Metrics for Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3

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 9 computations (10% saved)

sample1.0s (13.3%)

Memory

12.4MiB live, 1 328.5MiB allocated

Samples

733.0ms	7 936×	0	valid
22.0ms	66×	3	valid
18.0ms	122×	2	valid
12.0ms	132×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 298.0ms

ival-sub: 110.0ms (36.9% of total)

ival-div: 67.0ms (22.5% of total)

ival-fabs: 48.0ms (16.1% of total)

ival-add: 45.0ms (15.1% of total)

adjust: 13.0ms (4.4% of total)

ival-true: 7.0ms (2.3% of total)

exact: 5.0ms (1.7% of total)

ival-assert: 4.0ms (1.3% of total)

Bogosity

explain126.0ms (1.6%)

Memory

-25.7MiB live, 133.4MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
-	-	`(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))`
-	-	`(-.f64 y x)`
-	-	`y`
-	-	`#s(literal 2 binary64)`
-	-	`(fabs.f64 (-.f64 y x))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

42.0ms	492×	0	valid
2.0ms	16×	2	valid
0.0ms	2×	3	valid
0.0ms	2×	1	valid

Compiler

Compiled 60 to 25 computations (58.3% saved)

Precisions

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

ival-sub: 5.0ms (31.7% of total)

ival-div: 4.0ms (25.3% of total)

ival-fabs: 3.0ms (19% of total)

ival-add: 3.0ms (19% of total)

adjust: 1.0ms (6.3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess40.0ms (0.5%)

Memory

-2.2MiB live, 75.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	46	40
2	127	40
3	248	40
4	352	40
5	419	40
6	463	40
7	501	40
8	513	40
9	518	40
10	521	40
11	523	40
0	7	8
0	11	8
1	16	8
2	23	8
3	31	8
4	50	8
5	97	8
6	155	8
7	184	8
8	229	8
9	265	8
10	301	8
11	313	8
12	319	8
13	322	8
14	324	8
0	324	7

Stop Event

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

Calls

Call 1

Inputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Outputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y)) x)

Compiler

Compiled 8 to 7 computations (12.5% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.7MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify12.0ms (0.2%)

Memory

25.5MiB live, 25.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 y x)
cost-diff	0	(fabs.f64 (-.f64 y x))
cost-diff	128	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
cost-diff	384	(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
0	11	24
1	16	24
2	23	24
3	31	24
4	50	24
5	97	24
6	155	24
7	184	24
8	229	24
9	265	24
10	301	24
11	313	24
12	319	24
13	322	24
14	324	24
0	324	23

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
x
(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))
(fabs.f64 (-.f64 y x))
(-.f64 y x)
y
#s(literal 2 binary64)

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

localize23.0ms (0.3%)

Memory

-23.0MiB live, 57.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))
accuracy	0	(-.f64 y x)
accuracy	0	(fabs.f64 (-.f64 y x))
accuracy	0.046875	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Samples

14.0ms	246×	0	valid
1.0ms	8×	2	valid
0.0ms	1×	3	valid
0.0ms	1×	1	valid

Compiler

Compiled 26 to 9 computations (65.4% saved)

Precisions

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

ival-div: 3.0ms (35.6% of total)

ival-sub: 2.0ms (23.7% of total)

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

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

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

15.8MiB live, 15.8MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) (patch (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (fabs.f64 (-.f64 y x)) (patch (fabs.f64 (-.f64 y x)) #<representation binary64>) () ())
#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	((/ (fabs (- y x)) 2) (+ x (/ (fabs (- y x)) 2)) (fabs (- y x)) (- y x))
1.0ms	x	@	inf	((/ (fabs (- y x)) 2) (+ x (/ (fabs (- y x)) 2)) (fabs (- y x)) (- y x))
1.0ms	y	@	-inf	((/ (fabs (- y x)) 2) (+ x (/ (fabs (- y x)) 2)) (fabs (- y x)) (- y x))
1.0ms	x	@	-inf	((/ (fabs (- y x)) 2) (+ x (/ (fabs (- y x)) 2)) (fabs (- y x)) (- y x))
0.0ms	y	@	0	((/ (fabs (- y x)) 2) (+ x (/ (fabs (- y x)) 2)) (fabs (- y x)) (- y x))

simplify122.0ms (1.6%)

Memory

-4.9MiB live, 112.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	479
1	115	479
2	264	479
3	775	479
4	2401	479
5	3216	479
6	4243	479
7	5084	479
8	5657	479
9	6145	479
10	7847	479
0	8326	458

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 91

Calls

Call 1

Inputs
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(* -1 x)
(- y x)
(- y x)
(- y x)
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
x
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* 1/2 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (+ y (* -1 x))))
x
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))

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

rewrite162.0ms (2.1%)

Memory

-1.4MiB live, 211.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
0	11	21
1	51	21
2	380	21
3	5345	21
0	8350	20

Stop Event

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

Counts

4 → 239

Calls

Call 1

Inputs
(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))
(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
(fabs.f64 (-.f64 y x))
(-.f64 y x)

Outputs
#<batchref>
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eval40.0ms (0.5%)

Memory: 7.5MiB live, 83.6MiB allocated
Compiler: Compiled 6 166 to 927 computations (85% saved)

prune13.0ms (0.2%)

Memory

-3.3MiB live, 34.6MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	323	7	330
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	324	7	331

Accuracy

100.0%

Counts

331 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.3%	(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fabs.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) #s(literal -1 binary64)) (pow.f64 (fabs.f64 (+.f64 x y)) #s(literal -1 binary64)) x)
	99.3%	(fma.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64)) x)
▶	99.9%	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
▶	46.9%	(/.f64 (fma.f64 (pow.f64 (-.f64 x y) #s(literal 2 binary64)) #s(literal -1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (fabs.f64 (-.f64 x y)) x))
▶	99.3%	(+.f64 x (pow.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
▶	99.7%	(+.f64 x (/.f64 (fabs.f64 (.f64 (+.f64 x y) (.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64))))) #s(literal 2 binary64)))
▶	51.2%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)))

Compiler

Compiled 200 to 138 computations (31% saved)

simplify140.0ms (1.8%)

Memory

-24.9MiB live, 218.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y)))
cost-diff	128	(+.f64 x (pow.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
cost-diff	5824	(pow.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64))
cost-diff	7104	(pow.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
cost-diff	0	(-.f64 x y)
cost-diff	0	(pow.f64 (-.f64 x y) #s(literal 2 binary64))
cost-diff	0	(fma.f64 (pow.f64 (-.f64 x y) #s(literal 2 binary64)) #s(literal -1/4 binary64) (*.f64 x x))
cost-diff	0	(/.f64 (fma.f64 (pow.f64 (-.f64 x y) #s(literal 2 binary64)) #s(literal -1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (fabs.f64 (-.f64 x y)) x))
cost-diff	128	(+.f64 x (/.f64 (fabs.f64 (.f64 (+.f64 x y) (.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64))))) #s(literal 2 binary64)))
cost-diff	384	(/.f64 (fabs.f64 (.f64 (+.f64 x y) (.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64))))) #s(literal 2 binary64))
cost-diff	1408	(.f64 (+.f64 x y) (.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64))))
cost-diff	6080	(*.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64)))
cost-diff	0	(-.f64 y x)
cost-diff	0	(fabs.f64 (-.f64 y x))
cost-diff	0	(*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)))
cost-diff	0	(-.f64 x y)
cost-diff	0	(fabs.f64 (-.f64 x y))
cost-diff	0	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	235
0	59	184
1	89	184
2	151	182
3	399	181
4	1535	181
5	4261	181
0	8462	181

Stop Event

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

Calls

Call 1

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

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

localize110.0ms (1.4%)

