (* -1 (/ (pow x 2) y))) y)
(/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -2 binary64)))) (.f64 y y))) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) y)) y)
(/ (- (+ 1 (+ (* -1 (/ (+ (* (pow x 2) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2))))) (pow y 3))) (/ (pow x 2) y))) (+ (* -1 (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) (pow y 2))) (+ (* -1 (/ (pow x 2) y)) (/ (pow x 4) (pow y 2))))) y)
(/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 #s(literal 2 binary64) (.f64 x x))))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -2 binary64)))))) (.f64 y (.f64 y y)))) (+.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -2 binary64)))) (.f64 y (neg.f64 y))) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) y))) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(* -1 (/ (- (* -1 (/ (- (pow x 2) (* -1 (pow x 2))) y)) 1) y))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) y)) y)
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow x 4) y)) (+ (/ (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))) y) (pow x 2))) (* -1 (pow x 2))) y)) 1) y))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 x x (/.f64 (fma.f64 x (.f64 x (.f64 #s(literal 2 binary64) (.f64 x x))) (neg.f64 (.f64 (.f64 x x) (.f64 x x)))) y))) y)) y)
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* (pow x 2) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))))) y)) (/ (* (pow x 4) (- (pow x 2) (* -1 (pow x 2)))) y)) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2)))))) y)) (pow x 2)) (* -1 (pow x 2))) y)) 1) y))
(neg.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -2 binary64) (/.f64 (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -2 binary64)))) y) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) y) (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -2 binary64)))))) y)) y)) y))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(+ (sqrt (/ 1 y)) (* (pow x 2) (sqrt (/ 1 (pow y 3)))))
(fma.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y y)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (sqrt (/ 1 (pow y 3))) (* -1/2 (* (pow x 4) (sqrt (/ 1 (pow y 7))))))))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(+ (sqrt (/ 1 y)) (* (pow x 2) (+ (sqrt (/ 1 (pow y 3))) (* (pow x 4) (+ (* -1/2 (sqrt (/ 1 (pow y 7)))) (* -1/2 (* (pow x 2) (sqrt (/ 1 (pow y 9))))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 9 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/2 (/ (- y (* -1 y)) (pow x 2)))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 y y) (*.f64 x x)) #s(literal 1 binary64)) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ (- y (* -1 y)) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 y y) (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 y (.f64 y #s(literal -2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (- y (* -1 y)))) (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y))))) (pow x 6))) (* 1/2 (/ (- y (* -1 y)) (pow x 2)))))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (fma.f64 y (.f64 y #s(literal -2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (fma.f64 y (.f64 y (+.f64 y y)) (fma.f64 y (-.f64 (.f64 y y) (.f64 y (+.f64 y y))) (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 y y) (fma.f64 y (.f64 y #s(literal -2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 y y))))))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 y y) (*.f64 x x)) #s(literal 1 binary64))) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (/ (+ 1 (* 1/2 (/ (- y (* -1 y)) (pow x 2)))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 y y) (*.f64 x x)) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ (- y (* -1 y)) (pow x 2))))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 y y) (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 y (.f64 y #s(literal -2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (+ (* -1 (* y (- y (* -1 y)))) (+ (* 1/4 (pow (- y (* -1 y)) 2)) (pow y 2))) (- y (* -1 y)))) (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y))))) (pow x 6))) (* 1/2 (/ (- y (* -1 y)) (pow x 2)))))) x))
(neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (fma.f64 y (.f64 y #s(literal -2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (fma.f64 y (.f64 y (+.f64 y y)) (fma.f64 y (-.f64 (.f64 y y) (.f64 y (+.f64 y y))) (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 y y) (fma.f64 y (.f64 y #s(literal -2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 y y))))))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 y y) (*.f64 x x)) #s(literal 1 binary64))) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (/ 1 x) (/ y (pow x 3)))
(+.f64 (/.f64 y (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(+ (* y (+ (* -1/2 (/ (pow y 2) (pow x 7))) (/ 1 (pow x 3)))) (/ 1 x))
(fma.f64 y (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 y y) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(+ (* y (+ (* (pow y 2) (- (* -1/2 (/ y (pow x 9))) (* 1/2 (/ 1 (pow x 7))))) (/ 1 (pow x 3)))) (/ 1 x))
(fma.f64 y (fma.f64 (.f64 y y) (fma.f64 y (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 9 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) y))
(+ (sqrt (/ 1 y)) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2)))))))
(fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 2 binary64) (.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -2 binary64)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* y (pow (- (pow x 2) (* -1 (pow x 2))) 2))) (+ (* (pow x 2) (+ (* -1 (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))) (pow x 4))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2)))))))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -2 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 y (.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/4 binary64)) (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 #s(literal 2 binary64) (.f64 x x))))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -2 binary64))))))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
(+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))
(fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 2 binary64) (*.f64 x x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(fma.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 x (.f64 x (.f64 #s(literal 2 binary64) (.f64 x x))) (neg.f64 (.f64 (.f64 x x) (*.f64 x x)))))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(+ (* -1 (/ (+ (* -1/2 (* (sqrt y) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1 (* (pow x 2) (+ (* -1 (pow x 4)) (* (pow x 2) (- (pow x 2) (* -1 (pow x 2))))))) (+ (* -1/4 (/ (* y (pow (- (pow x 2) (* -1 (pow x 2))) 2)) (pow (sqrt -1) 2))) (* (pow x 4) (- (pow x 2) (* -1 (pow x 2))))))))) (pow y 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (- (pow x 2) (* -1 (pow x 2))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 2 binary64) (.f64 x x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (/.f64 (fma.f64 (sqrt.f64 y) (.f64 (fma.f64 x (.f64 x (.f64 #s(literal 2 binary64) (.f64 x x))) (neg.f64 (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -2 binary64))))) (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 #s(literal 2 binary64) (.f64 x x))))) (/.f64 (.f64 (.f64 #s(literal -1/4 binary64) y) (.f64 #s(literal 4 binary64) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1 binary64)))))) (.f64 y (.f64 y y))))

