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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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)

sample764.0ms (21.7%)

Memory

15.4MiB live, 1 368.3MiB allocated

Samples

533.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 341.0ms

ival-mult: 221.0ms (64.8% of total)

ival-add: 111.0ms (32.5% of total)

ival-true: 5.0ms (1.5% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain104.0ms (3%)

Memory

11.8MiB live, 243.8MiB 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

29.0ms

512×

valid

Compiler

Compiled 103 to 25 computations (75.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 8.0ms (50.5% of total)

ival-add: 7.0ms (44.2% of total)

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

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

preprocess42.0ms (1.2%)

Memory

-4.0MiB live, 49.9MiB 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 x x (.f64 (.f64 y y) #s(literal 3 binary64)))

Symmetry

(abs y)

(abs x)

Compiler

Compiled 17 to 7 computations (58.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 17 to 7 computations (58.8% saved)

simplify7.0ms (0.2%)

Memory

-23.5MiB live, 15.7MiB 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	320	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
cost-diff	384	(+.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 x x (.f64 (.f64 y y) #s(literal 3 binary64)))
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
(fma.f64 y (+.f64 y y) (*.f64 x x))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y

localize21.0ms (0.6%)

Memory

17.3MiB live, 56.1MiB 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	0.0546875	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Samples

14.0ms

256×

valid

Compiler

Compiled 43 to 9 computations (79.1% saved)

Precisions

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

ival-add: 3.0ms (45.7% of total)

ival-mult: 3.0ms (45.7% of total)

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

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

series5.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB 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 (+ (* 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 (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 (.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 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 (* 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 (* 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 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 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 (.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 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 (* 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 (* 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 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 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 (.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 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 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 (.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 x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#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 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 (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>) () ())) ())

Calls

24 calls:

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

simplify333.0ms (9.5%)

Memory

-20.7MiB live, 331.3MiB 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	660
1	86	588
2	215	588
3	851	588
4	2011	588
5	2650	588
6	4169	588
7	5649	588
8	6638	588
9	7914	588
0	8035	534

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

rewrite336.0ms (9.5%)