Memory

23.8MiB live, 218.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (-.f64 x y))
accuracy	0.0078125	(pow.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64))
accuracy	0.04296875	(+.f64 x (pow.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
accuracy	0.48828125	(pow.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
accuracy	0.015625	(pow.f64 (-.f64 x y) #s(literal 2 binary64))
accuracy	0.0859375	(fma.f64 #s(literal -1/2 binary64) (fabs.f64 (-.f64 x y)) x)
accuracy	15.601537729962475	(fma.f64 (pow.f64 (-.f64 x y) #s(literal 2 binary64)) #s(literal -1/4 binary64) (*.f64 x x))
accuracy	32.61459283863053	(/.f64 (fma.f64 (pow.f64 (-.f64 x y) #s(literal 2 binary64)) #s(literal -1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (fabs.f64 (-.f64 x y)) x))
accuracy	0.01171875	(pow.f64 (+.f64 x y) #s(literal -1 binary64))
accuracy	0.04296875	(+.f64 x (/.f64 (fabs.f64 (.f64 (+.f64 x y) (.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64))))) #s(literal 2 binary64)))
accuracy	0.046875	(.f64 (+.f64 x y) (.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64))))
accuracy	0.19140625	(*.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64)))
accuracy	0	(-.f64 y x)
accuracy	0	(*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64))
accuracy	0	(fabs.f64 (-.f64 y x))
accuracy	30.971287252794504	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)))
accuracy	0	(-.f64 x y)
accuracy	0	(fabs.f64 (-.f64 x y))
accuracy	0.04296875	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)

Samples

56.0ms	222×	0	valid
12.0ms	16×	2	valid
7.0ms	13×	1	valid
4.0ms	4×	3	valid
1.0ms	1×	5	exit

Compiler

Compiled 235 to 36 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-mult: 14.0ms (25.2% of total)

ival-add: 10.0ms (18% of total)

ival-div: 6.0ms (10.8% of total)

ival-pow2: 6.0ms (10.8% of total)

ival-pow: 5.0ms (9% of total)

adjust: 4.0ms (7.2% of total)

ival-sub: 4.0ms (7.2% of total)

ival-fabs: 4.0ms (7.2% of total)

ival-sqrt: 2.0ms (3.6% of total)

exact: 1.0ms (1.8% of total)

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

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

series51.0ms (0.7%)

Memory

-32.2MiB live, 96.2MiB allocated

Counts

20 → 480

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	y	@	inf	((+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- y x) (pow (+ x y) -1)) (* (+ x y) (* (- y x) (pow (+ x y) -1))) (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2) (+ x (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2) (pow (* 1/2 (fabs (- x y))) 1/2) (+ x (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2)) (* 1/2 (fabs (- x y))) (pow (+ x y) -1) (+ (* -1/2 (fabs (- x y))) x))
10.0ms	x	@	-inf	((+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- y x) (pow (+ x y) -1)) (* (+ x y) (* (- y x) (pow (+ x y) -1))) (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2) (+ x (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2) (pow (* 1/2 (fabs (- x y))) 1/2) (+ x (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2)) (* 1/2 (fabs (- x y))) (pow (+ x y) -1) (+ (* -1/2 (fabs (- x y))) x))
4.0ms	y	@	-inf	((+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- y x) (pow (+ x y) -1)) (* (+ x y) (* (- y x) (pow (+ x y) -1))) (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2) (+ x (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2) (pow (* 1/2 (fabs (- x y))) 1/2) (+ x (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2)) (* 1/2 (fabs (- x y))) (pow (+ x y) -1) (+ (* -1/2 (fabs (- x y))) x))
4.0ms	y	@	0	((+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- y x) (pow (+ x y) -1)) (* (+ x y) (* (- y x) (pow (+ x y) -1))) (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2) (+ x (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2) (pow (* 1/2 (fabs (- x y))) 1/2) (+ x (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2)) (* 1/2 (fabs (- x y))) (pow (+ x y) -1) (+ (* -1/2 (fabs (- x y))) x))
3.0ms	x	@	inf	((+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- y x) (pow (+ x y) -1)) (* (+ x y) (* (- y x) (pow (+ x y) -1))) (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2) (+ x (/ (fabs (* (+ x y) (* (- y x) (pow (+ x y) -1)))) 2)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2) (pow (* 1/2 (fabs (- x y))) 1/2) (+ x (pow (pow (* 1/2 (fabs (- x y))) 1/2) 2)) (* 1/2 (fabs (- x y))) (pow (+ x y) -1) (+ (* -1/2 (fabs (- x y))) x))

simplify232.0ms (3%)

Memory

30.7MiB live, 223.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	526	4603
1	1607	4426
2	4371	4361
0	8281	4086

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 461

Calls

Call 1

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

rewrite227.0ms (2.9%)

Memory

13.6MiB live, 288.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	179
0	59	138
1	239	136
2	1711	121
0	8775	121

Stop Event

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

Counts

20 → 1 355

Calls

Call 1

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

Outputs
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eval558.0ms (7.2%)

Memory: 12.8MiB live, 799.7MiB allocated
Compiler: Compiled 57 235 to 6 237 computations (89.1% saved)

prune74.0ms (0.9%)

Memory

3.7MiB live, 202.5MiB allocated

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	2 501	13	2 514
Fresh	2	0	2
Picked	4	1	5
Done	0	0	0
Total	2 507	14	2 521

Accuracy

100.0%

Counts

2 521 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	49.1%	(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 x y)) #s(literal -1/4 binary64)) (pow.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x y)) #s(literal 3/4 binary64)) x)
▶	54.6%	(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)
	49.0%	(fma.f64 (*.f64 (sqrt.f64 (-.f64 x y)) (sqrt.f64 (-.f64 x y))) #s(literal 1/2 binary64) x)
	49.0%	(fma.f64 (sqrt.f64 (-.f64 x y)) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 x y)))) x)
▶	48.2%	(fma.f64 (sqrt.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) (-.f64 x y))) (sqrt.f64 #s(literal 1/2 binary64)) x)
	48.9%	(fma.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y))) x)
	50.4%	(fma.f64 (sqrt.f64 (.f64 #s(literal -1/2 binary64) (-.f64 x y))) (sqrt.f64 (.f64 #s(literal -1/2 binary64) (-.f64 x y))) x)
✓	99.9%	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
	56.9%	(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)
▶	25.2%	(/.f64 (fma.f64 #s(approx (pow (- x y) 2) (.f64 x x)) #s(literal -1/4 binary64) (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (fabs.f64 (-.f64 x y)) x))
▶	12.0%	#s(approx (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (*.f64 #s(literal 3/4 binary64) x))
▶	99.7%	#s(approx (+ (* (fabs (- x y)) 1/2) x) (fma.f64 (fabs.f64 (-.f64 y x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) x))
	57.4%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (-.f64 x y) #s(literal 1/2 binary64)))
	6.9%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))

Compiler

Compiled 293 to 210 computations (28.3% saved)

simplify118.0ms (1.5%)

Memory

-13.5MiB live, 137.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x y)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) (-.f64 x y))
cost-diff	0	(sqrt.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) (-.f64 x y)))
cost-diff	0	(fma.f64 (sqrt.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) (-.f64 x y))) (sqrt.f64 #s(literal 1/2 binary64)) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (pow (- x y) 2) (*.f64 x x))
cost-diff	0	(fma.f64 #s(approx (pow (- x y) 2) (.f64 x x)) #s(literal -1/4 binary64) (.f64 x x))
cost-diff	0	(/.f64 (fma.f64 #s(approx (pow (- x y) 2) (.f64 x x)) #s(literal -1/4 binary64) (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (fabs.f64 (-.f64 x y)) x))
cost-diff	0	(-.f64 x y)
cost-diff	0	(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)
cost-diff	0	(*.f64 #s(literal 3/4 binary64) x)
cost-diff	0	#s(approx (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (*.f64 #s(literal 3/4 binary64) x))
cost-diff	0	(fabs.f64 (-.f64 y x))
cost-diff	0	(fma.f64 (fabs.f64 (-.f64 y x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) x)
cost-diff	0	#s(approx (+ (* (fabs (- x y)) 1/2) x) (fma.f64 (fabs.f64 (-.f64 y x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) x))
cost-diff	1024	(*.f64 (/.f64 #s(literal 1/2 binary64) x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	201
0	64	207
1	94	207
2	143	182
3	298	182
4	802	182
5	2326	182
6	5133	182
0	8196	181

Stop Event

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

Calls

Call 1

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

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

localize311.0ms (4%)

