Metrics for Linear.Quaternion:$c/ from linear-1.19.1.3, E

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample1.2s (14.3%)

Memory

36.8MiB live, 989.0MiB allocated

Samples

872.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 489.0ms

ival-mult: 329.0ms (67.3% of total)

ival-add: 150.0ms (30.7% of total)

ival-true: 6.0ms (1.2% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

explain191.0ms (2.3%)

Memory

-4.6MiB live, 116.7MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))`
-	-	`(+.f64 (.f64 x x) (.f64 y y))`
-	-	`y`
-	-	`(*.f64 y y)`
-	-	`(*.f64 x x)`
-	-	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

72.0ms

512×

valid

Compiler

Compiled 101 to 25 computations (75.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-mult: 52.0ms (88.5% of total)

ival-add: 6.0ms (10.2% of total)

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

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

preprocess44.0ms (0.5%)

Memory

-15.6MiB live, 21.0MiB allocated

Algorithm

1×	egg-herbie

Rules

188×	`unsub-neg`
188×	`sub-neg`
170×	`cancel-sign-sub`
142×	`distribute-lft-neg-in`
130×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	77
1	64	67
2	171	47
3	517	45
4	1117	45
5	1322	45
6	1332	45
0	7	15
0	12	15
1	18	13
2	28	9
3	40	9
4	48	9
5	51	9
0	51	8

Stop Event

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

Calls

Call 1

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

Outputs
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))

Symmetry

(abs y)

(abs x)

Compiler

Compiled 15 to 7 computations (53.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 15 to 7 computations (53.3% saved)

simplify4.0ms (0.1%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	192	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
cost-diff	512	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Rules

52×	`lower-fma.f64`
52×	`lower-fma.f32`
36×	`lower-+.f32`
30×	`lower-+.f64`
28×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	41
0	12	41
1	18	37
2	28	33
3	40	33
4	48	33
5	51	33
0	51	30

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
(fma.f64 #s(literal 2 binary64) (.f64 y y) (.f64 x x))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y

localize18.0ms (0.2%)

Memory

13.3MiB live, 13.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
accuracy	0.08203125	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Samples

13.0ms

256×

valid

Compiler

Compiled 43 to 9 computations (79.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 3.0ms (47.5% of total)

ival-mult: 3.0ms (47.5% of total)

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

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

series6.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

5 → 96

Calls

Call 1

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

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

6 calls:

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

simplify363.0ms (4.3%)

Memory

-161.4MiB live, 163.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 540×	`lower-fma.f64`
10 540×	`lower-fma.f32`
6 708×	`lower-*.f64`
6 708×	`lower-*.f32`
1 856×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	588
1	86	588
2	217	588
3	853	588
4	2013	588
5	2661	588
6	4205	588
7	5672	588
8	6662	588
9	7939	588
0	8060	534

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(pow x 2)
(+ (* 3 (pow y 2)) (pow x 2))
(+ (* 3 (pow y 2)) (pow x 2))
(+ (* 3 (pow y 2)) (pow x 2))
(pow x 2)
(+ (* 2 (pow y 2)) (pow x 2))
(+ (* 2 (pow y 2)) (pow x 2))
(+ (* 2 (pow y 2)) (pow x 2))
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* 3 (pow y 2))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(* 2 (pow y 2))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* 3 (pow y 2))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(* 2 (pow y 2))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(+ (* 2 (pow y 2)) (pow y 2))
(+ (* 2 (pow y 2)) (+ (pow x 2) (pow y 2)))
(+ (* 2 (pow y 2)) (+ (pow x 2) (pow y 2)))
(+ (* 2 (pow y 2)) (+ (pow x 2) (pow y 2)))
(* 2 (pow y 2))
(+ (* 2 (pow y 2)) (pow x 2))
(+ (* 2 (pow y 2)) (pow x 2))
(+ (* 2 (pow y 2)) (pow x 2))
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(pow x 2)
(*.f64 x x)
(+ (* 3 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(+ (* 3 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(+ (* 3 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (* 2 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(+ (* 2 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(+ (* 2 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* 3 (pow y 2))
(.f64 (.f64 y y) #s(literal 3 binary64))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* 3 (pow y 2))
(.f64 (.f64 y y) #s(literal 3 binary64))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* (pow y 2) (+ 3 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(* (pow y 2) (+ 2 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(+ (* 2 (pow y 2)) (pow y 2))
(.f64 (.f64 y y) #s(literal 3 binary64))
(+ (* 2 (pow y 2)) (+ (pow x 2) (pow y 2)))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(+ (* 2 (pow y 2)) (+ (pow x 2) (pow y 2)))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(+ (* 2 (pow y 2)) (+ (pow x 2) (pow y 2)))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* 2 (pow y 2))
(.f64 (.f64 y y) #s(literal 2 binary64))
(+ (* 2 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(+ (* 2 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(+ (* 2 (pow y 2)) (pow x 2))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.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) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.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) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (+ (* 2 (/ (pow y 2) (pow x 2))) (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (+ 1 (* 2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.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)

rewrite209.0ms (2.5%)