rewrite341.0ms (5.1%)

Memory

6.9MiB live, 681.0MiB allocated

Rules

11 444×	`lower-fma.f32`
11 436×	`lower-fma.f64`
6 218×	`lower-*.f32`
6 210×	`lower-*.f64`
3 182×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	131
0	39	131
1	138	131
2	991	126
0	9020	121

Stop Event

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

Counts

6 → 261

Calls

Call 1

Inputs
(.f64 #s(approx (sqrt (+ ( (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
#s(approx (sqrt (+ (* (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)
(.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64)))
(/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))

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

eval51.0ms (0.8%)

Memory: 15.1MiB live, 128.9MiB allocated
Compiler: Compiled 20 356 to 1 412 computations (93.1% saved)

prune57.0ms (0.9%)

Memory

-10.6MiB live, 110.8MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	398	0	398
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	398	6	404

Accuracy

100.0%

Counts

404 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	16.9%	(.f64 #s(approx (sqrt (+ ( (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
✓	66.6%	(sqrt.f64 (fma.f64 x x y))
✓	35.5%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	69.4%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x))
✓	33.9%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 164 to 62 computations (62.2% saved)

regimes17.0ms (0.3%)

Memory

2.3MiB live, 41.5MiB allocated

Counts

8 → 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 y (/.f64 #s(literal 1/2 binary64) x) x))
(sqrt.f64 (+.f64 (*.f64 x x) y))
(.f64 #s(approx (sqrt (+ ( (* x x) (- (* x x) y)) (* y y))) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (/.f64 #s(literal 3/8 binary64) y) #s(literal -1/2 binary64))) y)) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))

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

Calls

5 calls:

4.0ms	y
3.0ms	x
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
3.0ms	(+.f64 (*.f64 x x) y)
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
85.4%	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)

regimes11.0ms (0.2%)

Memory

25.5MiB live, 25.5MiB 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:

2.0ms	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
66.6%	1	`y`
66.6%	1	`x`
66.6%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
66.6%	1	`(+.f64 (*.f64 x x) y)`
66.6%	1	`(*.f64 x x)`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes59.0ms (0.9%)

Memory

-39.8MiB live, 19.1MiB 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
(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))