Memory

-224.0MiB live, 168.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0.01953125	(.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) (-.f64 x y))
accuracy	0.3515625	(fma.f64 (sqrt.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) (-.f64 x y))) (sqrt.f64 #s(literal 1/2 binary64)) x)
accuracy	32.581460398190295	(sqrt.f64 (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) (-.f64 x y)))
accuracy	0.0859375	(fma.f64 #s(literal -1/2 binary64) (fabs.f64 (-.f64 x y)) x)
accuracy	15.605443979962475	(fma.f64 #s(approx (pow (- x y) 2) (.f64 x x)) #s(literal -1/4 binary64) (.f64 x x))
accuracy	23.338674936152312	#s(approx (pow (- x y) 2) (*.f64 x x))
accuracy	32.61459283863053	(/.f64 (fma.f64 #s(approx (pow (- x y) 2) (.f64 x x)) #s(literal -1/4 binary64) (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (fabs.f64 (-.f64 x y)) x))
accuracy	0	(-.f64 x y)
accuracy	0.11328125	(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)
accuracy	0	(*.f64 #s(literal 3/4 binary64) x)
accuracy	56.315120580155444	#s(approx (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (*.f64 #s(literal 3/4 binary64) x))
accuracy	0	(fabs.f64 (-.f64 y x))
accuracy	0	#s(approx (+ (* (fabs (- x y)) 1/2) x) (fma.f64 (fabs.f64 (-.f64 y x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) x))
accuracy	0.046875	(fma.f64 (fabs.f64 (-.f64 y x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) x)
accuracy	0.205410009768442	(*.f64 (/.f64 #s(literal 1/2 binary64) x) x)

Samples

167.0ms	12×	1	valid
49.0ms	223×	0	valid
30.0ms	5×	3	valid
10.0ms	16×	2	valid

Compiler

Compiled 183 to 34 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

adjust: 29.0ms (39.4% of total)

ival-mult: 18.0ms (24.4% of total)

ival-add: 8.0ms (10.9% of total)

ival-div: 4.0ms (5.4% of total)

ival-sqrt: 4.0ms (5.4% of total)

ival-pow2: 3.0ms (4.1% of total)

ival-sub: 3.0ms (4.1% of total)

ival-fabs: 3.0ms (4.1% of total)

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

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

exact: 0.0ms (0% of total)

series43.0ms (0.6%)

Memory

17.9MiB live, 55.5MiB allocated

Counts

18 → 372

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
21.0ms	x	@	-inf	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (fabs (- y x)) (* (/ 1/2 x) x)) x) (fabs (- y x)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (* 3/4 x) (+ (* (- x y) 1/2) x) (- x y) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (* x x) (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (sqrt (* (* 1/2 (- x y)) (- x y))) (* 1/2 (- x y)) (+ (* -1/2 (fabs (- x y))) x) (* (* 1/2 (- x y)) (- x y)) (sqrt 1/2))
2.0ms	x	@	inf	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (fabs (- y x)) (* (/ 1/2 x) x)) x) (fabs (- y x)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (* 3/4 x) (+ (* (- x y) 1/2) x) (- x y) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (* x x) (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (sqrt (* (* 1/2 (- x y)) (- x y))) (* 1/2 (- x y)) (+ (* -1/2 (fabs (- x y))) x) (* (* 1/2 (- x y)) (- x y)) (sqrt 1/2))
2.0ms	x	@	0	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (fabs (- y x)) (* (/ 1/2 x) x)) x) (fabs (- y x)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (* 3/4 x) (+ (* (- x y) 1/2) x) (- x y) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (* x x) (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (sqrt (* (* 1/2 (- x y)) (- x y))) (* 1/2 (- x y)) (+ (* -1/2 (fabs (- x y))) x) (* (* 1/2 (- x y)) (- x y)) (sqrt 1/2))
2.0ms	y	@	inf	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (fabs (- y x)) (* (/ 1/2 x) x)) x) (fabs (- y x)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (* 3/4 x) (+ (* (- x y) 1/2) x) (- x y) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (* x x) (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (sqrt (* (* 1/2 (- x y)) (- x y))) (* 1/2 (- x y)) (+ (* -1/2 (fabs (- x y))) x) (* (* 1/2 (- x y)) (- x y)) (sqrt 1/2))
2.0ms	y	@	0	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (fabs (- y x)) (* (/ 1/2 x) x)) x) (fabs (- y x)) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (* 3/4 x) (+ (* (- x y) 1/2) x) (- x y) (/ (+ (* (pow (- x y) 2) -1/4) (* x x)) (+ (* -1/2 (fabs (- x y))) x)) (+ (* (pow (- x y) 2) -1/4) (* x x)) (pow (- x y) 2) (* x x) (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (sqrt (* (* 1/2 (- x y)) (- x y))) (* 1/2 (- x y)) (+ (* -1/2 (fabs (- x y))) x) (* (* 1/2 (- x y)) (- x y)) (sqrt 1/2))

simplify190.0ms (2.4%)

Memory

-26.7MiB live, 332.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	424	4608
1	1337	4329
2	3671	4090
0	8065	3788