Memory

-9.4MiB live, 258.1MiB allocated

Rules

9 354×	`lower-fma.f64`
9 354×	`lower-fma.f32`
4 470×	`lower-*.f32`
4 466×	`lower-*.f64`
3 310×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	39
0	12	39
1	54	35
2	517	29
3	7592	29
0	8199	26

Stop Event

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

Counts

5 → 337

Calls

Call 1

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

Outputs
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eval52.0ms (0.6%)

Memory: 3.1MiB live, 120.1MiB allocated
Compiler: Compiled 11 477 to 1 089 computations (90.5% saved)

prune15.0ms (0.2%)

Memory

9.2MiB live, 48.0MiB allocated

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	459	10	469
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	460	10	470

Accuracy

100.0%

Counts

470 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	16.2%	(fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)))
▶	99.9%	(fma.f64 (.f64 #s(literal 2 binary64) y) y (fma.f64 y y (.f64 x x)))
	99.9%	(fma.f64 y (fma.f64 #s(literal 2 binary64) y y) (*.f64 x x))
▶	99.9%	(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
	99.9%	(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
	16.7%	(+.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 x x #s(literal 0 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
▶	80.3%	(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
▶	49.7%	(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))))
	55.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
▶	60.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

Compiler

Compiled 260 to 172 computations (33.8% saved)

simplify233.0ms (2.7%)

Memory

8.2MiB live, 299.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
cost-diff	320	(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))))
cost-diff	8192	(*.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64)))
cost-diff	0	(*.f64 y y)
cost-diff	0	(.f64 #s(literal 3 binary64) (.f64 y y))
cost-diff	0	(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x))
cost-diff	128	(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 y y (*.f64 x x))
cost-diff	0	(*.f64 #s(literal 2 binary64) y)
cost-diff	384	(fma.f64 (.f64 #s(literal 2 binary64) y) y (fma.f64 y y (.f64 x x)))

Rules

21 618×	`lower-fma.f32`
21 608×	`lower-fma.f64`
4 582×	`lower-*.f32`
4 572×	`lower-*.f64`
2 642×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	192
0	43	175
1	76	141
2	161	141
3	426	141
4	1709	141
5	4163	141
6	5379	141
7	6145	141
8	6244	141
9	6344	141
10	6447	141
11	7269	141
0	8040	138

Stop Event

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

Calls

Call 1

Inputs
(fma.f64 (.f64 #s(literal 2 binary64) y) y (fma.f64 y y (.f64 x x)))
(*.f64 #s(literal 2 binary64) y)
#s(literal 2 binary64)
y
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
#s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
x
(.f64 #s(literal 3 binary64) (.f64 y y))
#s(literal 3 binary64)
(*.f64 y y)
y
(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
#s(literal 3 binary64)
(*.f64 y y)
y
(*.f64 x x)
x
(*.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64)))
(fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 x x #s(literal 0 binary64))
#s(literal 0 binary64)
(pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))
#s(literal -1 binary64)

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

localize137.0ms (1.6%)

Memory

-26.9MiB live, 92.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.09375	(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
accuracy	0.5668422255486473	(pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))
accuracy	31.121434880302342	(*.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64)))
accuracy	0	(*.f64 y y)
accuracy	0.00390625	(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
accuracy	0.16015625	(.f64 #s(literal 3 binary64) (.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.08203125	(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
accuracy	25.347446787370803	#s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	25.354840963812013	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
accuracy	0	(fma.f64 y y (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 #s(literal 2 binary64) y)
accuracy	0.0390625	(fma.f64 (.f64 #s(literal 2 binary64) y) y (fma.f64 y y (.f64 x x)))

Samples

118.0ms

256×

valid

Compiler

Compiled 201 to 25 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-add: 10.0ms (43.4% of total)

ival-mult: 10.0ms (43.4% of total)

ival-pow: 2.0ms (8.7% of total)

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

exact: 0.0ms (0% of total)

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

series19.0ms (0.2%)

Memory

3.5MiB live, 42.0MiB allocated

Counts

15 → 300

Calls

Call 1

Inputs
#s(alt (fma.f64 (.f64 #s(literal 2 binary64) y) y (fma.f64 y y (.f64 x x))) (patch (fma.f64 (.f64 #s(literal 2 binary64) y) y (fma.f64 y y (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) y) (patch (.f64 #s(literal 2 binary64) y) #<representation binary64>) () ())
#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 x x)) (patch #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y)) (patch (+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y)) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (patch #s(approx (+ (+ ( x x) (* y y)) (* y y)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())
#s(alt (fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y))) (patch (fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 3 binary64) (.f64 y y)) (patch (.f64 #s(literal 3 binary64) (.f64 y y)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))) (patch (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64)))) (patch (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 0 binary64)) (patch (fma.f64 x x #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (patch (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) #<representation binary64>) () ())
#s(alt (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())

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

Calls

6 calls:

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

simplify127.0ms (1.5%)

Memory

34.1MiB live, 188.5MiB allocated

Algorithm

1×	egg-herbie

Rules

8 654×	`lower-fma.f64`
8 654×	`lower-fma.f32`
3 526×	`lower-*.f64`
3 526×	`lower-*.f32`
1 858×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	2110
1	277	2094
2	741	2086
3	2633	2086
4	6526	2084
0	8136	1928

