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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 5 computations (50% saved)

sample954.0ms (3.3%)

Memory

24.2MiB live, 654.4MiB allocated

Samples

647.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 399.0ms

ival-hypot: 388.0ms (97.4% of total)

ival-true: 7.0ms (1.8% of total)

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

Bogosity

explain250.0ms (0.9%)

Memory

-14.5MiB live, 81.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
128	-	2	(-5.2479300994778304e-161 -5.006224485543276e-242)	`(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	112	0
↳	`(*.f64 y y)`	overflow	63
↳	`(*.f64 x x)`	overflow	71
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	112
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	14	0
↳	`(*.f64 y y)`	underflow	60
↳	`(*.f64 x x)`	underflow	60
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	14

Confusion

	Predicted +	Predicted -
+	126	2
-	0	128

Precision

1.0

Recall

0.984375

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	126	0	2
-	0	0	128

Precision?

1.0

Recall?

0.984375

Freqs

test

number	freq
0	130
1	126

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

118.0ms

512×

valid

Compiler

Compiled 81 to 28 computations (65.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-hypot: 10.0ms (51.4% of total)

ival-mult: 6.0ms (30.8% of total)

ival-add: 3.0ms (15.4% of total)

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

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

preprocess17.0ms (0.1%)

Memory

20.8MiB live, 20.8MiB allocated

Algorithm

1×	egg-herbie

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

prune45.0ms (0.2%)

Memory

-37.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.8%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0%)

Memory

4.0MiB live, 4.0MiB 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))

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

localize77.0ms (0.3%)

Memory

-0.8MiB live, 38.4MiB 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	29.571877910744718	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

16.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

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

ival-hypot: 5.0ms (53.8% of total)

ival-mult: 3.0ms (32.3% of total)

ival-add: 1.0ms (10.8% of total)

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

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

series6.0ms (0%)

Memory

15.3MiB live, 15.3MiB 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))))

simplify482.0ms (1.7%)

Memory

28.1MiB live, 179.2MiB allocated

Algorithm

1×	egg-herbie

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))

rewrite23.5s (82.3%)

Memory

-6.3MiB live, 149.7MiB allocated

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
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eval101.0ms (0.4%)

Memory: -23.3MiB live, 60.1MiB allocated
Compiler: Compiled 7 655 to 987 computations (87.1% saved)

prune9.0ms (0%)

Memory

19.3MiB live, 19.3MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	306	7	313
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	307	7	314

Accuracy

100.0%

Counts

314 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 y x)
	53.4%	(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
▶	53.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
▶	53.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	4.6%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
	99.1%	#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 96 to 76 computations (20.8% saved)

simplify5.0ms (0%)

Memory

2.4MiB live, 2.4MiB 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)

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

localize166.0ms (0.6%)

Memory

-23.2MiB live, 53.0MiB 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	29.571877910744718	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0	(*.f64 y y)
accuracy	0.24743501019429387	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	29.571877910744718	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0	(*.f64 x x)
accuracy	29.571877910744718	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
accuracy	52.72070576867854	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
accuracy	0	(neg.f64 x)
accuracy	62.862352722418045	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))
accuracy	0	(hypot.f64 y x)

Samples

84.0ms

256×

valid

Compiler

Compiled 136 to 24 computations (82.4% saved)

Precisions

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

ival-hypot: 9.0ms (57.4% of total)

ival-mult: 3.0ms (19.1% of total)

ival-add: 2.0ms (12.8% of total)

ival-neg: 1.0ms (6.4% of total)

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

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

series9.0ms (0%)

Memory

15.1MiB live, 15.1MiB 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>) () ())) ())
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#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))))
0.0ms	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	y	@	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))))

simplify300.0ms (1.1%)

Memory

-13.7MiB live, 189.1MiB allocated

Algorithm

1×	egg-herbie

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))

rewrite396.0ms (1.4%)

Memory

20.8MiB live, 260.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	77
0	24	68
1	58	68
2	338	68
3	3364	68
0	8576	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
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eval114.0ms (0.4%)

Memory: -5.2MiB live, 187.5MiB allocated
Compiler: Compiled 12 517 to 1 138 computations (90.9% saved)

prune41.0ms (0.1%)

Memory

-14.2MiB live, 92.8MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	653	1	654
Fresh	1	1	2
Picked	0	5	5
Done	0	0	0
Total	654	7	661

Accuracy

100.0%

Counts

661 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
▶	53.4%	(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
✓	53.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	53.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	4.6%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
▶	99.1%	#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 48 to 38 computations (20.8% saved)

simplify6.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	88
0	29	88
1	39	88
2	49	88
3	53	88
4	56	88
5	59	88
0	59	84

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

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

localize53.0ms (0.2%)

Memory

-1.9MiB live, 75.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 (/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x)))
accuracy	0	(sqrt.f64 (+.f64 y x))
accuracy	0.48046875	(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
accuracy	29.61873578576289	(/.f64 (fma.f64 y y (*.f64 x x)) (+.f64 y x))
accuracy	0	(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y)
accuracy	0	(/.f64 x y)
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.5855965684293705	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))