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 363

Calls

Call 1

Inputs
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(/ (+ (* -1/4 (pow x 2)) (pow x 2)) (+ x (* -1/2 (fabs (- x y)))))
(+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))) (+ (* 1/2 (/ (* x y) (+ x (* -1/2 (fabs (- x y)))))) (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))))
(+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))) (+ (* y (+ (* -1/4 (/ y (+ x (* -1/2 (fabs (- x y)))))) (* 1/2 (/ x (+ x (* -1/2 (fabs (- x y)))))))) (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))))
(+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))) (+ (* y (+ (* -1/4 (/ y (+ x (* -1/2 (fabs (- x y)))))) (* 1/2 (/ x (+ x (* -1/2 (fabs (- x y)))))))) (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))))
(+ x (* 1/2 x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(+ x (+ (* -1/2 y) (* 1/2 x)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(/ (+ (* -1/4 (pow x 2)) (pow x 2)) (+ x (* -1/2 (fabs (- x y)))))
(+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))) (+ (* 1/2 (/ (* x y) (+ x (* -1/2 (fabs (- x y)))))) (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))))
(+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))) (+ (* y (+ (* -1/4 (/ y (+ x (* -1/2 (fabs (- x y)))))) (* 1/2 (/ x (+ x (* -1/2 (fabs (- x y)))))))) (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))))
(+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))) (+ (* y (+ (* -1/4 (/ y (+ x (* -1/2 (fabs (- x y)))))) (* 1/2 (/ x (+ x (* -1/2 (fabs (- x y)))))))) (/ (pow x 2) (+ x (* -1/2 (fabs (- x y)))))))
(+ (* -1/4 (pow x 2)) (pow x 2))
(+ (* -1/4 (pow x 2)) (+ (* 1/2 (* x y)) (pow x 2)))
(+ (* -1/4 (pow x 2)) (+ (* y (+ (* -1/4 y) (* 1/2 x))) (pow x 2)))
(+ (* -1/4 (pow x 2)) (+ (* y (+ (* -1/4 y) (* 1/2 x))) (pow x 2)))
(pow x 2)
(+ (* -2 (* x y)) (pow x 2))
(+ (* y (+ y (* -2 x))) (pow x 2))
(+ (* y (+ y (* -2 x))) (pow x 2))
(+ x (* x (pow (sqrt 1/2) 2)))
(+ x (+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (pow (sqrt 1/2) 2))))
(+ x (+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (pow (sqrt 1/2) 2))))
(+ x (+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (pow (sqrt 1/2) 2))))
(* x (sqrt 1/2))
(+ (* -1 (* y (sqrt 1/2))) (* x (sqrt 1/2)))
(+ (* -1 (* y (sqrt 1/2))) (* x (sqrt 1/2)))
(+ (* -1 (* y (sqrt 1/2))) (* x (sqrt 1/2)))
(* 1/2 x)
(+ (* -1/2 y) (* 1/2 x))
(+ (* -1/2 y) (* 1/2 x))
(+ (* -1/2 y) (* 1/2 x))
(+ x (* -1/2 (fabs (- x y))))
(+ x (* -1/2 (fabs (- x y))))
(+ x (* -1/2 (fabs (- x y))))
(+ x (* -1/2 (fabs (- x y))))
(* 1/2 (pow x 2))
(+ (* -1 (* x y)) (* 1/2 (pow x 2)))
(+ (* 1/2 (pow x 2)) (* y (+ (* -1 x) (* 1/2 y))))
(+ (* 1/2 (pow x 2)) (* y (+ (* -1 x) (* 1/2 y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(* -1/4 (/ (pow y 2) (+ x (* -1/2 (fabs (- x y))))))
(* (pow y 2) (- (* 1/2 (/ x (* y (+ x (* -1/2 (fabs (- x y))))))) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (- x y))))))))
(* (pow y 2) (- (+ (* -1/4 (/ (pow x 2) (* (pow y 2) (+ x (* -1/2 (fabs (- x y))))))) (+ (* 1/2 (/ x (* y (+ x (* -1/2 (fabs (- x y))))))) (/ (pow x 2) (* (pow y 2) (+ x (* -1/2 (fabs (- x y)))))))) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (- x y))))))))
(* (pow y 2) (- (+ (* -1/4 (/ (pow x 2) (* (pow y 2) (+ x (* -1/2 (fabs (- x y))))))) (+ (* 1/2 (/ x (* y (+ x (* -1/2 (fabs (- x y))))))) (/ (pow x 2) (* (pow y 2) (+ x (* -1/2 (fabs (- x y)))))))) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (- x y))))))))
(* -1/2 y)
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1/4 (/ (pow y 2) (+ x (* -1/2 (fabs (- x y))))))
(* (pow y 2) (- (* 1/2 (/ x (* y (+ x (* -1/2 (fabs (- x y))))))) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (- x y))))))))
(* (pow y 2) (- (+ (* -1/4 (/ (pow x 2) (* (pow y 2) (+ x (* -1/2 (fabs (- x y))))))) (+ (* 1/2 (/ x (* y (+ x (* -1/2 (fabs (- x y))))))) (/ (pow x 2) (* (pow y 2) (+ x (* -1/2 (fabs (- x y)))))))) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (- x y))))))))
(* (pow y 2) (- (+ (* -1/4 (/ (pow x 2) (* (pow y 2) (+ x (* -1/2 (fabs (- x y))))))) (+ (* 1/2 (/ x (* y (+ x (* -1/2 (fabs (- x y))))))) (/ (pow x 2) (* (pow y 2) (+ x (* -1/2 (fabs (- x y)))))))) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (- x y))))))))
(* -1/4 (pow y 2))
(* (pow y 2) (- (* 1/2 (/ x y)) 1/4))
(* (pow y 2) (- (+ (* -1/4 (/ (pow x 2) (pow y 2))) (+ (* 1/2 (/ x y)) (/ (pow x 2) (pow y 2)))) 1/4))
(* (pow y 2) (- (+ (* -1/4 (/ (pow x 2) (pow y 2))) (+ (* 1/2 (/ x y)) (/ (pow x 2) (pow y 2)))) 1/4))
(pow y 2)
(* (pow y 2) (+ 1 (* -2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* -2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (* -2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* -1 (* y (pow (sqrt 1/2) 2)))
(* y (+ (* -1 (pow (sqrt 1/2) 2)) (+ (/ x y) (/ (* x (pow (sqrt 1/2) 2)) y))))
(* y (+ (* -1 (pow (sqrt 1/2) 2)) (+ (/ x y) (/ (* x (pow (sqrt 1/2) 2)) y))))
(* y (+ (* -1 (pow (sqrt 1/2) 2)) (+ (/ x y) (/ (* x (pow (sqrt 1/2) 2)) y))))
(* -1 (* y (sqrt 1/2)))
(* y (+ (* -1 (sqrt 1/2)) (/ (* x (sqrt 1/2)) y)))
(* y (+ (* -1 (sqrt 1/2)) (/ (* x (sqrt 1/2)) y)))
(* y (+ (* -1 (sqrt 1/2)) (/ (* x (sqrt 1/2)) y)))
(* -1/2 y)
(* y (- (* 1/2 (/ x y)) 1/2))
(* y (- (* 1/2 (/ x y)) 1/2))
(* y (- (* 1/2 (/ x y)) 1/2))
(+ x (* -1/2 (fabs (- x y))))
(+ x (* -1/2 (fabs (- x y))))
(+ x (* -1/2 (fabs (- x y))))
(+ x (* -1/2 (fabs (- x y))))
(* 1/2 (pow y 2))
(* (pow y 2) (+ 1/2 (* -1 (/ x y))))
(* (pow y 2) (+ 1/2 (+ (* -1 (/ x y)) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* (pow y 2) (+ 1/2 (+ (* -1 (/ x y)) (* 1/2 (/ (pow x 2) (pow y 2))))))
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(* -1/4 (/ (pow y 2) (+ x (* -1/2 (fabs (+ x (* -1 y)))))))
(* (pow y 2) (- (* 1/2 (/ x (* y (+ x (* -1/2 (fabs (+ x (* -1 y)))))))) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (+ x (* -1 y)))))))))
(* (pow y 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (+ x (* -1 y))))))) (/ (pow x 2) (+ x (* -1/2 (fabs (+ x (* -1 y))))))) y)) (* -1/2 (/ x (+ x (* -1/2 (fabs (+ x (* -1 y)))))))) y)) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (+ x (* -1 y)))))))))
(* (pow y 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (+ x (* -1 y))))))) (/ (pow x 2) (+ x (* -1/2 (fabs (+ x (* -1 y))))))) y)) (* -1/2 (/ x (+ x (* -1/2 (fabs (+ x (* -1 y)))))))) y)) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (+ x (* -1 y)))))))))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1/4 (/ (pow y 2) (+ x (* -1/2 (fabs (+ x (* -1 y)))))))
(* (pow y 2) (- (* 1/2 (/ x (* y (+ x (* -1/2 (fabs (+ x (* -1 y)))))))) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (+ x (* -1 y)))))))))
(* (pow y 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (+ x (* -1 y))))))) (/ (pow x 2) (+ x (* -1/2 (fabs (+ x (* -1 y))))))) y)) (* -1/2 (/ x (+ x (* -1/2 (fabs (+ x (* -1 y)))))))) y)) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (+ x (* -1 y)))))))))
(* (pow y 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow x 2) (+ x (* -1/2 (fabs (+ x (* -1 y))))))) (/ (pow x 2) (+ x (* -1/2 (fabs (+ x (* -1 y))))))) y)) (* -1/2 (/ x (+ x (* -1/2 (fabs (+ x (* -1 y)))))))) y)) (* 1/4 (/ 1 (+ x (* -1/2 (fabs (+ x (* -1 y)))))))))
(* -1/4 (pow y 2))
(* (pow y 2) (- (* 1/2 (/ x y)) 1/4))
(* (pow y 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (pow x 2)) (pow x 2)) y)) (* -1/2 x)) y)) 1/4))
(* (pow y 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (pow x 2)) (pow x 2)) y)) (* -1/2 x)) y)) 1/4))
(pow y 2)
(* (pow y 2) (+ 1 (* -2 (/ x y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (/ (pow x 2) y)) (* 2 x)) y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (/ (pow x 2) y)) (* 2 x)) y))))
(* -1 (* y (pow (sqrt 1/2) 2)))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* y (sqrt 1/2)))
(* -1 (* y (+ (sqrt 1/2) (* -1 (/ (* x (sqrt 1/2)) y)))))
(* -1 (* y (+ (sqrt 1/2) (* -1 (/ (* x (sqrt 1/2)) y)))))
(* -1 (* y (+ (sqrt 1/2) (* -1 (/ (* x (sqrt 1/2)) y)))))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))
(* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))
(* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))
(+ x (* -1/2 (fabs (+ x (* -1 y)))))
(+ x (* -1/2 (fabs (+ x (* -1 y)))))
(+ x (* -1/2 (fabs (+ x (* -1 y)))))
(+ x (* -1/2 (fabs (+ x (* -1 y)))))
(* 1/2 (pow y 2))
(* (pow y 2) (+ 1/2 (* -1 (/ x y))))
(* (pow y 2) (+ 1/2 (* -1 (/ (+ x (* -1/2 (/ (pow x 2) y))) y))))
(* (pow y 2) (+ 1/2 (* -1 (/ (+ x (* -1/2 (/ (pow x 2) y))) y))))
1/2
1/2
1/2
1/2
(* 1/2 (fabs (- x y)))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(* 1/2 (fabs (- y x)))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(* 1/2 (/ (pow y 2) (fabs (- x y))))