Memory

-4.4MiB live, 479.9MiB 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
(+.f64 (.f64 x x) (.f64 #s(literal 3 binary64) (*.f64 y y)))
(+.f64 (.f64 y y) (fma.f64 y (+.f64 y y) (.f64 x x)))
(+.f64 (fma.f64 x x (.f64 y y)) (.f64 y (+.f64 y y)))
(+.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (.f64 y y))
(+.f64 (.f64 y (+.f64 y y)) (fma.f64 x x (.f64 y y)))
(+.f64 (/.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (+.f64 y y) (.f64 x x))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 y y) (.f64 y y)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))))
(+.f64 (.f64 #s(literal 3 binary64) (.f64 y y)) (*.f64 x x))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 x y) (-.f64 x y))) (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))) (*.f64 y (+.f64 y y))))
(-.f64 (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (fma.f64 x x #s(literal 0 binary64))) (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 y y)) (fma.f64 x x #s(literal 0 binary64))) (*.f64 y y)))
(-.f64 (/.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (+.f64 y y) (.f64 x x))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 y y) (.f64 y y)) (neg.f64 (fma.f64 x x (.f64 y y)))) (/.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (+.f64 y y) (.f64 x x))) (neg.f64 (fma.f64 x x (.f64 y y)))))
(-.f64 (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (-.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 y y))) (/.f64 (.f64 y (+.f64 y y)) (-.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 y y))))
(-.f64 (fma.f64 y y (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (fma.f64 x x #s(literal 0 binary64)))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) (fma.f64 x x #s(literal 0 binary64))))
(-.f64 (fma.f64 y (+.f64 y y) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 x y) (-.f64 x y)))) (/.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))))
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
(fma.f64 y y (fma.f64 y (+.f64 y y) (*.f64 x x)))
(fma.f64 y (+.f64 y y) (fma.f64 x x (*.f64 y y)))
(fma.f64 y (+.f64 (+.f64 y y) y) (*.f64 x x))
(fma.f64 y (+.f64 y (+.f64 y y)) (*.f64 x x))
(fma.f64 y (.f64 (+.f64 y y) (.f64 y (+.f64 y y))) (fma.f64 x x (*.f64 y y)))
(fma.f64 (.f64 y y) #s(literal 2 binary64) (fma.f64 x x (.f64 y y)))
(fma.f64 (.f64 y y) (.f64 (+.f64 y y) (+.f64 y y)) (fma.f64 x x (*.f64 y y)))
(fma.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 (+.f64 x y) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x y) (-.f64 x y)))) (*.f64 y (+.f64 y y)))
(fma.f64 (fma.f64 x x (.f64 y y)) (/.f64 (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (+.f64 x y) (-.f64 x y))) (.f64 y (+.f64 y y)))
(fma.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (.f64 (fma.f64 x x #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))) (*.f64 y y))
(fma.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (/.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 y y) (*.f64 y y)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))))
(fma.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64))) (.f64 y y))
(fma.f64 #s(literal 2 binary64) (.f64 y y) (fma.f64 x x (.f64 y y)))
(fma.f64 #s(literal 2 binary64) (.f64 (.f64 y y) (.f64 y (+.f64 y y))) (fma.f64 x x (.f64 y y)))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(fma.f64 (fma.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (.f64 y y) (.f64 y y)))) (*.f64 y (+.f64 y y)))
(fma.f64 (fma.f64 (.f64 x x) (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (.f64 y y) (.f64 y y))) (.f64 (fma.f64 x x (.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (.f64 y y) (.f64 y y))))) (*.f64 y (+.f64 y y)))
(fma.f64 (fma.f64 (.f64 x x) (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (fma.f64 x x (.f64 y y)) (fma.f64 (.f64 x x) (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (.f64 y y) (.f64 y y)))) (.f64 y (+.f64 y y)))
(fma.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64))))) (*.f64 y y))
(fma.f64 (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64)))) (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64)))))) (*.f64 y y))
(fma.f64 (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64)))) (/.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64))))) (.f64 y y))
(fma.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (+.f64 y y) (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 y y) (.f64 y y)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))))
(fma.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x y) (-.f64 x y))) (*.f64 y (+.f64 y y)))
(fma.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))) (*.f64 y y))
(fma.f64 (.f64 y (+.f64 y y)) (.f64 y (+.f64 y y)) (fma.f64 x x (*.f64 y y)))
(fma.f64 #s(literal 4 binary64) (.f64 (.f64 y y) (.f64 y y)) (fma.f64 x x (.f64 y y)))
(fma.f64 (neg.f64 (fma.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (.f64 y y) (.f64 y y))))) (*.f64 y (+.f64 y y)))
(fma.f64 (neg.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y)))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (+.f64 x y) (-.f64 x y)))) (*.f64 y (+.f64 y y)))
(fma.f64 (neg.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64)))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64)))))) (*.f64 y y))
(fma.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 x (neg.f64 x) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) #s(literal 0 binary64))) (*.f64 y y))
(fma.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y (+.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y y) (.f64 y y) #s(literal 0 binary64))) (fma.f64 x x (.f64 y y)))
(fma.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 y (+.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 y (+.f64 y y))) (.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
(fma.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y y)) (.f64 y (+.f64 y y)))
(fma.f64 #s(literal 1 binary64) (fma.f64 y (+.f64 y y) (.f64 x x)) (.f64 y y))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (.f64 y y) (.f64 y y)))) (fma.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (*.f64 y (+.f64 y y)))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x y) (-.f64 x y))) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))) (*.f64 y (+.f64 y y)))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64))))) (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64))))) (*.f64 y y))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))) (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 x x #s(literal 0 binary64))) (*.f64 y y))