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

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

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

rewrite293.0ms (3.5%)

Memory

0.8MiB live, 357.5MiB allocated

Rules

7 680×	`lower-fma.f32`
7 670×	`lower-fma.f64`
4 834×	`lower-*.f32`
4 824×	`lower-*.f64`
4 608×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	156
0	43	153
1	191	108
2	1753	108
0	9071	105

Stop Event

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

Counts

15 → 1 163

Calls

Call 1

Inputs
(fma.f64 (.f64 #s(literal 2 binary64) y) y (fma.f64 y y (.f64 x x)))
(*.f64 #s(literal 2 binary64) y)
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
#s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x))
(*.f64 y y)
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
(.f64 #s(literal 3 binary64) (.f64 y y))
(*.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))))
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))

Outputs
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eval234.0ms (2.8%)

Memory: 18.8MiB live, 508.3MiB allocated
Compiler: Compiled 54 292 to 2 802 computations (94.8% saved)

prune57.0ms (0.7%)

Memory

-1.0MiB live, 171.1MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1 833	6	1 839
Fresh	3	2	5
Picked	4	1	5
Done	0	0	0
Total	1 840	9	1 849

Accuracy

100.0%

Counts

1 849 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	16.2%	(fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)))
	55.5%	(fma.f64 (.f64 #s(literal 2 binary64) y) y #s(approx (+ ( y y) (* x x)) (*.f64 y y)))
▶	99.9%	(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))
	80.3%	(fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x)))
▶	99.9%	(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
▶	44.0%	(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
	25.9%	(.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal -1 binary64)) (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (fma.f64 y y (.f64 x x))))
▶	55.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
✓	60.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

Compiler

Compiled 218 to 144 computations (33.9% saved)

simplify397.0ms (4.7%)

Memory

-16.0MiB live, 220.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 y #s(literal 6 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64)))
cost-diff	192	(+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))
cost-diff	320	(fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)))
cost-diff	0	(*.f64 y y)
cost-diff	0	(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
cost-diff	0	(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
cost-diff	0	(*.f64 #s(literal 3 binary64) y)
cost-diff	0	(.f64 (.f64 #s(literal 3 binary64) y) y)
cost-diff	0	(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
cost-diff	0	(*.f64 y y)
cost-diff	0	(.f64 (.f64 y y) #s(literal 3 binary64))
cost-diff	0	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
cost-diff	-128	(+.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 y y (*.f64 x x))
cost-diff	384	(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))

Rules

21 094×	`lower-fma.f32`
21 082×	`lower-fma.f64`
3 512×	`lower-+.f32`
3 508×	`lower-+.f64`
2 740×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	238
0	67	227
1	111	226
2	209	214
3	505	214
4	1334	214
5	3272	214
6	3619	214
7	4025	214
8	4285	214
9	4377	214
10	5208	214
11	5225	214
12	5227	214
13	5227	214
14	5270	214
15	5916	214
16	6188	214
17	6223	214
18	6223	214
19	6965	214
20	7167	214
21	7167	214
22	7167	214
23	7167	214
0	8050	213

Stop Event

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

Calls

Call 1

Inputs
(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))
y
(+.f64 y y)
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(.f64 (.f64 y y) #s(literal 3 binary64))
(*.f64 y y)
y
#s(literal 3 binary64)
(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
x
(.f64 (.f64 #s(literal 3 binary64) y) y)
(*.f64 #s(literal 3 binary64) y)
#s(literal 3 binary64)
y
(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
#s(literal 3 binary64)
(*.f64 y y)
y
(*.f64 x x)
x
(.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
(fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 x x #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)))
(*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64)))
#s(literal 2 binary64)
(pow.f64 y #s(literal 6 binary64))
y
#s(literal 6 binary64)
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64))))
#s(literal 1 binary64)
(+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))
#s(literal 0 binary64)
(pow.f64 y #s(literal 4 binary64))
#s(literal 4 binary64)
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x

Outputs
(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))
(fma.f64 (.f64 #s(literal 3 binary64) y) y (.f64 x x))
y
(+.f64 y y)
(*.f64 #s(literal 2 binary64) y)
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
(.f64 (.f64 y y) #s(literal 3 binary64))
(.f64 (.f64 #s(literal 3 binary64) y) y)
(*.f64 y y)
y
#s(literal 3 binary64)
(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
(fma.f64 (.f64 #s(literal 3 binary64) y) y (.f64 x x))
x
(.f64 (.f64 #s(literal 3 binary64) y) y)
(*.f64 #s(literal 3 binary64) y)
#s(literal 3 binary64)
y
(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
(.f64 (.f64 #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (.f64 y y))) (fma.f64 y y (.f64 x x))) (fma.f64 (.f64 #s(literal 3 binary64) y) y (.f64 x x)))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(fma.f64 (.f64 #s(literal 3 binary64) y) y (.f64 x x))
#s(literal 3 binary64)
(*.f64 y y)
y
(*.f64 x x)
x
(.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
(.f64 #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (.f64 y y))) (fma.f64 y y (.f64 x x)))
(fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 y y (*.f64 x x))
(fma.f64 x x #s(literal 0 binary64))
(*.f64 x x)
#s(literal 0 binary64)
#s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)))
(fma.f64 (/.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 6 binary64)) (fma.f64 y y (*.f64 x x)))
(*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64)))
(*.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 y #s(literal 6 binary64))
y
#s(literal 6 binary64)
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 4 binary64))
#s(literal 1 binary64)
(+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))
(pow.f64 y #s(literal 4 binary64))
#s(literal 0 binary64)
(pow.f64 y #s(literal 4 binary64))
#s(literal 4 binary64)
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x

localize140.0ms (1.6%)

