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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 5 computations (50% saved)

sample815.0ms (25.5%)

Memory

-8.5MiB live, 993.7MiB allocated

Samples

614.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 199.0ms

ival-hypot: 190.0ms (95.4% of total)

ival-true: 6.0ms (3% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain99.0ms (3.1%)

Memory

-14.2MiB live, 218.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
138	-	2	(2.0498877978083265e-157 6.176446033661168e-273)	`(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	125	0
↳	`(*.f64 y y)`	overflow	62
↳	`(*.f64 x x)`	overflow	79
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	125
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	11	0
↳	`(*.f64 y y)`	underflow	59
↳	`(*.f64 x x)`	underflow	57
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	11

Confusion

	Predicted +	Predicted -
+	136	2
-	0	118

Precision

1.0

Recall

0.9855072463768116

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	136	0	2
-	0	0	118

Precision?

1.0

Recall?

0.9855072463768116

Freqs

test

number	freq
0	120
1	136

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

49.0ms

512×

valid

Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 22.0ms (66.1% of total)

ival-hypot: 8.0ms (24.1% of total)

ival-add: 2.0ms (6% of total)

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

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

preprocess20.0ms (0.6%)

Memory

26.2MiB live, 63.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 10 to 6 computations (40% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.2%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify10.0ms (0.3%)

Memory

-28.4MiB live, 13.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize21.0ms (0.6%)

Memory

29.0MiB live, 67.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 y y))
accuracy	31.85839252627237	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

16.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-hypot: 4.0ms (47.6% of total)

ival-mult: 3.0ms (35.7% of total)

ival-add: 1.0ms (11.9% of total)

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

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

series8.0ms (0.2%)

Memory

-16.1MiB live, 21.9MiB 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 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	((+ (* x x) (* y y)) (sqrt (+ (* x x) (* y y))) (* x x) (* y y))
1.0ms	y	@	0	((+ (* x x) (* y y)) (sqrt (+ (* x x) (* y y))) (* x x) (* y y))
1.0ms	x	@	inf	((+ (* x x) (* y y)) (sqrt (+ (* x x) (* y y))) (* x x) (* y y))
1.0ms	y	@	-inf	((+ (* x x) (* y y)) (sqrt (+ (* x x) (* y y))) (* x x) (* y y))
1.0ms	x	@	0	((+ (* x x) (* y y)) (sqrt (+ (* x x) (* y y))) (* x x) (* y y))

simplify343.0ms (10.7%)

Memory

-15.6MiB live, 274.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

Calls

Call 1

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

rewrite215.0ms (6.7%)

Memory

26.6MiB live, 219.7MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 245

Calls

Call 1

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

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

eval74.0ms (2.3%)

Memory: -15.3MiB live, 67.2MiB allocated
Compiler: Compiled 14 217 to 964 computations (93.2% saved)

prune47.0ms (1.5%)

Memory

-9.3MiB live, 104.2MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	308	5	313
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	309	5	314

Accuracy

100.0%

Counts

314 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.2%	(sqrt.f64 (fma.f64 x x (*.f64 y y)))
▶	49.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
▶	4.5%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
▶	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
▶	1.7%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 78 to 44 computations (43.6% saved)

simplify9.0ms (0.3%)

Memory

15.8MiB live, 15.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

68×	`lower-fma.f32`
64×	`lower-fma.f64`
60×	`lower-+.f64`
60×	`lower-+.f32`
48×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	114
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	131	114
8	140	114
9	146	114
10	146	114
0	146	102

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize40.0ms (1.3%)

Memory

11.6MiB live, 59.0MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0.00390625	(fma.f64 x x (*.f64 y y))
accuracy	31.85839252627237	(sqrt.f64 (fma.f64 x x (*.f64 y y)))
accuracy	0	(*.f64 y y)
accuracy	0.2839014798977374	#s(approx (+ (* x x) (* y y)) (*.f64 y y))
accuracy	31.85839252627237	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
accuracy	0	(*.f64 x x)
accuracy	31.85839252627237	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
accuracy	54.909774890785116	#s(approx (+ (* x x) (* y y)) (*.f64 x x))
accuracy	0	(neg.f64 x)
accuracy	62.889872189742654	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 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	0.09924122650394328	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))

Samples

30.0ms

256×

valid

Compiler

Compiled 97 to 14 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 10.0ms (50.2% of total)

ival-hypot: 4.0ms (20.1% of total)

ival-div: 2.0ms (10% of total)

ival-add: 2.0ms (10% of total)

ival-neg: 1.0ms (5% of total)

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

exact: 0.0ms (0% of total)

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

series31.0ms (1%)

Memory

-10.6MiB live, 28.1MiB allocated

Counts

14 → 288

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	y	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (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) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)))
2.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (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) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)))
2.0ms	x	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (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) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)))
1.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (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) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)))
1.0ms	y	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* (* 1/2 x) (/ x y)) y) (* 1/2 x) (/ x y) (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) (sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)))

simplify251.0ms (7.8%)