(fma.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 y x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x y) (-.f64 y x))) (*.f64 y (+.f64 y y)))
(fma.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (+.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (*.f64 y y))
(fma.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (neg.f64 (.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 x x))) (*.f64 y y))
(fma.f64 (.f64 y (.f64 y y)) (pow.f64 (+.f64 y y) #s(literal 3 binary64)) (fma.f64 x x (*.f64 y y)))
(fma.f64 (+.f64 y y) y (fma.f64 x x (*.f64 y y)))
(fma.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) (fma.f64 x x (*.f64 y y)))
(fma.f64 #s(literal 8 binary64) (.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y))) (fma.f64 x x (.f64 y y)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (.f64 #s(literal 3 binary64) (.f64 y y)))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (fma.f64 y (+.f64 y y) (*.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x (.f64 y y)) (+.f64 x y)) (+.f64 x y) (.f64 y (+.f64 y y)))
(fma.f64 (pow.f64 (.f64 y (+.f64 y y)) #s(literal 3/2 binary64)) (pow.f64 (.f64 y (+.f64 y y)) #s(literal 3/2 binary64)) (fma.f64 x x (*.f64 y y)))
(fma.f64 (.f64 (.f64 y (+.f64 y y)) y) (+.f64 y y) (fma.f64 x x (*.f64 y y)))
(fma.f64 (.f64 (.f64 y (+.f64 y y)) #s(literal 2 binary64)) (.f64 y y) (fma.f64 x x (.f64 y y)))
(fma.f64 (/.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 x x #s(literal 0 binary64))) (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))) (fma.f64 y (+.f64 y y) (.f64 x x)) (.f64 y y))
(fma.f64 (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y)))) (fma.f64 x x (.f64 y y)) (.f64 y (+.f64 y y)))
(fma.f64 (/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (fma.f64 (.f64 (.f64 y y) (.f64 (+.f64 x y) (-.f64 y x))) (.f64 (.f64 (.f64 y y) (.f64 (+.f64 x y) (-.f64 y x))) (.f64 (.f64 y y) (.f64 (+.f64 x y) (-.f64 y x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (fma.f64 (.f64 (.f64 y y) (.f64 (+.f64 x y) (-.f64 y x))) (-.f64 (.f64 (.f64 y y) (.f64 (+.f64 x y) (-.f64 y x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (*.f64 y (+.f64 y y)))
(fma.f64 (/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (fma.f64 (.f64 x x) (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (.f64 y y) (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (+.f64 x y) (-.f64 y x)))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (+.f64 x y) (-.f64 y x)))) (.f64 y (+.f64 y y)))
(fma.f64 (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))) (.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 y y) (fma.f64 x x (.f64 y y)))) (*.f64 y (+.f64 y y)))
(fma.f64 (/.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (+.f64 y y) (.f64 x x))) (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))) (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (neg.f64 (/.f64 (.f64 (.f64 y y) (*.f64 y y)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))))
(fma.f64 (/.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (+.f64 y y) (.f64 x x))) (.f64 (fma.f64 (.f64 y y) (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (+.f64 y y) (.f64 x x)))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))) (fma.f64 (.f64 y y) (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (+.f64 y y) (.f64 x x)))) (neg.f64 (/.f64 (.f64 (.f64 y y) (*.f64 y y)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))))
(fma.f64 (/.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64))))) (fma.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))))) (.f64 (.f64 (.f64 x (.f64 x y)) (neg.f64 y)) (.f64 (.f64 (.f64 x (.f64 x y)) (neg.f64 y)) (.f64 (.f64 x (.f64 x y)) (neg.f64 y)))))) (fma.f64 (.f64 (.f64 x (.f64 x y)) (neg.f64 y)) (-.f64 (.f64 (.f64 x (.f64 x y)) (neg.f64 y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y)))) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y)))))) (.f64 y y))
(fma.f64 (/.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64))))) (.f64 (fma.f64 y (.f64 y (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x #s(literal 0 binary64)))) (fma.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 x x #s(literal 0 binary64)) (.f64 (.f64 y y) (fma.f64 x x (.f64 y y)))))) (fma.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 x x #s(literal 0 binary64)) (.f64 (.f64 y y) (fma.f64 x x (.f64 y y)))) (.f64 y y))
(fma.f64 (/.f64 (.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 x x #s(literal 0 binary64))) (.f64 (fma.f64 (.f64 y y) (fma.f64 y (+.f64 y y) (.f64 x x)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y)))) (fma.f64 x x #s(literal 0 binary64)))) (fma.f64 (.f64 y y) (fma.f64 y (+.f64 y y) (.f64 x x)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y)))) (.f64 y y))
(neg.f64 (/.f64 (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (fma.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (.f64 (.f64 y y) (.f64 y y)))) (neg.f64 (fma.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (.f64 (.f64 y y) (*.f64 y y))))))
(neg.f64 (/.f64 (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (*.f64 x x)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))) (neg.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))))
(neg.f64 (/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x)) (fma.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (.f64 (.f64 y y) (.f64 y y))))) (fma.f64 (fma.f64 y (+.f64 y y) (.f64 x x)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (.f64 (.f64 y y) (*.f64 y y)))))
(neg.f64 (/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 3 binary64) (.f64 y y) (*.f64 x x)) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))))
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(.f64 (/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (fma.f64 (.f64 x x) (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (.f64 y y) (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (+.f64 x y) (-.f64 y x)))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (+.f64 x y) (-.f64 y x)))))
(.f64 (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))) (.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 y y) (fma.f64 x x (*.f64 y y)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)))
(pow.f64 y #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(*.f64 y y)
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))