Memory

20.4MiB live, 175.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64)))
accuracy	0.17633021161743684	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64))))
accuracy	47.34517781660706	(fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)))
accuracy	0.09375	(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
accuracy	0.3629925051781313	(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	28.461996100820237	#s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
accuracy	31.121434880302342	(.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
accuracy	0	(*.f64 #s(literal 3 binary64) y)
accuracy	0.00390625	(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
accuracy	0.14453125	(.f64 (.f64 #s(literal 3 binary64) y) y)
accuracy	0	(*.f64 y y)
accuracy	0.16015625	(.f64 (.f64 y y) #s(literal 3 binary64))
accuracy	28.450520951761835	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
accuracy	0	(fma.f64 y y (*.f64 x x))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.0390625	(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))

Samples

115.0ms

256×

valid

Compiler

Compiled 238 to 39 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 97.0ms

ival-mult: 66.0ms (68.3% of total)

ival-pow: 15.0ms (15.5% of total)

ival-add: 12.0ms (12.4% of total)

ival-div: 3.0ms (3.1% of total)

exact: 1.0ms (1% of total)

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

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

series24.0ms (0.3%)

Memory

-19.2MiB live, 55.9MiB allocated

Counts

21 → 360

Calls

Call 1

Inputs
#s(alt (fma.f64 y (+.f64 y y) (fma.f64 y y (.f64 x x))) (patch (fma.f64 y (+.f64 y y) (fma.f64 y y (.f64 x x))) #<representation binary64>) () ())
#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64))) (patch #s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 y y) #s(literal 3 binary64)) (patch (.f64 (.f64 y y) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())
#s(alt (fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y)) (patch (fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 3 binary64) y) y) (patch (.f64 (.f64 #s(literal 3 binary64) y) y) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 3 binary64) y) (patch (.f64 #s(literal 3 binary64) y) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 0 binary64)) (patch (fma.f64 x x #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (.f64 y y))))) (patch (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (patch (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x))) (patch (fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64))) (patch (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 y #s(literal 6 binary64)) (patch (pow.f64 y #s(literal 6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())
#s(alt #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (.f64 y y))) (patch #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 y y)) (patch (/.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	y	@	inf	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* y y) 3) (* y y) (+ (* x x) (* (* 3 y) y)) (* (* 3 y) y) (* 3 y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (+ (* (* 2 (pow y 6)) (/ 1 (+ 0 (pow y 4)))) (+ (* y y) (* x x))) (+ 0 (pow y 4)) (* 2 (pow y 6)) (pow y 6) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)) (/ 1 (+ 0 (pow y 4))))
3.0ms	y	@	-inf	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* y y) 3) (* y y) (+ (* x x) (* (* 3 y) y)) (* (* 3 y) y) (* 3 y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (+ (* (* 2 (pow y 6)) (/ 1 (+ 0 (pow y 4)))) (+ (* y y) (* x x))) (+ 0 (pow y 4)) (* 2 (pow y 6)) (pow y 6) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)) (/ 1 (+ 0 (pow y 4))))
2.0ms	y	@	0	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* y y) 3) (* y y) (+ (* x x) (* (* 3 y) y)) (* (* 3 y) y) (* 3 y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (+ (* (* 2 (pow y 6)) (/ 1 (+ 0 (pow y 4)))) (+ (* y y) (* x x))) (+ 0 (pow y 4)) (* 2 (pow y 6)) (pow y 6) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)) (/ 1 (+ 0 (pow y 4))))
1.0ms	x	@	-inf	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* y y) 3) (* y y) (+ (* x x) (* (* 3 y) y)) (* (* 3 y) y) (* 3 y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (+ (* (* 2 (pow y 6)) (/ 1 (+ 0 (pow y 4)))) (+ (* y y) (* x x))) (+ 0 (pow y 4)) (* 2 (pow y 6)) (pow y 6) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)) (/ 1 (+ 0 (pow y 4))))
1.0ms	x	@	inf	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* y y) 3) (* y y) (+ (* x x) (* (* 3 y) y)) (* (* 3 y) y) (* 3 y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (+ (* (* 2 (pow y 6)) (/ 1 (+ 0 (pow y 4)))) (+ (* y y) (* x x))) (+ 0 (pow y 4)) (* 2 (pow y 6)) (pow y 6) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)) (/ 1 (+ 0 (pow y 4))))

simplify296.0ms (3.5%)

Memory

-25.3MiB live, 236.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 632×	`lower-fma.f64`
8 632×	`lower-fma.f32`
3 362×	`lower-*.f64`
3 362×	`lower-*.f32`
1 866×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	2272
1	266	2256
2	712	2248
3	2495	2248
4	6311	2246
0	8133	2108

