Metrics for Data.Octree.Internal:octantDistance from Octree-0.5.4.2

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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 10 to 5 computations (50% saved)

sample739.0ms (2.7%)

Memory

43.9MiB live, 794.3MiB allocated

Samples

419.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 187.0ms

ival-hypot: 176.0ms (94.3% of total)

ival-true: 7.0ms (3.8% of total)

ival-assert: 4.0ms (2.1% of total)

Bogosity

explain129.0ms (0.5%)

Memory

-11.5MiB live, 140.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
121	-	1	(-7.644517428224627e-162 -9.050085761351939e-169)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`y`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	oflow-rescue	110	0
↳	`(*.f64 y y)`	overflow	56
↳	`(*.f64 x x)`	overflow	66
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	110
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	10	0
↳	`(*.f64 y y)`	underflow	58
↳	`(*.f64 x x)`	underflow	49
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	10

Confusion

	Predicted +	Predicted -
+	120	1
-	0	135

Precision

1.0

Recall

0.9917355371900827

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	0	1
-	0	0	135

Precision?

1.0

Recall?

0.9917355371900827

Freqs

test

number	freq
0	136
1	120

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

84.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-hypot: 16.0ms (63.3% of total)

ival-mult: 7.0ms (27.7% of total)

ival-add: 2.0ms (7.9% of total)

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

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

preprocess19.0ms (0.1%)

Memory

4.0MiB live, 39.4MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`sub-neg`
30×	`distribute-lft-neg-in`
30×	`neg-sub0`
28×	`unsub-neg`
24×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	35	42
2	77	42
3	145	42
4	204	42
5	217	42
6	219	42
0	6	8
0	10	8
1	11	8
0	11	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.0%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Memory

7.3MiB live, 7.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	-5120	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (.f64 x x) (.f64 y y))

Rules

4×	`lower-hypot.f32`
4×	`lower-hypot.f64`
4×	`lower-fma.f64`
4×	`lift-*.f64`
4×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	11	23
0	11	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize22.0ms (0.1%)

Memory

0.4MiB live, 38.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (.f64 x x) (.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	28.191507677389602	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

17.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-hypot: 4.0ms (44.3% of total)

ival-mult: 3.0ms (33.2% of total)

ival-add: 2.0ms (22.2% of total)

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

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

series6.0ms (0%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

4 → 72

Calls

Call 1

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

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

Calls

6 calls:

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

simplify250.0ms (0.9%)

Memory

-27.1MiB live, 201.8MiB allocated

Algorithm

1×	egg-herbie

Rules

18 004×	`lower-fma.f64`
18 004×	`lower-fma.f32`
5 072×	`lower-*.f64`
5 072×	`lower-*.f32`
2 260×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	620
1	296	620
2	953	618
3	3667	584
4	6426	582
0	8051	530

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

Calls

Call 1

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

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

rewrite202.0ms (0.7%)

Memory

-16.3MiB live, 179.1MiB allocated

Rules

5 720×	`lower-fma.f64`
5 720×	`lower-fma.f32`
4 038×	`lower-/.f64`
4 038×	`lower-/.f32`
3 184×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	29	21
2	196	21
3	1788	21
0	8624	15

Stop Event

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

Counts

4 → 245

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval75.0ms (0.3%)

Memory: 11.9MiB live, 83.6MiB allocated
Compiler: Compiled 7 655 to 987 computations (87.1% saved)

prune14.0ms (0.1%)

Memory

-21.3MiB live, 28.4MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	307	6	313
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	308	6	314

Accuracy

100.0%

Counts

314 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
▶	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	55.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	4.5%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
	99.5%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
▶	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 64 to 58 computations (9.4% saved)

simplify6.0ms (0%)

Memory

9.3MiB live, 9.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	-5120	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 y y (*.f64 x x))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
cost-diff	0	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
cost-diff	0	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
cost-diff	0	(hypot.f64 y x)

Rules

24×	`lower-+.f64`
24×	`lower-+.f32`
12×	`lower-fma.f32`
10×	`lower-fma.f64`
8×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	87
0	24	78
1	29	78
2	31	78
3	33	78
4	35	78
5	39	78
6	48	78
7	54	78
8	58	78
0	58	78