Samples

36.0ms

256×

valid

Compiler

Compiled 168 to 32 computations (81% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 9.0ms (34.3% of total)

ival-hypot: 5.0ms (19.1% of total)

ival-sqrt: 4.0ms (15.2% of total)

ival-div: 3.0ms (11.4% of total)

ival-add: 3.0ms (11.4% of total)

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

exact: 0.0ms (0% of total)

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

series25.0ms (0.1%)

Memory

9.5MiB live, 47.0MiB allocated

Counts

9 → 204

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	y	@	-inf	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))
3.0ms	x	@	-inf	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))
3.0ms	x	@	inf	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))
2.0ms	y	@	inf	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))
2.0ms	y	@	0	((sqrt (+ (* y y) (* x x))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (* (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (sqrt (+ y x))) (sqrt (/ (+ (* y y) (* x x)) (+ y x))) (/ (+ (* y y) (* x x)) (+ y x)) (+ (* y y) (* x x)) (sqrt (+ y x)))

simplify236.0ms (0.8%)

Memory

3.7MiB live, 274.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	458	2943
1	1451	2807
2	4873	2721
0	8129	2532

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 187

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

rewrite254.0ms (0.9%)

Memory

-28.7MiB live, 256.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	77
0	29	76
1	95	68
2	679	68
3	7994	68
0	9167	57

Stop Event

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

Counts

9 → 620

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

Outputs
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eval106.0ms (0.4%)

Memory: 27.7MiB live, 255.4MiB allocated
Compiler: Compiled 21 427 to 2 903 computations (86.5% saved)

prune23.0ms (0.1%)

Memory

-14.1MiB live, 69.1MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	806	1	807
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	806	8	814

Accuracy

100.0%

Counts

814 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	53.4%	(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
✓	53.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	53.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	4.6%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
✓	99.1%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
▶	98.8%	#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 x y) (.f64 x #s(literal 1/2 binary64)) y) (.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)))))
✓	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 78 to 55 computations (29.5% saved)

simplify146.0ms (0.5%)

Memory

13.1MiB live, 206.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (/.f64 x y) (*.f64 x #s(literal 1/2 binary64)) y)
cost-diff	0	#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 x y) (.f64 x #s(literal 1/2 binary64)) y) (.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)))))
cost-diff	320	(.f64 (fma.f64 (/.f64 x y) (.f64 x #s(literal 1/2 binary64)) y) (.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y))))
cost-diff	3968	(.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	145
0	35	124
1	65	124
2	127	122
3	446	118
4	2047	84
5	7836	84
0	8160	79

Stop Event

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

Calls

Call 1

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

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

localize80.0ms (0.3%)

Memory

2.3MiB live, 134.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
accuracy	0.1171875	(*.f64 (/.f64 x y) x)
accuracy	0.203125	(.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)))
accuracy	0.5855965684293705	#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 x y) (.f64 x #s(literal 1/2 binary64)) y) (.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)))))

Samples

68.0ms

256×

valid

Compiler

Compiled 263 to 39 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-div: 29.0ms (50.7% of total)

ival-mult: 17.0ms (29.7% of total)

ival-hypot: 6.0ms (10.5% of total)

ival-add: 3.0ms (5.2% of total)

ival-neg: 1.0ms (1.7% of total)

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

exact: 0.0ms (0% of total)

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

series59.0ms (0.2%)

Memory

-21.1MiB live, 55.6MiB allocated

Counts

6 → 144

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	y	@	0	((* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y))) (* (+ (* (/ x y) (* x 1/2)) y) (* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y)))) (sqrt (+ (* y y) (* x x))) (+ (* (/ x y) (* x 1/2)) y) (* (/ x y) x) (* (/ x y) 1/2))
3.0ms	y	@	-inf	((* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y))) (* (+ (* (/ x y) (* x 1/2)) y) (* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y)))) (sqrt (+ (* y y) (* x x))) (+ (* (/ x y) (* x 1/2)) y) (* (/ x y) x) (* (/ x y) 1/2))
3.0ms	x	@	inf	((* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y))) (* (+ (* (/ x y) (* x 1/2)) y) (* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y)))) (sqrt (+ (* y y) (* x x))) (+ (* (/ x y) (* x 1/2)) y) (* (/ x y) x) (* (/ x y) 1/2))
2.0ms	x	@	0	((* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y))) (* (+ (* (/ x y) (* x 1/2)) y) (* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y)))) (sqrt (+ (* y y) (* x x))) (+ (* (/ x y) (* x 1/2)) y) (* (/ x y) x) (* (/ x y) 1/2))
2.0ms	y	@	inf	((* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y))) (* (+ (* (/ x y) (* x 1/2)) y) (* (+ (* (* (/ x y) 1/2) x) (neg y)) (/ -1 (+ (* -1/2 (* (/ x y) x)) y)))) (sqrt (+ (* y y) (* x x))) (+ (* (/ x y) (* x 1/2)) y) (* (/ x y) x) (* (/ x y) 1/2))

simplify182.0ms (0.6%)