eval60.0ms (1.7%)

Memory: 18.4MiB live, 129.5MiB allocated
Compiler: Compiled 16 883 to 1 066 computations (93.7% saved)

prune59.0ms (1.7%)

Memory

19.1MiB live, 146.8MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	465	4	469
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	466	4	470

Accuracy

100.0%

Counts

470 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (+.f64 y y) y (fma.f64 x x (*.f64 y y)))
▶	99.9%	(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
▶	58.9%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 y (.f64 y #s(literal 3 binary64))))
▶	58.9%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

Compiler

Compiled 37 to 20 computations (45.9% saved)

simplify7.0ms (0.2%)

Memory

-25.5MiB live, 13.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(fma.f64 x x (*.f64 y y))
cost-diff	0	(+.f64 y y)
cost-diff	256	(fma.f64 (+.f64 y y) y (fma.f64 x x (*.f64 y y)))
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 #s(literal 3 binary64))
cost-diff	0	(.f64 y (.f64 y #s(literal 3 binary64)))
cost-diff	0	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 y (.f64 y #s(literal 3 binary64))))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	96
0	30	105
1	48	93
2	57	81
3	64	81
4	66	81
0	66	81

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize67.0ms (1.9%)

Memory

-17.5MiB live, 109.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x (*.f64 y y))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 y y)
accuracy	0.01171875	(fma.f64 (+.f64 y y) y (fma.f64 x x (*.f64 y y)))
accuracy	0	(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
accuracy	0	(*.f64 y y)
accuracy	0.13671875	(.f64 #s(literal 3 binary64) (.f64 y y))
accuracy	0	(*.f64 y #s(literal 3 binary64))
accuracy	0.11328125	(.f64 y (.f64 y #s(literal 3 binary64)))
accuracy	26.22130469190846	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 y (.f64 y #s(literal 3 binary64))))
accuracy	0	(*.f64 x x)
accuracy	26.30707322493601	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

Samples

50.0ms

256×

valid

Compiler

Compiled 94 to 17 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-add: 26.0ms (74.8% of total)

ival-mult: 9.0ms (25.9% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

28.0MiB live, 28.0MiB allocated

Counts

11 → 192

Calls

Call 1

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

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

Calls

48 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(+ y y)
0.0ms	y	@	inf	(* y (* y 3))
0.0ms	y	@	inf	(+ y y)
0.0ms	y	@	-inf	(* y 3)
0.0ms	y	@	0	(* y (* y 3))

simplify285.0ms (8.1%)

Memory

-6.5MiB live, 340.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 684×	`lower-fma.f64`
13 684×	`lower-fma.f32`
6 062×	`lower-*.f64`
6 062×	`lower-*.f32`
1 670×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	1440
1	84	1152
2	208	1152
3	808	1152
4	2341	1152
5	3252	1152
6	4808	1152
7	6213	1152
8	7051	1152
0	8177	1062

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

rewrite75.0ms (2.1%)

Memory

-7.3MiB live, 112.6MiB allocated

Rules

782×	`lower-fma.f32`
776×	`lower-fma.f64`
504×	`lower-*.f32`
494×	`lower-*.f64`
336×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	85
0	30	88
1	109	76
0	953	73