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

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

rewrite333.0ms (3.9%)

Memory

7.1MiB live, 361.7MiB allocated

Rules

8 802×	`lower-fma.f32`
8 794×	`lower-fma.f64`
3 476×	`lower-/.f32`
3 472×	`lower-/.f64`
3 096×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	194
0	67	177
1	284	145
2	2602	145
0	8895	145

Stop Event

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

Counts

21 → 1 582

Calls

Call 1

Inputs
(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
(+.f64 y y)
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(.f64 (.f64 y y) #s(literal 3 binary64))
(*.f64 y y)
(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
(.f64 (.f64 #s(literal 3 binary64) y) y)
(*.f64 #s(literal 3 binary64) y)
(fma.f64 x x #s(literal 0 binary64))
(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)))
(+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))
(*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64)))
(pow.f64 y #s(literal 6 binary64))
(.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
#s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64))))

Outputs
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eval714.0ms (8.4%)

Memory: 46.6MiB live, 616.4MiB allocated
Compiler: Compiled 71 523 to 4 264 computations (94% saved)

prune182.0ms (2.1%)

Memory

-40.9MiB live, 156.8MiB allocated

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	2 662	6	2 668
Fresh	3	0	3
Picked	2	3	5
Done	0	1	1
Total	2 667	10	2 677

Accuracy

100.0%

Counts

2 677 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	77.1%	(fma.f64 y (+.f64 y y) (fma.f64 y y (fma.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 x y)) (/.f64 (fma.f64 y y (.f64 x x)) (-.f64 x y)) (*.f64 y y))))
✓	99.9%	(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))
▶	55.5%	(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
▶	81.2%	(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))
▶	80.3%	(fma.f64 y y (*.f64 x x))
✓	99.9%	(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
▶	39.0%	(.f64 #s(approx (+ ( 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
✓	55.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
▶	55.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
✓	60.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

Compiler

Compiled 195 to 120 computations (38.5% saved)

simplify11.0ms (0.1%)

Memory

17.6MiB live, 17.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 y y) #s(literal 3 binary64))
cost-diff	0	#s(approx (+ (* 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
cost-diff	-128	(+.f64 y y)
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (* y y) (* x x)) (*.f64 y y))
cost-diff	0	(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 y y (*.f64 x x))
cost-diff	0	(*.f64 #s(literal 3 binary64) y)
cost-diff	0	(.f64 (.f64 #s(literal 3 binary64) y) y)
cost-diff	0	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
cost-diff	-128	(+.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* y y) (* x x)) (*.f64 x x))
cost-diff	0	(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))

Rules

260×	`lower-fma.f32`
252×	`lower-fma.f64`
164×	`lower-*.f32`
160×	`lower-+.f32`
158×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	228
0	53	221
1	88	221
2	156	215
3	275	215
4	390	215
5	393	215
0	393	212

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))
y
(+.f64 y y)
#s(approx (+ (* y y) (* x x)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
(.f64 (.f64 #s(literal 3 binary64) y) y)
(*.f64 #s(literal 3 binary64) y)
#s(literal 3 binary64)
y
(fma.f64 y y (*.f64 x x))
y
(*.f64 x x)
x
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
y
(+.f64 y y)
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
(*.f64 y y)
(.f64 #s(approx (+ ( 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
#s(approx (+ (* 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(.f64 (.f64 y y) #s(literal 3 binary64))
(*.f64 y y)
y
#s(literal 3 binary64)
(.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
(fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 x x #s(literal 0 binary64))
x
#s(literal 0 binary64)
#s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)

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

localize126.0ms (1.5%)

Memory

-20.4MiB live, 98.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.3629925051781313	(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	28.450520951761835	#s(approx (+ (* 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64)))
accuracy	28.461996100820237	#s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
accuracy	31.121434880302342	(.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 y y)
accuracy	0.0390625	(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
accuracy	28.458277149058603	#s(approx (+ (* y y) (* x x)) (*.f64 y y))
accuracy	0	(fma.f64 y y (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 #s(literal 3 binary64) y)
accuracy	0.14453125	(.f64 (.f64 #s(literal 3 binary64) y) y)
accuracy	28.450520951761835	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.0390625	(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))
accuracy	25.33478792185533	#s(approx (+ (* y y) (* x x)) (*.f64 x x))

Samples

52.0ms

256×

valid

Compiler

Compiled 198 to 28 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-add: 21.0ms (55.8% of total)

ival-mult: 12.0ms (31.9% of total)

ival-div: 2.0ms (5.3% of total)

ival-pow: 2.0ms (5.3% of total)

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

exact: 0.0ms (0% of total)

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

series16.0ms (0.2%)