(+ (* 1/2 (/ (pow y 2) (fabs (- x y)))) (* x (- (* -1 (/ y (fabs (- x y)))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2))))))
(+ (* 1/2 (/ (pow y 2) (fabs (- x y)))) (* x (- (+ (* -1 (* x (+ (* -2 (/ (- (* -1 (/ y (fabs (- x y)))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2)))) (fabs (- x y)))) (* 3/2 (/ 1 (fabs (- x y))))))) (* -1 (/ y (fabs (- x y))))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2))))))
(+ (* 1/2 (/ (pow y 2) (fabs (- x y)))) (* x (- (+ (* -1 (/ y (fabs (- x y)))) (* x (- (* -2 (/ (* x (+ (* -2 (/ (- (* -1 (/ y (fabs (- x y)))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2)))) (fabs (- x y)))) (* 3/2 (/ 1 (fabs (- x y)))))) (fabs (- x y)))) (+ (* -2 (/ (- (* -1 (/ y (fabs (- x y)))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2)))) (fabs (- x y)))) (* 3/2 (/ 1 (fabs (- x y)))))))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2))))))
(* 3/4 x)
(* 3/4 x)
(* 3/4 x)
(* 3/4 x)
(* -1/2 y)
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(* -1 y)
(- x y)
(- x y)
(- x y)
(* 1/2 (/ (pow y 2) (fabs (- x y))))
(+ (* 1/2 (/ (pow y 2) (fabs (- x y)))) (* x (- (* -1 (/ y (fabs (- x y)))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2))))))
(+ (* 1/2 (/ (pow y 2) (fabs (- x y)))) (* x (- (+ (* -1 (* x (+ (* -2 (/ (- (* -1 (/ y (fabs (- x y)))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2)))) (fabs (- x y)))) (* 3/2 (/ 1 (fabs (- x y))))))) (* -1 (/ y (fabs (- x y))))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2))))))
(+ (* 1/2 (/ (pow y 2) (fabs (- x y)))) (* x (- (+ (* -1 (/ y (fabs (- x y)))) (* x (- (* -2 (/ (* x (+ (* -2 (/ (- (* -1 (/ y (fabs (- x y)))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2)))) (fabs (- x y)))) (* 3/2 (/ 1 (fabs (- x y)))))) (fabs (- x y)))) (+ (* -2 (/ (- (* -1 (/ y (fabs (- x y)))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2)))) (fabs (- x y)))) (* 3/2 (/ 1 (fabs (- x y)))))))) (* -1 (/ (pow y 2) (pow (fabs (- x y)) 2))))))
(* -1/4 (pow y 2))
(+ (* -1/4 (pow y 2)) (* 1/2 (* x y)))
(+ (* -1/4 (pow y 2)) (* x (+ (* 1/2 y) (* 3/4 x))))
(+ (* -1/4 (pow y 2)) (* x (+ (* 1/2 y) (* 3/4 x))))
(pow y 2)
(+ (* -2 (* x y)) (pow y 2))
(+ (* x (+ x (* -2 y))) (pow y 2))
(+ (* x (+ x (* -2 y))) (pow y 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* y (pow (sqrt 1/2) 2)))
(+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (+ 1 (pow (sqrt 1/2) 2))))
(+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (+ 1 (pow (sqrt 1/2) 2))))
(+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (+ 1 (pow (sqrt 1/2) 2))))
(* -1 (* y (sqrt 1/2)))
(+ (* -1 (* y (sqrt 1/2))) (* x (sqrt 1/2)))
(+ (* -1 (* y (sqrt 1/2))) (* x (sqrt 1/2)))
(+ (* -1 (* y (sqrt 1/2))) (* x (sqrt 1/2)))
(* -1/2 y)
(+ (* -1/2 y) (* 1/2 x))
(+ (* -1/2 y) (* 1/2 x))
(+ (* -1/2 y) (* 1/2 x))
(* -1/2 (fabs (- x y)))
(+ x (* -1/2 (fabs (- x y))))
(+ x (* -1/2 (fabs (- x y))))
(+ x (* -1/2 (fabs (- x y))))
(* 1/2 (pow y 2))
(+ (* -1 (* x y)) (* 1/2 (pow y 2)))
(+ (* 1/2 (pow y 2)) (* x (+ (* -1 y) (* 1/2 x))))
(+ (* 1/2 (pow y 2)) (* x (+ (* -1 y) (* 1/2 x))))
1/2
1/2
1/2
1/2
x
(* x (+ 1 (* 1/2 (/ (fabs (- x y)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- x y)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- x y)) x))))
x
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(* 3/4 x)
(* x (- (+ 3/4 (* 1/2 (/ y x))) (* -3/8 (/ (fabs (- x y)) x))))
(* x (- (+ 3/4 (+ (* -1/4 (/ (pow y 2) (pow x 2))) (* 1/2 (/ y x)))) (+ (* -1/2 (/ (* (fabs (- x y)) (- (* 1/2 y) (* -3/8 (fabs (- x y))))) (pow x 2))) (* -3/8 (/ (fabs (- x y)) x)))))
(* x (- (+ 3/4 (+ (* -1/4 (/ (pow y 2) (pow x 2))) (+ (* 1/2 (/ y x)) (* 1/2 (/ (* (fabs (- x y)) (- (* -1/4 (pow y 2)) (* -1/2 (* (fabs (- x y)) (- (* 1/2 y) (* -3/8 (fabs (- x y)))))))) (pow x 3)))))) (+ (* -1/2 (/ (* (fabs (- x y)) (- (* 1/2 y) (* -3/8 (fabs (- x y))))) (pow x 2))) (* -3/8 (/ (fabs (- x y)) x)))))
(* 3/4 x)
(* 3/4 x)
(* 3/4 x)
(* 3/4 x)
(* 3/2 x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(* x (+ 3/2 (* -1/2 (/ y x))))
(* x (+ 3/2 (* -1/2 (/ y x))))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* 3/4 x)
(* x (- (+ 3/4 (* 1/2 (/ y x))) (* -3/8 (/ (fabs (- x y)) x))))
(* x (- (+ 3/4 (+ (* -1/4 (/ (pow y 2) (pow x 2))) (* 1/2 (/ y x)))) (+ (* -1/2 (/ (* (fabs (- x y)) (- (* 1/2 y) (* -3/8 (fabs (- x y))))) (pow x 2))) (* -3/8 (/ (fabs (- x y)) x)))))
(* x (- (+ 3/4 (+ (* -1/4 (/ (pow y 2) (pow x 2))) (+ (* 1/2 (/ y x)) (* 1/2 (/ (* (fabs (- x y)) (- (* -1/4 (pow y 2)) (* -1/2 (* (fabs (- x y)) (- (* 1/2 y) (* -3/8 (fabs (- x y)))))))) (pow x 3)))))) (+ (* -1/2 (/ (* (fabs (- x y)) (- (* 1/2 y) (* -3/8 (fabs (- x y))))) (pow x 2))) (* -3/8 (/ (fabs (- x y)) x)))))
(* 3/4 (pow x 2))
(* (pow x 2) (+ 3/4 (* 1/2 (/ y x))))
(* (pow x 2) (+ 3/4 (+ (* -1/4 (/ (pow y 2) (pow x 2))) (* 1/2 (/ y x)))))
(* (pow x 2) (+ 3/4 (+ (* -1/4 (/ (pow y 2) (pow x 2))) (* 1/2 (/ y x)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* -2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (+ 1 (pow (sqrt 1/2) 2)))
(* x (+ 1 (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2))))
(* x (+ 1 (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2))))
(* x (+ 1 (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* -1 (/ (* y (sqrt 1/2)) x))))
(* x (+ (sqrt 1/2) (* -1 (/ (* y (sqrt 1/2)) x))))
(* x (+ (sqrt 1/2) (* -1 (/ (* y (sqrt 1/2)) x))))
(* 1/2 x)
(* x (+ 1/2 (* -1/2 (/ y x))))
(* x (+ 1/2 (* -1/2 (/ y x))))
(* x (+ 1/2 (* -1/2 (/ y x))))
x
(* x (+ 1 (* -1/2 (/ (fabs (- x y)) x))))
(* x (+ 1 (* -1/2 (/ (fabs (- x y)) x))))
(* x (+ 1 (* -1/2 (/ (fabs (- x y)) x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1 (/ y x))))
(* (pow x 2) (+ 1/2 (+ (* -1 (/ y x)) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* (pow x 2) (+ 1/2 (+ (* -1 (/ y x)) (* 1/2 (/ (pow y 2) (pow x 2))))))
1/2
1/2
1/2
1/2
x
(* -1 (* x (- (* -1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
x
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(* 3/4 x)
(* -1 (* x (- (* -1 (/ (- (* 1/2 y) (* -3/8 (fabs (neg (+ y (* -1 x)))))) x)) 3/4)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (pow y 2)) (* 1/2 (* (fabs (neg (+ y (* -1 x)))) (- (* 1/2 y) (* -3/8 (fabs (neg (+ y (* -1 x))))))))) x)) (* 1/2 y)) (* -3/8 (fabs (neg (+ y (* -1 x)))))) x)) 3/4)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/4 (pow y 2)) (* 1/2 (/ (* (fabs (neg (+ y (* -1 x)))) (- (* 1/4 (pow y 2)) (* 1/2 (* (fabs (neg (+ y (* -1 x)))) (- (* 1/2 y) (* -3/8 (fabs (neg (+ y (* -1 x)))))))))) x))) (* 1/2 (* (fabs (neg (+ y (* -1 x)))) (- (* 1/2 y) (* -3/8 (fabs (neg (+ y (* -1 x))))))))) x)) (* 1/2 y)) (* -3/8 (fabs (neg (+ y (* -1 x)))))) x)) 3/4)))
(* 3/4 x)
(* 3/4 x)
(* 3/4 x)
(* 3/4 x)
(* 3/2 x)
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* 3/4 x)
(* -1 (* x (- (* -1 (/ (- (* 1/2 y) (* -3/8 (fabs (neg (+ y (* -1 x)))))) x)) 3/4)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (pow y 2)) (* 1/2 (* (fabs (neg (+ y (* -1 x)))) (- (* 1/2 y) (* -3/8 (fabs (neg (+ y (* -1 x))))))))) x)) (* 1/2 y)) (* -3/8 (fabs (neg (+ y (* -1 x)))))) x)) 3/4)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/4 (pow y 2)) (* 1/2 (/ (* (fabs (neg (+ y (* -1 x)))) (- (* 1/4 (pow y 2)) (* 1/2 (* (fabs (neg (+ y (* -1 x)))) (- (* 1/2 y) (* -3/8 (fabs (neg (+ y (* -1 x)))))))))) x))) (* 1/2 (* (fabs (neg (+ y (* -1 x)))) (- (* 1/2 y) (* -3/8 (fabs (neg (+ y (* -1 x))))))))) x)) (* 1/2 y)) (* -3/8 (fabs (neg (+ y (* -1 x)))))) x)) 3/4)))
(* 3/4 (pow x 2))
(* (pow x 2) (+ 3/4 (* 1/2 (/ y x))))
(* (pow x 2) (+ 3/4 (* -1 (/ (+ (* -1/2 y) (* 1/4 (/ (pow y 2) x))) x))))
(* (pow x 2) (+ 3/4 (* -1 (/ (+ (* -1/2 y) (* 1/4 (/ (pow y 2) x))) x))))
(pow x 2)
(* (pow x 2) (+ 1 (* -2 (/ y x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (/ (pow y 2) x)) (* 2 y)) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (/ (pow y 2) x)) (* 2 y)) x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* x (- (pow (sqrt 1/2) 2) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2)) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2)) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2)) 1)))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (* y (sqrt 1/2)) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (* y (sqrt 1/2)) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (* y (sqrt 1/2)) x)))))
(* 1/2 x)
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
x
(* -1 (* x (- (* 1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
(* -1 (* x (- (* 1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
(* -1 (* x (- (* 1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1 (/ y x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (+ y (* -1/2 (/ (pow y 2) x))) x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (+ y (* -1/2 (/ (pow y 2) x))) x))))