Stop Event

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

Counts

11 → 124

Calls

Call 1

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

Outputs
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(.f64 y (.f64 y #s(literal 3 binary64)))
(.f64 (.f64 y y) #s(literal 3 binary64))
(.f64 #s(literal 3 binary64) (.f64 y y))
(.f64 (.f64 y #s(literal 3 binary64)) y)
(*.f64 y #s(literal 3 binary64))
(*.f64 #s(literal 3 binary64) y)
(+.f64 (.f64 x x) (.f64 (*.f64 y y) #s(literal 3 binary64)))
(+.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (*.f64 x x))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 x x (.f64 #s(literal -3 binary64) (.f64 y y)))) (/.f64 (.f64 (.f64 y (.f64 y (.f64 y y))) #s(literal 9 binary64)) (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 y (.f64 y #s(literal 3 binary64)) (.f64 x x))
(fma.f64 (.f64 y y) #s(literal 3 binary64) (.f64 x x))
(fma.f64 #s(literal 3 binary64) (.f64 y y) (.f64 x x))
(fma.f64 (.f64 y #s(literal 3 binary64)) y (.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (.f64 (.f64 y y) #s(literal 3 binary64)))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))) #s(literal 27 binary64))) (fma.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (-.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))) #s(literal 27 binary64))) (fma.f64 (.f64 y (.f64 y (.f64 y y))) #s(literal 9 binary64) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x (.f64 (.f64 y y) #s(literal 3 binary64)))))))
(/.f64 (.f64 (fma.f64 x x (.f64 (.f64 y y) #s(literal 3 binary64))) (fma.f64 x x (.f64 #s(literal -3 binary64) (.f64 y y)))) (fma.f64 x x (.f64 #s(literal -3 binary64) (*.f64 y y))))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))) #s(literal 27 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (-.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x (.f64 (.f64 y y) #s(literal 3 binary64))) (fma.f64 x x (.f64 #s(literal -3 binary64) (.f64 y y))))) (neg.f64 (fma.f64 x x (.f64 #s(literal -3 binary64) (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (-.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))) #s(literal 27 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (.f64 #s(literal -3 binary64) (.f64 y y))) (.f64 (fma.f64 x x (.f64 (.f64 y y) #s(literal 3 binary64))) (fma.f64 x x (.f64 #s(literal -3 binary64) (*.f64 y y))))))
(/.f64 (-.f64 (.f64 (.f64 y (.f64 y (.f64 y y))) #s(literal 9 binary64)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (.f64 x x)))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))) #s(literal 27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (-.f64 (.f64 (.f64 y y) #s(literal 3 binary64)) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (.f64 (fma.f64 x x (.f64 (.f64 y y) #s(literal 3 binary64))) (fma.f64 x x (.f64 #s(literal -3 binary64) (.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 #s(literal -3 binary64) (.f64 y y)))))
(.f64 y (.f64 y #s(literal 3 binary64)))
(.f64 (.f64 y y) #s(literal 3 binary64))
(.f64 #s(literal 3 binary64) (.f64 y y))
(.f64 (.f64 y #s(literal 3 binary64)) y)
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(pow.f64 y #s(literal 2 binary64))
(*.f64 y y)
(*.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)))
(+.f64 (*.f64 y y) (fma.f64 x x (+.f64 y y)))
(+.f64 (fma.f64 x x (+.f64 y y)) (*.f64 y y))
(+.f64 (.f64 x x) (fma.f64 y #s(literal 2 binary64) (.f64 y y)))
(+.f64 (*.f64 x x) (fma.f64 y y (+.f64 y y)))
(+.f64 (fma.f64 x x (*.f64 y y)) (+.f64 y y))
(+.f64 (+.f64 y y) (fma.f64 x x (*.f64 y y)))
(+.f64 (fma.f64 y #s(literal 2 binary64) (.f64 y y)) (.f64 x x))
(-.f64 (/.f64 (.f64 (+.f64 y y) (+.f64 y y)) (-.f64 (fma.f64 y y #s(literal 0 binary64)) (.f64 x x))) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (-.f64 (fma.f64 y y #s(literal 0 binary64)) (.f64 x x))))
(-.f64 (/.f64 (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))) (/.f64 (.f64 y (.f64 y (.f64 y y))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))))
(fma.f64 x x (fma.f64 y #s(literal 2 binary64) (*.f64 y y)))
(fma.f64 x x (fma.f64 y y (+.f64 y y)))
(fma.f64 y y (fma.f64 x x (+.f64 y y)))
(fma.f64 y (+.f64 y y) (fma.f64 x x (*.f64 y y)))
(fma.f64 y #s(literal 2 binary64) (fma.f64 x x (*.f64 y y)))
(fma.f64 (+.f64 y y) y (fma.f64 x x (*.f64 y y)))
(fma.f64 #s(literal 2 binary64) y (fma.f64 x x (*.f64 y y)))
(fma.f64 #s(literal 2 binary64) (.f64 y y) (fma.f64 x x (.f64 y y)))
(fma.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))) (fma.f64 x x (.f64 y y)))
(fma.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) (fma.f64 x x (*.f64 y y)))
(fma.f64 (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (fma.f64 x x (.f64 y y))) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))))) (.f64 y y))
(fma.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))) (+.f64 y y))
(fma.f64 (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))) (.f64 y y))
(fma.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x y) (-.f64 x y))) (+.f64 y y))
(fma.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)) (fma.f64 x x (+.f64 y y)))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (fma.f64 y #s(literal 2 binary64) (*.f64 y y)))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (fma.f64 y y (+.f64 y y)))
(/.f64 (fma.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (+.f64 y y) (.f64 (+.f64 y y) (+.f64 y y)))) (fma.f64 (fma.f64 x x (.f64 y y)) (-.f64 (fma.f64 x x (.f64 y y)) (+.f64 y y)) (*.f64 (+.f64 y y) (+.f64 y y))))