Memory

21.1MiB live, 21.1MiB allocated

Counts

18 → 336

Calls

Call 1

Inputs
#s(alt (fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (.f64 x x))) (patch (fma.f64 y (+.f64 y y) #s(approx (+ ( y y) (* x x)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* y y) (* x x)) (.f64 x x)) (patch #s(approx (+ ( y y) (* x x)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y)) (patch #s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 3 binary64) y) y) (patch (.f64 (.f64 #s(literal 3 binary64) y) y) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 3 binary64) y) (patch (.f64 #s(literal 3 binary64) y) #<representation binary64>) () ())
#s(alt (fma.f64 y y (.f64 x x)) (patch (fma.f64 y y (.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (.f64 y y))) (patch (fma.f64 y (+.f64 y y) #s(approx (+ ( y y) (* x x)) (*.f64 y y))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* y y) (* x x)) (.f64 y y)) (patch #s(approx (+ ( y y) (* x x)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 0 binary64)) (patch (fma.f64 x x #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (.f64 y y))))) (patch (.f64 #s(approx (+ (* 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (patch #s(approx (+ (* 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 y y) #s(literal 3 binary64)) (patch (.f64 (.f64 y y) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())
#s(alt #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (.f64 y y))) (patch #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 y y)) (patch (/.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* 3 y) y) (* 3 y) (+ (* y y) (* x x)) (+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* y y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (* (* y y) 3) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)))
1.0ms	y	@	inf	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* 3 y) y) (* 3 y) (+ (* y y) (* x x)) (+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* y y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (* (* y y) 3) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)))
1.0ms	y	@	0	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* 3 y) y) (* 3 y) (+ (* y y) (* x x)) (+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* y y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (* (* y y) 3) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)))
1.0ms	x	@	-inf	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* 3 y) y) (* 3 y) (+ (* y y) (* x x)) (+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* y y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (* (* y y) 3) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)))
1.0ms	x	@	inf	((+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x) (+ y y) (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (* (* 3 y) y) (* 3 y) (+ (* y y) (* x x)) (+ (* y (+ y y)) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* y y) (+ (* x x) 0) (* (+ (* 3 (* y y)) (* x x)) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1))) (+ (* 3 (* y y)) (* x x)) (* (* y y) 3) (* (+ (* y y) (+ (* x x) 0)) (pow (+ (* y y) (+ (* x x) 0)) -1)) (pow (+ (* y y) (+ (* x x) 0)) -1) (/ 1 (* y y)))

simplify260.0ms (3.1%)

Memory

-22.8MiB live, 85.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8 632×	`lower-fma.f64`
8 632×	`lower-fma.f32`
3 358×	`lower-*.f64`
3 358×	`lower-*.f32`
1 866×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	2182
1	264	2166
2	710	2158
3	2502	2158
4	6294	2156
0	8113	2000

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

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

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

rewrite248.0ms (2.9%)

Memory

16.4MiB live, 295.4MiB allocated

Rules

5 570×	`lower-fma.f32`
5 566×	`lower-fma.f64`
4 954×	`lower-*.f32`
4 940×	`lower-*.f64`
4 294×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	200
0	53	191
1	204	169
2	1790	169
0	8820	167

Stop Event

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

Counts

18 → 1 100

Calls

Call 1

Inputs
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))
#s(approx (+ (* y y) (* x x)) (*.f64 x x))
(*.f64 x x)
(+.f64 y y)
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
(.f64 (.f64 #s(literal 3 binary64) y) y)
(*.f64 #s(literal 3 binary64) y)
(fma.f64 y y (*.f64 x x))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
(*.f64 y y)
(fma.f64 x x #s(literal 0 binary64))
(.f64 #s(approx (+ ( 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
#s(approx (+ (* 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(.f64 (.f64 y y) #s(literal 3 binary64))
(.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
#s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))

Outputs
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eval244.0ms (2.9%)

Memory: 9.3MiB live, 505.6MiB allocated
Compiler: Compiled 58 290 to 3 963 computations (93.2% saved)

prune130.0ms (1.5%)

Memory

17.9MiB live, 139.6MiB allocated

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	1 814	2	1 816
Fresh	0	1	1
Picked	1	4	5
Done	0	4	4
Total	1 815	11	1 826

Accuracy

100.0%

Counts

1 826 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	77.1%	(fma.f64 y (+.f64 y y) (fma.f64 y y (fma.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 x y)) (/.f64 (fma.f64 y y (.f64 x x)) (-.f64 x y)) (*.f64 y y))))
✓	99.9%	(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))
✓	55.5%	(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
✓	81.2%	(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))
✓	80.3%	(fma.f64 y y (*.f64 x x))
✓	99.9%	(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
	39.0%	(.f64 #s(approx (+ ( 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (.f64 (fma.f64 y y (.f64 x x)) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
✓	55.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
✓	55.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
✓	60.4%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
	36.5%	#s(approx (+ (* y y) (* x x)) (*.f64 y y))

Compiler

Compiled 449 to 147 computations (67.3% saved)

regimes225.0ms (2.7%)