Memory

25.8MiB live, 262.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	169	1379
1	493	1297
2	1745	1225
3	5854	1083
0	8488	1010

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 134

Calls

Call 1

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

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

rewrite49.0ms (0.2%)

Memory

10.7MiB live, 49.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	105
0	35	105
1	134	92
0	1049	87

Stop Event

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

Counts

6 → 135

Calls

Call 1

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

Outputs
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eval66.0ms (0.2%)

Memory: -30.3MiB live, 83.6MiB allocated
Compiler: Compiled 8 257 to 686 computations (91.7% saved)

prune11.0ms (0%)

Memory

36.4MiB live, 36.4MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	269	8	277

Accuracy

100.0%

Counts

277 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 y x)
✓	53.4%	(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
✓	53.8%	(sqrt.f64 (fma.f64 y y (*.f64 x x)))
✓	53.4%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	4.6%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
✓	99.1%	#s(approx (sqrt (+ (* y y) (* x x))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
✓	98.8%	#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 x y) (.f64 x #s(literal 1/2 binary64)) y) (.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)))))
✓	1.8%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 173 to 94 computations (45.7% saved)

regimes29.0ms (0.1%)

Memory

-21.2MiB live, 52.7MiB allocated

Counts

10 → 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)))
(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 x y) (.f64 x #s(literal 1/2 binary64)) y) (.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) y)))))
(hypot.f64 y x)

Outputs
(hypot.f64 y x)

Calls

6 calls:

7.0ms	x
6.0ms	(*.f64 y y)
4.0ms	y
4.0ms	(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)

regimes26.0ms (0.1%)

Memory

-9.9MiB live, 48.2MiB allocated

Counts

9 → 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)))
(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
#s(approx (sqrt (+ (* y y) (* x x))) (.f64 (fma.f64 (/.f64 x y) (.f64 x #s(literal 1/2 binary64)) y) (.f64 (fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) x (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x y) x) 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:

9.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	x
4.0ms	y
3.0ms	(*.f64 y y)
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`y`
99.1%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.1%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.1%	1	`(*.f64 x x)`
99.1%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes15.0ms (0.1%)

Memory

-6.5MiB live, 32.4MiB 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:

3.0ms	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
53.8%	1	`x`
53.8%	1	`y`
53.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
53.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
53.8%	1	`(*.f64 x x)`
53.8%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes13.0ms (0%)

Memory

-4.9MiB live, 34.0MiB 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:

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

Results

Accuracy	Segments	Branch
53.4%	1	`(*.f64 x x)`
53.4%	1	`x`
53.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
53.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
53.4%	1	`(*.f64 y y)`
53.4%	1	`y`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes10.0ms (0%)

Memory

27.4MiB live, 27.4MiB 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	x
2.0ms	y
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	(+.f64 (.f64 x x) (.f64 y y))
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
4.6%	1	`x`
4.6%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
4.6%	1	`(+.f64 (.f64 x x) (.f64 y y))`
4.6%	1	`(*.f64 y y)`
4.6%	1	`y`
4.6%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes9.0ms (0%)

Memory

-15.2MiB live, 23.6MiB 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:

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

Results

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

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify26.0ms (0.1%)

Memory

13.3MiB live, 54.8MiB allocated

Algorithm

1×	egg-herbie

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))

soundness543.0ms (1.9%)

Memory

-13.4MiB live, 338.8MiB allocated

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

Stop Event

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

Compiler

Compiled 76 to 50 computations (34.2% saved)

preprocess114.0ms (0.4%)

Memory

-0.8MiB live, 76.4MiB 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%)

sample954.0ms (3.3%)

explain250.0ms (0.9%)

preprocess17.0ms (0.1%)

eval0.0ms (0%)

prune45.0ms (0.2%)

simplify4.0ms (0%)

localize77.0ms (0.3%)

series6.0ms (0%)

simplify482.0ms (1.7%)

rewrite23.5s (82.3%)

eval101.0ms (0.4%)

prune9.0ms (0%)

simplify5.0ms (0%)

localize166.0ms (0.6%)

series9.0ms (0%)

simplify300.0ms (1.1%)

rewrite396.0ms (1.4%)

eval114.0ms (0.4%)

prune41.0ms (0.1%)

simplify6.0ms (0%)

localize53.0ms (0.2%)

series25.0ms (0.1%)

simplify236.0ms (0.8%)

rewrite254.0ms (0.9%)

eval106.0ms (0.4%)

prune23.0ms (0.1%)

simplify146.0ms (0.5%)

localize80.0ms (0.3%)

series59.0ms (0.2%)

simplify182.0ms (0.6%)

rewrite49.0ms (0.2%)

eval66.0ms (0.2%)

prune11.0ms (0%)

regimes29.0ms (0.1%)

regimes26.0ms (0.1%)

regimes15.0ms (0.1%)

regimes13.0ms (0%)

regimes10.0ms (0%)

regimes9.0ms (0%)

simplify26.0ms (0.1%)

soundness543.0ms (1.9%)

preprocess114.0ms (0.4%)

end0.0ms (0%)

Profiling