Calls

5 calls:

51.0ms	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
42.6%	4	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
42.6%	4	`(+.f64 (*.f64 x x) y)`
54.6%	2	`(*.f64 x x)`
54.6%	2	`x`
55.8%	2	`y`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes8.0ms (0.1%)

Memory

16.0MiB live, 16.0MiB 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	(+.f64 (*.f64 x x) y)
2.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
33.9%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
33.9%	1	`(+.f64 (*.f64 x x) y)`
33.9%	1	`(*.f64 x x)`
33.9%	1	`x`
33.9%	1	`y`

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes11.0ms (0.2%)

Memory

-24.1MiB live, 15.5MiB 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:

6.0ms	(*.f64 x x)
1.0ms	y
1.0ms	x
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

Results

Accuracy	Segments	Branch
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)`
1.2%	1	`x`

Compiler

Compiled 26 to 16 computations (38.5% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.833151345526589e+285	5.35518524453294e+289

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch12.0ms (0.2%)

Memory

24.7MiB live, 24.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	7.771483858971434e-135	8.548841077667719e-127

Samples

6.0ms

144×

valid

Compiler

Compiled 137 to 91 computations (33.6% saved)

Precisions

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

ival-add: 1.0ms (35.7% of total)

ival-mult: 1.0ms (35.7% of total)

ival-sqrt: 1.0ms (35.7% of total)

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

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

simplify8.0ms (0.1%)

Memory

-22.3MiB live, 16.5MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`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 5000000000000000164943055170434837427135440057522539318423791570869012863893044939457394359293162206430058690814701199200294101105758807930912040583618895295566352963538529190225559103961304787468696490024321895827150961861074155612506360583410417131562672326958643646649953541871894528 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 y #s(literal 405827311541079/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088 binary64)) (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)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Outputs
(if (<=.f64 (.f64 x x) #s(literal 5000000000000000164943055170434837427135440057522539318423791570869012863893044939457394359293162206430058690814701199200294101105758807930912040583618895295566352963538529190225559103961304787468696490024321895827150961861074155612506360583410417131562672326958643646649953541871894528 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 y #s(literal 405827311541079/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088 binary64)) (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)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

soundness536.0ms (8.1%)

Memory

2.4MiB live, 316.9MiB allocated

Rules

23 136×	`lower-fma.f64`
23 136×	`lower-fma.f32`
5 482×	`lower-*.f64`
5 482×	`lower-*.f32`
5 034×	`lower-fma.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
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12

Stop Event

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

Compiler

Compiled 95 to 49 computations (48.4% saved)

preprocess88.0ms (1.3%)

Memory: 24.4MiB live, 102.8MiB 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%)

analyze17.0ms (0.3%)

sample932.0ms (14.1%)

explain289.0ms (4.4%)

preprocess53.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize17.0ms (0.2%)

series5.0ms (0.1%)

simplify498.0ms (7.5%)

rewrite477.0ms (7.2%)

eval122.0ms (1.8%)

prune208.0ms (3.1%)

simplify75.0ms (1.1%)

localize195.0ms (2.9%)

series11.0ms (0.2%)

simplify394.0ms (6%)

rewrite298.0ms (4.5%)

eval89.0ms (1.3%)

prune49.0ms (0.7%)

simplify97.0ms (1.5%)

localize57.0ms (0.9%)

series18.0ms (0.3%)

simplify273.0ms (4.1%)

rewrite326.0ms (4.9%)

eval111.0ms (1.7%)

prune107.0ms (1.6%)

simplify308.0ms (4.6%)

localize80.0ms (1.2%)

series15.0ms (0.2%)

simplify302.0ms (4.6%)

rewrite341.0ms (5.1%)

eval51.0ms (0.8%)

prune57.0ms (0.9%)

regimes17.0ms (0.3%)

regimes11.0ms (0.2%)

regimes59.0ms (0.9%)

regimes8.0ms (0.1%)

regimes11.0ms (0.2%)

bsearch0.0ms (0%)

bsearch12.0ms (0.2%)

simplify8.0ms (0.1%)

soundness536.0ms (8.1%)

preprocess88.0ms (1.3%)

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