(/.f64 (fma.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (+.f64 y y) (.f64 (+.f64 y y) (+.f64 y y)))) (fma.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y)) (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (fma.f64 x x (*.f64 y y)) (+.f64 y y)))))
(/.f64 (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (fma.f64 x x (+.f64 y y)) (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y))))) (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (fma.f64 x x (+.f64 y y))) (*.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y)))))
(/.f64 (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (fma.f64 x x (+.f64 y y)) (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y))))) (fma.f64 y (.f64 y (.f64 y y)) (-.f64 (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y))) (.f64 (*.f64 y y) (fma.f64 x x (+.f64 y y))))))
(/.f64 (.f64 (fma.f64 y y (fma.f64 x x (+.f64 y y))) (-.f64 (fma.f64 y y #s(literal 0 binary64)) (.f64 x x))) (-.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 x x)))
(/.f64 (*.f64 (fma.f64 y y (fma.f64 x x (+.f64 y y))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (neg.f64 (fma.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (+.f64 y y) (.f64 (+.f64 y y) (+.f64 y y))))) (neg.f64 (fma.f64 (fma.f64 x x (.f64 y y)) (-.f64 (fma.f64 x x (.f64 y y)) (+.f64 y y)) (*.f64 (+.f64 y y) (+.f64 y y)))))
(/.f64 (neg.f64 (.f64 (fma.f64 y y (fma.f64 x x (+.f64 y y))) (-.f64 (fma.f64 y y #s(literal 0 binary64)) (.f64 x x)))) (neg.f64 (-.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (fma.f64 x x (+.f64 y y)) (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y)))))) (neg.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (fma.f64 x x (+.f64 y y))) (*.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y (fma.f64 x x (+.f64 y y))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))) (neg.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 x x (.f64 y y)) (-.f64 (fma.f64 x x (.f64 y y)) (+.f64 y y)) (.f64 (+.f64 y y) (+.f64 y y))) (fma.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (+.f64 y y) (*.f64 (+.f64 y y) (+.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 y y #s(literal 0 binary64)) (.f64 x x)) (.f64 (fma.f64 y y (fma.f64 x x (+.f64 y y))) (-.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (fma.f64 x x (+.f64 y y))) (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y)))) (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (fma.f64 x x (+.f64 y y)) (*.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))) (*.f64 (fma.f64 y y (fma.f64 x x (+.f64 y y))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64))))))
(/.f64 (-.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (fma.f64 x x (*.f64 y y)) (+.f64 y y)))
(/.f64 (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y)))) (-.f64 (*.f64 y y) (fma.f64 x x (+.f64 y y))))
(.f64 (fma.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (+.f64 y y) (.f64 (+.f64 y y) (+.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x (.f64 y y)) (-.f64 (fma.f64 x x (.f64 y y)) (+.f64 y y)) (.f64 (+.f64 y y) (+.f64 y y)))))
(.f64 (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (fma.f64 x x (+.f64 y y)) (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (fma.f64 x x (+.f64 y y))) (.f64 (fma.f64 x x (+.f64 y y)) (fma.f64 x x (+.f64 y y))))))
(.f64 (.f64 (fma.f64 y y (fma.f64 x x (+.f64 y y))) (-.f64 (fma.f64 y y #s(literal 0 binary64)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 y y #s(literal 0 binary64)) (.f64 x x))))
(.f64 (.f64 (fma.f64 y y (fma.f64 x x (+.f64 y y))) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 y y (fma.f64 x x #s(literal 0 binary64)))))
(+.f64 y y)
(+.f64 (.f64 y y) (.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(fma.f64 y y (*.f64 y y))
(fma.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)) (*.f64 y y))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (fma.f64 y (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 y (.f64 y (*.f64 y y))))))
(/.f64 (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 (.f64 y (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(*.f64 y (+.f64 y y))
(*.f64 y #s(literal 2 binary64))
(*.f64 (+.f64 y y) y)
(*.f64 #s(literal 2 binary64) y)
(.f64 #s(literal 2 binary64) (.f64 y y))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(+.f64 (.f64 y y) (.f64 x x))
(+.f64 (.f64 x x) (.f64 y y))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 x y) (-.f64 x y))) (/.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (+.f64 x y) (-.f64 x y))))
(fma.f64 x x (*.f64 y y))
(fma.f64 y y (*.f64 x x))
(fma.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 y y))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x))))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (fma.f64 y (.f64 y (.f64 y y)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x (*.f64 y y))))))
(/.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))) (.f64 (+.f64 x y) (-.f64 x y)))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))) (neg.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y)))) (neg.f64 (.f64 (+.f64 x y) (-.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (.f64 y (.f64 y (*.f64 y y)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 x y) (-.f64 x y)) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y)))))
(/.f64 (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 y y) (.f64 x x)))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (+.f64 x y) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x y) (-.f64 x y))))