Memory

24.2MiB live, 213.0MiB allocated

Algorithm

1×	egg-herbie

Rules

16 212×	`lower-fma.f64`
16 212×	`lower-fma.f32`
4 244×	`lower-*.f64`
4 244×	`lower-*.f32`
2 514×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	2908
1	326	2908
2	1025	2898
3	3967	2668
4	7526	2668
0	8271	2436

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 265

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

rewrite186.0ms (5.8%)

Memory

-1.3MiB live, 192.3MiB allocated

Rules

5 258×	`lower-fma.f32`
5 254×	`lower-fma.f64`
4 200×	`lower-*.f32`
4 194×	`lower-*.f64`
2 138×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	103
0	31	103
1	80	103
2	470	103
3	5421	103
0	8184	91

Stop Event

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

Counts

14 → 344

Calls

Call 1

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

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

eval261.0ms (8.2%)

Memory: -4.0MiB live, 112.5MiB allocated
Compiler: Compiled 12 892 to 1 001 computations (92.2% saved)

prune80.0ms (2.5%)

Memory

7.7MiB live, 97.9MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	630	0	630
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	630	5	635

Accuracy

100.0%

Counts

635 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.2%	(sqrt.f64 (fma.f64 x x (*.f64 y y)))
✓	49.8%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 y y)))
✓	4.5%	(sqrt.f64 #s(approx (+ (* x x) (* y y)) (*.f64 x x)))
✓	99.8%	#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 x y) y))
✓	1.7%	#s(approx (sqrt (+ (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 78 to 37 computations (52.6% saved)

regimes23.0ms (0.7%)

Memory

-9.0MiB live, 29.3MiB allocated

Counts

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

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

Calls

6 calls:

10.0ms	(*.f64 y y)
3.0ms	x
3.0ms	y
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`y`
99.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.8%	1	`(*.f64 x x)`
99.8%	1	`(*.f64 y y)`

Compiler

Compiled 35 to 21 computations (40% saved)

regimes16.0ms (0.5%)

Memory

1.7MiB live, 39.1MiB 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 x x (*.f64 y y)))

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
50.2%	1	`x`
50.2%	1	`y`
50.2%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
50.2%	1	`(+.f64 (.f64 x x) (.f64 y y))`
50.2%	1	`(*.f64 x x)`
50.2%	1	`(*.f64 y y)`

Compiler

Compiled 35 to 21 computations (40% saved)

regimes14.0ms (0.4%)

Memory

-3.5MiB live, 34.3MiB 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:

4.0ms	y
2.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
49.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
49.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
49.8%	1	`(*.f64 y y)`
49.8%	1	`y`
49.8%	1	`x`
49.8%	1	`(*.f64 x x)`

Compiler

Compiled 35 to 21 computations (40% saved)

regimes42.0ms (1.3%)

Memory

-14.3MiB live, 34.3MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

6 calls:

34.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	y
2.0ms	x
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 35 to 21 computations (40% saved)

regimes8.0ms (0.2%)

Memory

16.5MiB live, 16.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
1.7%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
1.7%	1	`(+.f64 (.f64 x x) (.f64 y y))`
1.7%	1	`(*.f64 y y)`
1.7%	1	`y`
1.7%	1	`x`
1.7%	1	`(*.f64 x x)`

Compiler

Compiled 35 to 21 computations (40% saved)

simplify16.0ms (0.5%)

Memory

-20.8MiB live, 17.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	59
1	26	59
2	28	59
3	29	59

Stop Event

1×

saturated

Calls

Call 1

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

soundness508.0ms (15.9%)

Memory

6.0MiB live, 361.2MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 74 to 38 computations (48.6% saved)

preprocess59.0ms (1.8%)

Memory: 25.1MiB live, 145.5MiB allocated
Compiler: Compiled 190 to 100 computations (47.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	114
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	131	114
8	140	114
9	146	114
10	146	114
0	146	102

Iter	Nodes	Cost
0	21	114
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	131	114
8	140	114
9	146	114
10	146	114
0	146	102

start0.0ms (0%)

analyze0.0ms (0%)

sample815.0ms (25.5%)

explain99.0ms (3.1%)

preprocess20.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify10.0ms (0.3%)

localize21.0ms (0.6%)

series8.0ms (0.2%)

simplify343.0ms (10.7%)

rewrite215.0ms (6.7%)

eval74.0ms (2.3%)

prune47.0ms (1.5%)

simplify9.0ms (0.3%)

localize40.0ms (1.3%)

series31.0ms (1%)

simplify251.0ms (7.8%)

rewrite186.0ms (5.8%)

eval261.0ms (8.2%)

prune80.0ms (2.5%)

regimes23.0ms (0.7%)

regimes16.0ms (0.5%)

regimes14.0ms (0.4%)

regimes42.0ms (1.3%)

regimes8.0ms (0.2%)

simplify16.0ms (0.5%)

soundness508.0ms (15.9%)

preprocess59.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	114
0	31	114
1	43	114
2	55	114
3	61	114
4	66	114
5	73	114
6	103	114
7	131	114
8	140	114
9	146	114
10	146	114
0	146	102