Memory

17.2MiB live, 56.0MiB allocated

Counts

25 → 1

Calls

Call 1

Inputs
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
(fma.f64 (.f64 #s(literal 2 binary64) y) y #s(approx (+ ( y y) (* x x)) (*.f64 y y)))
(fma.f64 y (fma.f64 #s(literal 2 binary64) y y) (*.f64 x x))
(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))
(fma.f64 (.f64 #s(literal 2 binary64) y) y (fma.f64 y y (.f64 x x)))
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
(.f64 #s(approx (+ ( 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (.f64 (fma.f64 y y (.f64 x x)) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
(.f64 #s(approx (+ ( 3 (* y y)) (* x x)) (.f64 (.f64 y y) #s(literal 3 binary64))) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ ( y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(approx (pow (+ (* y y) (+ (* x x) 0)) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))
(fma.f64 y (+.f64 y y) (fma.f64 y y (fma.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 x y)) (/.f64 (fma.f64 y y (.f64 x x)) (-.f64 x y)) (*.f64 y y))))
(.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal -1 binary64)) (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (fma.f64 y y (.f64 x x))))
(.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (pow.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64))))
(fma.f64 (.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)))
(+.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 x x #s(literal 0 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))

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

Calls

5 calls:

196.0ms	(*.f64 x x)
7.0ms	y
7.0ms	x
7.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
7.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
99.9%	1	`(*.f64 x x)`
99.9%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes189.0ms (2.2%)

Memory

-25.1MiB live, 42.6MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
(fma.f64 x x (.f64 (.f64 #s(literal 3 binary64) y) y))
(fma.f64 (.f64 #s(literal 2 binary64) y) y #s(approx (+ ( y y) (* x x)) (*.f64 y y)))
(fma.f64 y (fma.f64 #s(literal 2 binary64) y y) (*.f64 x x))

Outputs
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))

Calls

5 calls:

171.0ms	(*.f64 y y)
5.0ms	x
5.0ms	y
4.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
4.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
99.9%	1	`(*.f64 x x)`
99.9%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes209.0ms (2.5%)

Memory

-26.3MiB live, 52.2MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))

Outputs
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))

Calls

5 calls:

192.0ms	(*.f64 y y)
5.0ms	x
4.0ms	y
3.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
99.9%	1	`(*.f64 x x)`
99.9%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes18.0ms (0.2%)

Memory

8.7MiB live, 47.5MiB allocated

Counts

9 → 2

Calls

Call 1

Inputs
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 y y)))

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
91.7%	2	`x`
83.8%	2	`y`
81.2%	1	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
91.7%	2	`(*.f64 x x)`
83.8%	2	`(*.f64 y y)`

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes6.0ms (0.1%)

Memory

16.0MiB live, 16.0MiB allocated

Counts

8 → 2

Calls

Call 1

Inputs
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))

Outputs
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x)))

Calls

2 calls:

3.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
91.7%	2	`x`
91.7%	2	`(*.f64 x x)`

Compiler

Compiled 4 to 5 computations (-25% saved)

regimes8.0ms (0.1%)

Memory

-26.8MiB live, 13.8MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(+.f64 #s(approx (+ (+ (* x x) (* y y)) (* y y)) (.f64 x x)) (.f64 y y))

Outputs
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x)))

Calls

2 calls:

4.0ms	(*.f64 x x)
3.0ms	x

Results

Accuracy	Segments	Branch
91.2%	2	`x`
91.2%	2	`(*.f64 x x)`

Compiler

Compiled 4 to 5 computations (-25% saved)

regimes11.0ms (0.1%)

Memory

27.4MiB live, 27.4MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))

Outputs
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
60.4%	1	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
82.7%	2	`y`
82.7%	2	`(*.f64 y y)`
82.6%	2	`x`
82.6%	2	`(*.f64 x x)`

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes7.0ms (0.1%)

Memory

-20.5MiB live, 18.6MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
68.9%	2	`x`
68.9%	2	`(*.f64 x x)`
77.3%	2	`y`
77.3%	2	`(*.f64 y y)`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes6.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
36.5%	1	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
36.5%	1	`x`
36.5%	1	`(*.f64 x x)`
36.5%	1	`y`
36.5%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 17 computations (26.1% saved)

bsearch12.0ms (0.1%)

Memory

-2.5MiB live, 36.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	1.1337074553368748e-295	2.8942926685291536e-292

Samples

5.0ms

128×

valid

Compiler

Compiled 146 to 116 computations (20.5% saved)

Precisions

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

ival-add: 1.0ms (39.6% of total)

ival-mult: 1.0ms (39.6% of total)

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

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

bsearch1.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.1337074553368748e-295	2.8942926685291536e-292

Compiler

Compiled 122 to 116 computations (4.9% saved)

bsearch1.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.1337074553368748e-295	2.8942926685291536e-292

Compiler

Compiled 106 to 108 computations (-1.9% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	52793266801.61275	6.475818321668593e+20

Compiler

Compiled 14 to 12 computations (14.3% saved)

bsearch15.0ms (0.2%)

Memory

-6.0MiB live, 33.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.1379064209980048e+293	2.9754387068148715e+296

Samples

5.0ms	105×	0	valid
2.0ms	10×	3	valid
1.0ms	6×	4	valid
1.0ms	4×	2	valid
0.0ms	3×	1	valid

Compiler

Compiled 62 to 84 computations (-35.5% saved)

Precisions

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

ival-add: 2.0ms (41.7% of total)

adjust: 1.0ms (20.9% of total)

ival-mult: 1.0ms (20.9% of total)

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

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

simplify26.0ms (0.3%)

Memory

-8.3MiB live, 72.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	246
1	43	246