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize37.0ms (0.1%)

Memory

-3.2MiB live, 71.6MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	28.191507677389602	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0	(*.f64 y y)
accuracy	0.34317155315548376	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	28.191507677389602	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0	(*.f64 x x)
accuracy	28.191507677389602	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
accuracy	56.07979179289992	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
accuracy	0	(neg.f64 x)
accuracy	62.85995749600993	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0	(hypot.f64 y x)

Samples

24.0ms

256×

valid

Compiler

Compiled 81 to 11 computations (86.4% saved)

Precisions

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

ival-hypot: 8.0ms (56.4% of total)

ival-mult: 3.0ms (21.2% of total)

ival-add: 2.0ms (14.1% of total)

ival-neg: 1.0ms (7.1% of total)

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

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

series9.0ms (0%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

11 → 228

Calls

Call 1

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

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

Calls

6 calls:

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

simplify377.0ms (1.4%)

Memory

12.7MiB live, 158.0MiB allocated

Algorithm

1×	egg-herbie

Rules

18 004×	`lower-fma.f64`
18 004×	`lower-fma.f32`
5 072×	`lower-*.f64`
5 072×	`lower-*.f32`
2 260×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	2548
1	296	2548
2	953	2538
3	3671	2368
4	6433	2358
0	8058	2134

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 208

Calls

Call 1

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

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

rewrite224.0ms (0.8%)

Memory

-5.1MiB live, 291.3MiB allocated

Rules

3 958×	`lower-fma.f32`
3 956×	`lower-fma.f64`
3 618×	`lower-*.f32`
3 614×	`lower-*.f64`
2 154×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	77
0	24	68
1	58	68
2	338	68
3	3368	68
0	8587	68

Stop Event

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

Counts

11 → 421

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval75.0ms (0.3%)

Memory: -6.1MiB live, 189.2MiB allocated
Compiler: Compiled 12 517 to 1 138 computations (90.9% saved)

prune19.0ms (0.1%)

Memory

11.0MiB live, 47.8MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	653	1	654
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	654	6	660

Accuracy

100.0%

Counts

660 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	55.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	4.5%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
▶	99.5%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
✓	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 32 to 29 computations (9.4% saved)

simplify5.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

44×	`lower-*.f32`
42×	`lower-*.f64`
20×	`lower-fma.f32`
18×	`lower-fma.f64`
12×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
0	15	34
1	23	34
2	33	34
3	37	34
4	40	34
5	43	34
0	43	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize27.0ms (0.1%)

Memory

-6.8MiB live, 41.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 x y)
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.00390625	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
accuracy	0.32109605105101824	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))

Samples

21.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

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

ival-hypot: 5.0ms (45.9% of total)

ival-mult: 3.0ms (27.6% of total)

ival-div: 2.0ms (18.4% of total)

ival-add: 1.0ms (9.2% of total)

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

exact: 0.0ms (0% of total)

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

series13.0ms (0%)

Memory

-22.6MiB live, 14.9MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	y	@	inf	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y))
1.0ms	x	@	inf	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y))
1.0ms	y	@	0	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y))
1.0ms	x	@	-inf	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y))
1.0ms	x	@	0	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y))

simplify186.0ms (0.7%)

Memory

27.9MiB live, 223.8MiB allocated

Algorithm

1×	egg-herbie

Rules

17 774×	`lower-fma.f64`
17 774×	`lower-fma.f32`
4 270×	`lower-*.f64`
4 270×	`lower-*.f32`
2 472×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	764
1	304	764
2	977	762
3	3628	666
4	7494	666
0	8232	616

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

rewrite156.0ms (0.6%)

Memory

4.1MiB live, 202.6MiB allocated

Rules

6 772×	`lower-fma.f32`
6 770×	`lower-fma.f64`
4 216×	`lower-*.f32`
4 214×	`lower-*.f64`
2 100×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
0	15	31
1	59	31
2	429	31
3	5166	31
0	8900	26

Stop Event

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

Counts

4 → 128

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval86.0ms (0.3%)

Memory: -29.3MiB live, 54.0MiB allocated
Compiler: Compiled 4 063 to 564 computations (86.1% saved)

prune11.0ms (0%)