eval34.0ms (1%)

Memory: 34.5MiB live, 68.6MiB allocated
Compiler: Compiled 4 678 to 305 computations (93.5% saved)

prune27.0ms (0.8%)

Memory

11.2MiB live, 49.0MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	330	2	332
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	331	5	336

Accuracy

100.0%

Counts

336 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.0%	(fma.f64 (+.f64 y y) y #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.9%	(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
▶	58.9%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
✓	58.9%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 y (.f64 y #s(literal 3 binary64))))
✓	58.9%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

Compiler

Compiled 43 to 24 computations (44.2% saved)

simplify53.0ms (1.5%)

Memory

-57.1MiB live, 43.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
cost-diff	0	(+.f64 y y)
cost-diff	0	(fma.f64 (+.f64 y y) y #s(approx (+ (* x x) (* y y)) (*.f64 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)))

Rules

64×	`lower-fma.f32`
62×	`lower-fma.f64`
48×	`lower-+.f32`
46×	`lower-+.f64`
28×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
0	20	65
1	33	63
2	47	59
3	60	59
4	64	59
0	64	56

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize56.0ms (1.6%)

Memory

25.4MiB live, 64.1MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 y y)
accuracy	0.01171875	(fma.f64 (+.f64 y y) y #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	26.226302049066913	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	0.13671875	(.f64 (.f64 y y) #s(literal 3 binary64))
accuracy	26.22130469190846	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))

Samples

19.0ms

256×

valid

Compiler

Compiled 54 to 14 computations (74.1% saved)

Precisions

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

ival-mult: 6.0ms (53.5% of total)

ival-add: 5.0ms (44.6% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

6 → 108

Calls

Call 1

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

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

Calls

27 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
0.0ms	y	@	0	(* (* y y) 3)
0.0ms	x	@	0	(+ (* (+ y y) y) (+ (* x x) (* y y)))
0.0ms	y	@	inf	(* (* y y) 3)
0.0ms	x	@	inf	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify228.0ms (6.5%)

Memory

-7.0MiB live, 295.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 296×	`lower-fma.f64`
11 296×	`lower-fma.f32`
6 082×	`lower-*.f64`
6 082×	`lower-*.f32`
1 602×	`distribute-rgt-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	792
1	73	648
2	186	648
3	721	648
4	2394	648
5	3473	648
6	4933	648
7	6394	648
8	7552	648
0	8235	594

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

rewrite57.0ms (1.6%)

Memory

-9.7MiB live, 80.7MiB allocated

Rules

574×	`lower-fma.f32`
572×	`lower-fma.f64`
392×	`lower-*.f32`
388×	`lower-*.f64`
284×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
0	20	59
1	86	54
0	772	49

Stop Event

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

Counts

6 → 52

Calls

Call 1

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

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

eval18.0ms (0.5%)

Memory: 4.2MiB live, 40.9MiB allocated
Compiler: Compiled 2 030 to 131 computations (93.5% saved)

prune14.0ms (0.4%)

Memory

-6.8MiB live, 31.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	176	5	181

Accuracy

100.0%

Counts

181 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	59.0%	(fma.f64 (+.f64 y y) y #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	99.9%	(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
✓	58.9%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 (.f64 y y) #s(literal 3 binary64)))
✓	58.9%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (.f64 y (.f64 y #s(literal 3 binary64))))
✓	58.9%	#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

Compiler

Compiled 104 to 41 computations (60.6% saved)

regimes14.0ms (0.4%)

Memory

31.4MiB live, 31.4MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	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)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
100.0%	1	`(*.f64 x x)`
100.0%	1	`(*.f64 y y)`

Compiler

Compiled 33 to 17 computations (48.5% saved)

regimes14.0ms (0.4%)

Memory

-8.6MiB live, 29.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	y
2.0ms	x
2.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
2.0ms	(*.f64 y y)
2.0ms	(*.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 33 to 17 computations (48.5% saved)

regimes21.0ms (0.6%)

Memory

-13.8MiB live, 32.9MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

5 calls:

13.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
2.0ms	y
2.0ms	x
2.0ms	(*.f64 y y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
82.7%	2	`x`
85.8%	2	`y`
63.3%	2	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
82.7%	2	`(*.f64 x x)`
85.8%	2	`(*.f64 y y)`

Compiler

Compiled 33 to 17 computations (48.5% saved)

regimes4.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

#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 y y) #s(literal 3 binary64)))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
85.8%	2	`y`
85.8%	2	`(*.f64 y y)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes3.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