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

rewrite190.0ms (2.4%)

Memory

39.0MiB live, 261.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	170
0	64	169
1	224	169
2	1617	136
0	9201	135

Stop Event

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

Counts

18 → 702

Calls

Call 1

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

Outputs
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eval340.0ms (4.4%)

Memory: 4.4MiB live, 477.7MiB allocated
Compiler: Compiled 33 065 to 3 326 computations (89.9% saved)

prune38.0ms (0.5%)

Memory

-4.9MiB live, 117.1MiB allocated

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	1 472	6	1 478
Fresh	6	2	8
Picked	4	1	5
Done	0	1	1
Total	1 482	10	1 492

Accuracy

100.0%

Counts

1 492 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.6%	(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)
✓	99.9%	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
▶	56.9%	(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)
	35.9%	(fma.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 1/2 binary64) x)
	54.6%	#s(approx (+ (* (- x y) 1/2) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))
▶	28.8%	#s(approx (+ (* (- x y) 1/2) x) (*.f64 #s(literal 3/2 binary64) x))
	27.7%	#s(approx (+ (* (- x y) 1/2) x) (*.f64 #s(literal -1/2 binary64) y))
▶	50.8%	#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64)) x))
▶	33.5%	#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 #s(literal 1/2 binary64) x))
▶	6.9%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))

Compiler

Compiled 109 to 111 computations (-1.8% saved)

simplify168.0ms (2.2%)

Memory

-17.4MiB live, 195.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64)) x))
cost-diff	896	(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (- y x) (neg.f64 x))
cost-diff	0	(fabs.f64 #s(approx (- y x) (neg.f64 x)))
cost-diff	0	(*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 #s(literal 3/2 binary64) x)
cost-diff	0	#s(approx (+ (* (- x y) 1/2) x) (*.f64 #s(literal 3/2 binary64) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(neg.f64 y)
cost-diff	0	#s(approx (- x y) (neg.f64 y))
cost-diff	0	(fabs.f64 #s(approx (- x y) (neg.f64 y)))
cost-diff	0	(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	156
0	48	156
1	75	156
2	112	156
3	237	156
4	751	150
5	1387	150
6	2683	150
7	7321	150
0	8086	146

Stop Event

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

Calls

Call 1

Inputs
(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)
(fabs.f64 #s(approx (- x y) (neg.f64 y)))
#s(approx (- x y) (neg.f64 y))
(neg.f64 y)
y
#s(literal 1/2 binary64)
x
#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (+ (* (- x y) 1/2) x) (*.f64 #s(literal 3/2 binary64) x))
(*.f64 #s(literal 3/2 binary64) x)
#s(literal 3/2 binary64)
x
#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64))
(fabs.f64 #s(approx (- y x) (neg.f64 x)))
#s(approx (- y x) (neg.f64 x))
(neg.f64 x)
x
#s(literal 1/2 binary64)
#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64)) x)
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
y

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

localize145.0ms (1.9%)

Memory

16.8MiB live, 143.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.09375	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64))
accuracy	5.908563731831584	(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64)) x)
accuracy	28.664858604216196	#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64)) x))
accuracy	0	(neg.f64 x)
accuracy	0	(fabs.f64 #s(approx (- y x) (neg.f64 x)))
accuracy	31.217819531326995	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))
accuracy	31.287823917704426	#s(approx (- y x) (neg.f64 x))
accuracy	0	(*.f64 #s(literal 3/2 binary64) x)
accuracy	31.314942876374687	#s(approx (+ (* (- x y) 1/2) x) (*.f64 #s(literal 3/2 binary64) x))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	42.532417947819305	#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0	(neg.f64 y)
accuracy	0	(fabs.f64 #s(approx (- x y) (neg.f64 y)))
accuracy	0.046875	(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)
accuracy	32.79879229270938	#s(approx (- x y) (neg.f64 y))

Samples

111.0ms	223×	0	valid
9.0ms	17×	2	valid
4.0ms	12×	1	valid
3.0ms	4×	3	valid

Compiler

Compiled 116 to 32 computations (72.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-mult: 16.0ms (37.9% of total)

ival-add: 7.0ms (16.6% of total)

ival-sqrt: 4.0ms (9.5% of total)

ival-div: 4.0ms (9.5% of total)

adjust: 3.0ms (7.1% of total)

ival-sub: 3.0ms (7.1% of total)

ival-fabs: 3.0ms (7.1% of total)

ival-neg: 2.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series26.0ms (0.3%)

Memory

-25.5MiB live, 47.3MiB allocated

Counts

17 → 348

Calls

Call 1

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

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

Calls

6 calls:

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

simplify201.0ms (2.6%)

Memory

30.7MiB live, 262.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	141	2205
1	405	1642
2	1121	1642
3	3562	1642
0	8066	1534