Memory

24.9MiB live, 24.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	205	6	211

Accuracy

100.0%

Counts

211 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	56.0%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	55.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	4.5%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
✓	99.5%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
✓	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 81 to 50 computations (38.3% saved)

regimes98.0ms (0.4%)

Memory

-4.5MiB live, 33.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
(hypot.f64 y x)

Calls

6 calls:

82.0ms	(*.f64 y y)
3.0ms	x
3.0ms	y
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes93.0ms (0.3%)

Memory

-5.8MiB live, 32.1MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

6 calls:

77.0ms	(*.f64 x x)
3.0ms	x
3.0ms	y
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`y`
99.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.5%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.5%	1	`(*.f64 x x)`
99.5%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes91.0ms (0.3%)

Memory

-17.8MiB live, 24.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

6 calls:

80.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(*.f64 y y)
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
56.0%	1	`x`
56.0%	1	`y`
56.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
56.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
56.0%	1	`(*.f64 x x)`
56.0%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes97.0ms (0.4%)

Memory

-4.5MiB live, 32.8MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
55.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
55.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
55.4%	1	`(*.f64 y y)`
55.4%	1	`y`
55.4%	1	`x`
55.4%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes10.0ms (0%)

Memory

32.3MiB live, 32.3MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
4.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
4.5%	1	`(+.f64 (.f64 x x) (.f64 y y))`
4.5%	1	`(*.f64 y y)`
4.5%	1	`y`
4.5%	1	`x`
4.5%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes91.0ms (0.3%)

Memory

-18.6MiB live, 20.8MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

84.0ms	(*.f64 y y)
1.0ms	x
1.0ms	y
1.0ms	(+.f64 (.f64 x x) (.f64 y y))
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Results

Accuracy	Segments	Branch
1.8%	1	`y`
1.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
1.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
1.8%	1	`(*.f64 y y)`
1.8%	1	`x`
1.8%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify26.0ms (0.1%)

Memory

-3.1MiB live, 36.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-commutative-binary64-.f64`
2×	`neg-sub0-binary64--.f64-neg.f64`
2×	`+-commutative-binary64-+.f64`
2×	`neg-mul-1-binary64-*.f64-neg.f64`
2×	`sub-neg-binary64-neg.f64-+.f64--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	62
1	27	62
2	29	62
3	30	62

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness23.9s (87.7%)

Memory

26.4MiB live, 299.8MiB allocated

Rules

18 004×	`lower-fma.f64`
18 004×	`lower-fma.f32`
5 720×	`lower-fma.f64`
5 720×	`lower-fma.f32`
5 072×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	29	21
2	196	21
3	1788	21
0	8624	15
0	104	620
1	296	620
2	953	618
3	3667	584
4	6426	582
0	8051	530

Stop Event

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

Compiler

Compiled 76 to 50 computations (34.2% saved)

preprocess162.0ms (0.6%)

Memory

-21.4MiB live, 104.0MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 136 to 92 computations (32.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample739.0ms (2.7%)

explain129.0ms (0.5%)

preprocess19.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize22.0ms (0.1%)

series6.0ms (0%)

simplify250.0ms (0.9%)

rewrite202.0ms (0.7%)

eval75.0ms (0.3%)

prune14.0ms (0.1%)

simplify6.0ms (0%)

localize37.0ms (0.1%)

series9.0ms (0%)

simplify377.0ms (1.4%)

rewrite224.0ms (0.8%)

eval75.0ms (0.3%)

prune19.0ms (0.1%)

simplify5.0ms (0%)

localize27.0ms (0.1%)

series13.0ms (0%)

simplify186.0ms (0.7%)

rewrite156.0ms (0.6%)

eval86.0ms (0.3%)

prune11.0ms (0%)

regimes98.0ms (0.4%)

regimes93.0ms (0.3%)

regimes91.0ms (0.3%)

regimes97.0ms (0.4%)

regimes10.0ms (0%)

regimes91.0ms (0.3%)

simplify26.0ms (0.1%)

soundness23.9s (87.7%)

preprocess162.0ms (0.6%)

end0.0ms (0%)

Profiling