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(if (<=.f64 (.f64 x x) #s(literal 5572848718073179/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216 binary64)) (fma.f64 y (+.f64 y y) #s(approx (+ ( y y) (* x x)) (.f64 y y))) (fma.f64 y (+.f64 y y) #s(approx (+ ( y y) (* x x)) (*.f64 x x))))
(if (<=.f64 (.f64 x x) #s(literal 5572848718073179/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64))) (fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x))))
(if (<=.f64 (.f64 x x) #s(literal 5572848718073179/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64))) (fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x))))
(if (<=.f64 (.f64 y y) #s(literal 100000000000 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 x x)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y)))
(if (<=.f64 (.f64 y y) #s(literal 24999999999999999533716943015575103944538901799551453325246209301117119708198752099710744316957136451843406742510056453931925734217612339775038822400420123747218018059850511710497240661140849146219719878711450012256896302751036161227459906532977089715608225651061819811426276325353451459612508160 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 x x)) #s(approx (+ ( y y) (* x x)) (*.f64 y y)))
#s(approx (+ (* y y) (* x x)) (*.f64 y y))

Outputs
(fma.f64 y (+.f64 y y) (fma.f64 y y (*.f64 x x)))
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
(fma.f64 x x (.f64 (.f64 y y) #s(literal 3 binary64)))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(if (<=.f64 (.f64 x x) #s(literal 5572848718073179/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216 binary64)) (fma.f64 y (+.f64 y y) #s(approx (+ ( y y) (* x x)) (.f64 y y))) (fma.f64 y (+.f64 y y) #s(approx (+ ( y y) (* x x)) (*.f64 x x))))
(if (<=.f64 (.f64 x x) #s(literal 5572848718073179/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64))) (fma.f64 y (+.f64 y y) #s(approx (+ (* y y) (* x x)) (*.f64 x x))))
(if (<=.f64 (.f64 x x) #s(literal 5572848718073179/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64))) (fma.f64 y y #s(approx (+ (+ (* x x) (* y y)) (* y y)) (*.f64 x x))))
(if (<=.f64 (.f64 y y) #s(literal 100000000000 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 x x)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 #s(literal 3 binary64) y) y)))
(if (<=.f64 (.f64 y y) #s(literal 24999999999999999533716943015575103944538901799551453325246209301117119708198752099710744316957136451843406742510056453931925734217612339775038822400420123747218018059850511710497240661140849146219719878711450012256896302751036161227459906532977089715608225651061819811426276325353451459612508160 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 x x)) #s(approx (+ ( y y) (* x x)) (*.f64 y y)))
#s(approx (+ (* y y) (* x x)) (*.f64 y y))

soundness1.3s (15.9%)

Memory

-23.1MiB live, 1 028.0MiB allocated

Rules

10 540×	`lower-fma.f64`
10 540×	`lower-fma.f32`
9 354×	`lower-fma.f64`
9 354×	`lower-fma.f32`
8 802×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	588
1	86	588
2	217	588
3	853	588
4	2013	588
5	2661	588
6	4205	588
7	5672	588
8	6662	588
9	7939	588
0	8060	534
0	102	2182
1	264	2166
2	710	2158
3	2502	2158
4	6294	2156
0	8113	2000
0	27	156
0	43	153
1	191	108
2	1753	108
0	9071	105
0	7	39
0	12	39
1	54	35
2	517	29
3	7592	29
0	8199	26
0	40	194
0	67	177
1	284	145
2	2602	145
0	8895	145
0	103	2272
1	266	2256
2	712	2248
3	2495	2248
4	6311	2246
0	8133	2108

Stop Event

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

Compiler

Compiled 644 to 250 computations (61.2% saved)

preprocess61.0ms (0.7%)

Memory

0.8MiB live, 153.9MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 390 to 142 computations (63.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.2s (14.3%)

explain191.0ms (2.3%)

preprocess44.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize18.0ms (0.2%)

series6.0ms (0.1%)

simplify363.0ms (4.3%)

rewrite209.0ms (2.5%)

eval52.0ms (0.6%)

prune15.0ms (0.2%)

simplify233.0ms (2.7%)

localize137.0ms (1.6%)

series19.0ms (0.2%)

simplify127.0ms (1.5%)

rewrite293.0ms (3.5%)

eval234.0ms (2.8%)

prune57.0ms (0.7%)

simplify397.0ms (4.7%)

localize140.0ms (1.6%)

series24.0ms (0.3%)

simplify296.0ms (3.5%)

rewrite333.0ms (3.9%)

eval714.0ms (8.4%)

prune182.0ms (2.1%)

simplify11.0ms (0.1%)

localize126.0ms (1.5%)

series16.0ms (0.2%)

simplify260.0ms (3.1%)

rewrite248.0ms (2.9%)

eval244.0ms (2.9%)

prune130.0ms (1.5%)

regimes225.0ms (2.7%)

regimes189.0ms (2.2%)

regimes209.0ms (2.5%)

regimes18.0ms (0.2%)

regimes6.0ms (0.1%)

regimes8.0ms (0.1%)

regimes11.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch12.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch15.0ms (0.2%)

simplify26.0ms (0.3%)

soundness1.3s (15.9%)

preprocess61.0ms (0.7%)

end0.0ms (0%)

Profiling