2 → 2

Calls

Call 1

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
85.8%	2	`y`
85.8%	2	`(*.f64 y y)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes7.0ms (0.2%)

Memory

-18.8MiB live, 19.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#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))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
58.9%	1	`(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))`
58.9%	1	`x`
58.9%	1	`(*.f64 x x)`
58.9%	1	`y`
58.9%	1	`(*.f64 y y)`

Compiler

Compiled 33 to 17 computations (48.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.610899645752843e+23	1.3352259007101304e+33

Compiler

Compiled 16 to 12 computations (25% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.610899645752843e+23	1.3352259007101304e+33

Compiler

Compiled 16 to 12 computations (25% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0781824972269349e+54	2.2233913458269895e+55

Compiler

Compiled 16 to 12 computations (25% saved)

simplify7.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	171
1	33	171

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (+.f64 y y) y (fma.f64 x x (*.f64 y y)))
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
(if (<=.f64 (.f64 y y) #s(literal 499999999999999991611392 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 x x)) (fma.f64 (+.f64 y y) y #s(approx (+ ( x x) (* y y)) (*.f64 y y))))
(if (<=.f64 (.f64 y y) #s(literal 499999999999999991611392 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 y y) #s(literal 3 binary64))))
(if (<=.f64 (.f64 y y) #s(literal 2000000000000000156583080809192487684610720599772233728 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 y (.f64 y #s(literal 3 binary64)))))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

Outputs
(fma.f64 (+.f64 y y) y (fma.f64 x x (*.f64 y y)))
(fma.f64 x x (.f64 #s(literal 3 binary64) (.f64 y y)))
(fma.f64 x x (.f64 (.f64 y y) #s(literal 3 binary64)))
(if (<=.f64 (.f64 y y) #s(literal 499999999999999991611392 binary64)) #s(approx (+ (+ (+ ( x x) (* y y)) (* y y)) (* y y)) (.f64 x x)) (fma.f64 (+.f64 y y) y #s(approx (+ ( x x) (* y y)) (*.f64 y y))))
(if (<=.f64 (.f64 y y) #s(literal 499999999999999991611392 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 y y) #s(literal 3 binary64))))
(if (<=.f64 (.f64 y y) #s(literal 2000000000000000156583080809192487684610720599772233728 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 y (.f64 y #s(literal 3 binary64)))))
#s(approx (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)) (*.f64 x x))

soundness701.0ms (19.9%)

Memory

-4.8MiB live, 430.8MiB allocated

Rules

13 684×	`lower-fma.f64`
13 684×	`lower-fma.f32`
10 540×	`lower-fma.f64`
10 540×	`lower-fma.f32`
9 354×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	85
0	30	88
1	109	76
0	953	73
0	30	1440
1	84	1152
2	208	1152
3	808	1152
4	2341	1152
5	3252	1152
6	4808	1152
7	6213	1152
8	7051	1152
0	8177	1062
0	30	660
1	86	588
2	215	588
3	851	588
4	2011	588
5	2650	588
6	4169	588
7	5649	588
8	6638	588
9	7914	588
0	8035	534
0	7	39
0	12	39
1	54	35
2	517	29
3	7592	29
0	8199	26

Stop Event

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

Compiler

Compiled 233 to 84 computations (63.9% saved)

preprocess90.0ms (2.6%)

Memory

-0.2MiB live, 76.0MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 316 to 116 computations (63.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample764.0ms (21.7%)

explain104.0ms (3%)

preprocess42.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.2%)

localize21.0ms (0.6%)

series5.0ms (0.1%)

simplify333.0ms (9.5%)

rewrite336.0ms (9.5%)

eval60.0ms (1.7%)

prune59.0ms (1.7%)

simplify7.0ms (0.2%)

localize67.0ms (1.9%)

series8.0ms (0.2%)

simplify285.0ms (8.1%)

rewrite75.0ms (2.1%)

eval34.0ms (1%)

prune27.0ms (0.8%)

simplify53.0ms (1.5%)

localize56.0ms (1.6%)

series4.0ms (0.1%)

simplify228.0ms (6.5%)

rewrite57.0ms (1.6%)

eval18.0ms (0.5%)

prune14.0ms (0.4%)

regimes14.0ms (0.4%)

regimes14.0ms (0.4%)

regimes21.0ms (0.6%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes7.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify7.0ms (0.2%)

soundness701.0ms (19.9%)

preprocess90.0ms (2.6%)

end0.0ms (0%)

Profiling