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 338

Calls

Call 1

Inputs
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(+ x (* x (pow (sqrt 1/2) 2)))
(+ x (+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (pow (sqrt 1/2) 2))))
(+ x (+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (pow (sqrt 1/2) 2))))
(+ x (+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (pow (sqrt 1/2) 2))))
(+ x (* 1/2 x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(* -1 x)
(- y x)
(- y x)
(- y x)
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(+ x (* x (pow (sqrt 1/2) 2)))
(+ x (+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (pow (sqrt 1/2) 2))))
(+ x (+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (pow (sqrt 1/2) 2))))
(+ x (+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (pow (sqrt 1/2) 2))))
1/2
(+ 1/2 (* 1/2 (/ y x)))
(+ 1/2 (* 1/2 (/ y x)))
(+ 1/2 (* 1/2 (/ y x)))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 (* y (pow (sqrt 1/2) 2)))
(* y (+ (* -1 (pow (sqrt 1/2) 2)) (+ (/ x y) (/ (* x (pow (sqrt 1/2) 2)) y))))
(* y (+ (* -1 (pow (sqrt 1/2) 2)) (+ (/ x y) (/ (* x (pow (sqrt 1/2) 2)) y))))
(* y (+ (* -1 (pow (sqrt 1/2) 2)) (+ (/ x y) (/ (* x (pow (sqrt 1/2) 2)) y))))
(* -1/2 y)
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* 1/2 y)
(* y (+ 1/2 (* 1/2 (/ x y))))
(* y (+ 1/2 (* 1/2 (/ x y))))
(* y (+ 1/2 (* 1/2 (/ x y))))
(* -1 (* y (pow (sqrt 1/2) 2)))
(* y (+ (* -1 (pow (sqrt 1/2) 2)) (+ (/ x y) (/ (* x (pow (sqrt 1/2) 2)) y))))
(* y (+ (* -1 (pow (sqrt 1/2) 2)) (+ (/ x y) (/ (* x (pow (sqrt 1/2) 2)) y))))
(* y (+ (* -1 (pow (sqrt 1/2) 2)) (+ (/ x y) (/ (* x (pow (sqrt 1/2) 2)) y))))
(* 1/2 (/ y x))
(* y (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* y (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* y (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 (* y (pow (sqrt 1/2) 2)))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(* 1/2 (fabs (neg (+ x (* -1 y)))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
(fabs (neg (+ x (* -1 y))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* 1/2 y)
(* -1 (* y (- (* -1/2 (/ x y)) 1/2)))
(* -1 (* y (- (* -1/2 (/ x y)) 1/2)))
(* -1 (* y (- (* -1/2 (/ x y)) 1/2)))
(* -1 (* y (pow (sqrt 1/2) 2)))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* 1/2 (/ y x))
(* y (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* y (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* y (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))
(* 1/2 (fabs (- x y)))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(+ x (* 1/2 (fabs (- x y))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(* -1 y)
(- x y)
(- x y)
(- x y)
(* -1 (* y (pow (sqrt 1/2) 2)))
(+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (+ 1 (pow (sqrt 1/2) 2))))
(+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (+ 1 (pow (sqrt 1/2) 2))))
(+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (+ 1 (pow (sqrt 1/2) 2))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -1/2 y)
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 1/2 (fabs (- y x)))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(+ x (* 1/2 (fabs (- y x))))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(* 1/2 y)
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(+ (* 1/2 x) (* 1/2 y))
(* -1 (* y (pow (sqrt 1/2) 2)))
(+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (+ 1 (pow (sqrt 1/2) 2))))
(+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (+ 1 (pow (sqrt 1/2) 2))))
(+ (* -1 (* y (pow (sqrt 1/2) 2))) (* x (+ 1 (pow (sqrt 1/2) 2))))
(* 1/2 (/ y x))
(/ (+ (* 1/2 x) (* 1/2 y)) x)
(/ (+ (* 1/2 x) (* 1/2 y)) x)
(/ (+ (* 1/2 x) (* 1/2 y)) x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
x
(* x (+ 1 (* 1/2 (/ (fabs (- x y)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- x y)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- x y)) x))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (pow (sqrt 1/2) 2)))
(* x (+ 1 (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2))))
(* x (+ 1 (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2))))
(* x (+ 1 (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 3/2 x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(* x (+ 3/2 (* -1/2 (/ y x))))
(* x (+ 3/2 (* -1/2 (/ y x))))
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
x
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(* 1/2 (fabs (- y x)))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(fabs (- y x))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1/2 (* 1/2 (/ y x))))
(* x (+ 1 (pow (sqrt 1/2) 2)))
(* x (+ 1 (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2))))
(* x (+ 1 (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2))))
(* x (+ 1 (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2))))
1/2
(+ 1/2 (* 1/2 (/ y x)))
(+ 1/2 (* 1/2 (/ y x)))
(+ 1/2 (* 1/2 (/ y x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
x
(* -1 (* x (- (* -1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (pow (sqrt 1/2) 2) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2)) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2)) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2)) 1)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 3/2 x)
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
x
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* 1/2 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (+ y (* -1 x))))
(* 1/2 (fabs (+ y (* -1 x))))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(fabs (+ y (* -1 x)))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (* -1/2 (/ y x)) 1/2)))
(* -1 (* x (- (pow (sqrt 1/2) 2) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2)) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2)) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt 1/2) 2)) x)) (pow (sqrt 1/2) 2)) 1)))
1/2
(+ 1/2 (* 1/2 (/ y x)))
(+ 1/2 (* 1/2 (/ y x)))
(+ 1/2 (* 1/2 (/ y x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)

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

rewrite277.0ms (3.6%)

Memory

-31.4MiB live, 332.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	144
0	48	142
1	180	134
2	1247	127
0	8712	123

Stop Event

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

Counts

17 → 203

Calls

Call 1

Inputs
(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)
(fabs.f64 #s(approx (- x y) (neg.f64 y)))
#s(approx (- x y) (neg.f64 y))
(neg.f64 y)
#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (+ (* (- x y) 1/2) x) (*.f64 #s(literal 3/2 binary64) x))
(*.f64 #s(literal 3/2 binary64) x)
#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64))
(fabs.f64 #s(approx (- y x) (neg.f64 x)))
#s(approx (- y x) (neg.f64 x))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64)) x)
#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64)) x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) x)
(neg.f64 x)

Outputs
#<batchref>
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#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval94.0ms (1.2%)

Memory: 38.1MiB live, 117.8MiB allocated
Compiler: Compiled 6 418 to 816 computations (87.3% saved)

prune23.0ms (0.3%)

Memory

-5.6MiB live, 67.2MiB allocated

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	539	2	541
Fresh	0	3	3
Picked	3	2	5
Done	1	1	2
Total	543	8	551

Accuracy

100.0%

Counts

551 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.6%	(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)
	35.9%	(fma.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 1/2 binary64) x)
	54.6%	#s(approx (+ (* (- x y) 1/2) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))
✓	28.8%	#s(approx (+ (* (- x y) 1/2) x) (*.f64 #s(literal 3/2 binary64) x))
	27.7%	#s(approx (+ (* (- x y) 1/2) x) (*.f64 #s(literal -1/2 binary64) y))
	55.2%	#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))
✓	33.5%	#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 #s(literal 1/2 binary64) x))
	23.5%	#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 y #s(literal 1/2 binary64))))

Compiler

Compiled 338 to 147 computations (56.5% saved)

regimes42.0ms (0.5%)

Memory

-0.4MiB live, 36.8MiB allocated

Counts

29 → 1

Calls

Call 1

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

Outputs
(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)

Calls

3 calls:

23.0ms	y
9.0ms	x
9.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes25.0ms (0.3%)

Memory

-26.8MiB live, 19.2MiB allocated

Counts

13 → 3

Calls

Call 1

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

Outputs

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

(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)

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

Calls

3 calls:

15.0ms	x
5.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
5.0ms	y

Results

Accuracy	Segments	Branch
88.8%	3	`x`
81.7%	3	`y`
86.6%	5	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes5.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

12 → 3

Calls

Call 1

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

Outputs

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

(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)

(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
88.8%	3	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes5.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

11 → 3

Calls

Call 1

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

Outputs

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

#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)))

(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
88.4%	3	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes40.0ms (0.5%)

Memory

-12.0MiB live, 26.0MiB allocated

Counts

10 → 3

Calls

Call 1

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

Outputs

#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (-.f64 x y) #s(literal 1/2 binary64)))

(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)

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

Calls

3 calls:

32.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
4.0ms	x
4.0ms	y

Results

Accuracy	Segments	Branch
81.7%	3	`y`
78.9%	2	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
81.0%	4	`x`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes4.0ms (0.1%)

Memory

8.6MiB live, 8.6MiB allocated

Counts

9 → 3

Calls

Call 1

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

Outputs

#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (-.f64 x y) #s(literal 1/2 binary64)))

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
81.3%	3	`y`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes9.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs

#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (-.f64 x y) #s(literal 1/2 binary64)))

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

Calls

3 calls:

3.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
69.1%	3	`x`
61.5%	3	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
67.7%	2	`y`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes30.0ms (0.4%)

Memory

-25.9MiB live, 12.4MiB allocated

Counts

5 → 4

Calls

Call 1

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

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

Calls

2 calls:

27.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
64.4%	4	`x`
59.9%	4	`y`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes6.0ms (0.1%)

Memory

17.0MiB live, 17.0MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

Calls

3 calls:

2.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
58.1%	3	`y`
58.9%	4	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
49.5%	2	`x`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes4.0ms (0%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs

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

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

Outputs

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

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

Calls

2 calls:

2.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
2.0ms	y

Results

Accuracy	Segments	Branch
50.1%	2	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
43.5%	2	`y`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes7.0ms (0.1%)

Memory

-22.6MiB live, 13.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
23.5%	1	`y`
23.5%	1	`x`
23.5%	1	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

bsearch52.0ms (0.7%)

Memory

-20.2MiB live, 73.7MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
37.0ms	2.354131113729128e-35	1.5319428654725712e-33
11.0ms	-4.623327282508322e-127	-5.860467083346999e-130

Samples

25.0ms	234×	0	valid
1.0ms	6×	1	valid

Compiler

Compiled 213 to 244 computations (-14.6% saved)

Precisions

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

ival-fabs: 16.0ms (78.2% of total)

ival-div: 2.0ms (9.8% of total)

ival-add: 1.0ms (4.9% of total)

ival-sub: 1.0ms (4.9% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.354131113729128e-35	1.5319428654725712e-33
1.0ms	-4.623327282508322e-127	-5.860467083346999e-130

Compiler

Compiled 206 to 230 computations (-11.7% saved)

bsearch13.0ms (0.2%)

Memory

-4.8MiB live, 33.4MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
2.0ms	2.354131113729128e-35	1.5319428654725712e-33
10.0ms	-4.623327282508322e-127	-5.860467083346999e-130

Samples

5.0ms

112×

valid

Compiler

Compiled 206 to 230 computations (-11.7% saved)

Precisions

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

ival-sub: 1.0ms (37.4% of total)

ival-div: 1.0ms (37.4% of total)

ival-fabs: 1.0ms (37.4% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch45.0ms (0.6%)

Memory

24.7MiB live, 63.7MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	4.72083461770378e-273	2.7934915919820752e-269
30.0ms	-1.3054446860827693e-254	-6.635458282069749e-258

Samples

19.0ms	8×	3	valid
11.0ms	234×	0	valid
1.0ms	10×	2	valid
0.0ms	4×	1	valid

Compiler

Compiled 203 to 220 computations (-8.4% saved)

Precisions

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

ival-div: 2.0ms (25% of total)

ival-sub: 2.0ms (25% of total)

ival-fabs: 2.0ms (25% of total)

adjust: 1.0ms (12.5% of total)

ival-add: 1.0ms (12.5% of total)

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

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

exact: 0.0ms (0% of total)

bsearch38.0ms (0.5%)

Memory

6.5MiB live, 51.7MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
11.0ms	2.513251043371369e-298	1.1508103973747772e-294
24.0ms	-1.3054446860827693e-254	-6.635458282069749e-258

Samples

24.0ms	224×	0	valid
1.0ms	6×	3	valid
1.0ms	6×	2	valid
0.0ms	4×	1	valid

Compiler

Compiled 171 to 220 computations (-28.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-fabs: 15.0ms (72.6% of total)

ival-div: 2.0ms (9.7% of total)

ival-sub: 2.0ms (9.7% of total)

adjust: 1.0ms (4.8% of total)

ival-add: 1.0ms (4.8% of total)

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

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

exact: 0.0ms (0% of total)

bsearch18.0ms (0.2%)

Memory

-5.1MiB live, 32.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	9.269975063214028e+24	4.6374236292922e+34

Samples

10.0ms	159×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 121 to 152 computations (-25.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 1.0ms (25.8% of total)

ival-add: 1.0ms (25.8% of total)

ival-fabs: 1.0ms (25.8% of total)

ival-sub: 1.0ms (25.8% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

bsearch25.0ms (0.3%)

Memory

-22.9MiB live, 52.8MiB allocated

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
6.0ms	2.354131113729128e-35	1.5319428654725712e-33
13.0ms	8.595380074414842e-266	4.332284167046831e-259
1.0ms	-4.623327282508322e-127	-5.860467083346999e-130

Samples

11.0ms	203×	0	valid
0.0ms	4×	1	valid
0.0ms	1×	2	valid

Compiler

Compiled 219 to 316 computations (-44.3% saved)

Precisions

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

ival-div: 1.0ms (18.6% of total)

ival-sub: 1.0ms (18.6% of total)

ival-add: 1.0ms (18.6% of total)

ival-fabs: 1.0ms (18.6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

bsearch11.0ms (0.1%)

Memory

30.3MiB live, 30.4MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	9.269975063214028e+24	4.6374236292922e+34
8.0ms	-1.0273569599143354e-71	-1.9979614624438342e-72

Samples

4.0ms	91×	0	valid
0.0ms	3×	2	valid
0.0ms	2×	1	valid

Compiler

Compiled 149 to 214 computations (-43.6% saved)

Precisions

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

ival-div: 1.0ms (38.3% of total)

ival-sub: 1.0ms (38.3% of total)

ival-fabs: 1.0ms (38.3% of total)

adjust: 0.0ms (0% of total)

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

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

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

exact: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.261801265197587e-240	3.762852672864609e-234

Compiler

Compiled 11 to 12 computations (-9.1% saved)

simplify30.0ms (0.4%)

Memory

-19.7MiB live, 65.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	542
1	111	542
2	117	542
3	120	542
4	121	542

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
(if (<=.f64 x #s(literal -5609391926349049/24388660549343689307668728357759111763660922989570087116087163747073216709529418907189891430183531024686147899385989241370687309994439728955392 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 (+.f64 y x) #s(literal 1/2 binary64))) (if (<=.f64 x #s(literal 2151330410151089/46768052394588893382517914646921056628989841375232 binary64)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x) #s(approx (+ ( (- x y) 1/2) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))))
(if (<=.f64 x #s(literal -5609391926349049/24388660549343689307668728357759111763660922989570087116087163747073216709529418907189891430183531024686147899385989241370687309994439728955392 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (if (<=.f64 x #s(literal 2151330410151089/46768052394588893382517914646921056628989841375232 binary64)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)))
(if (<=.f64 x #s(literal -4370447970442389/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 (+.f64 y x) #s(literal 1/2 binary64))) (if (<=.f64 x #s(literal 2151330410151089/46768052394588893382517914646921056628989841375232 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64))) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)))
(if (<=.f64 y #s(literal -6339534373627983/528294531135665246352339784916516606518847326036121522127960709026673902556724859474417255887657187894674394993257128678882347559502685537250538978462939576908386683999005084168731517676426441053024232908211188404148028292751561738838396898767036476489538580897737998336 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (-.f64 x y) #s(literal 1/2 binary64))) (if (<=.f64 y #s(literal 404468599105957/2379227053564452900476899997039840896210016322655031134489234974905505051456646997672269303193850160943677958064308756880727336392871849132465328929763831401252753344715935798308298255734876378992382713251762299529708397931004608141051358304557852932819272168726630260518024558103494656 binary64)) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))))
(if (<=.f64 y #s(literal -3110598199326797/67621699985365151533099492469314125634412457732623554832378970755414259527260782012725408753620120050518322559136912470896940487616343748768068989243256265844273495551872650773597634262582584454787101812251032115730947621472199902571314803042180668990660938354910463787008 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (-.f64 x y) #s(literal 1/2 binary64))) (if (<=.f64 y #s(literal 5752618031559411/46020944252475287237870212884199033180620210660923048261998100776379565006208246561973370194536329221406749153247076699560650180816490655358168942243705375840708580716765564230733368217919000094579989235733761476822566574679670497657321756298451772713817730735254092349426494960250807374037851220383801379127296 binary64)) #s(approx (+ ( (- x y) 1/2) x) (.f64 #s(literal 3/2 binary64) x)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))))
(if (<=.f64 y #s(literal 2450000000000000073786195968 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (-.f64 x y) #s(literal 1/2 binary64))) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 y #s(literal 1/2 binary64)))))
(if (<=.f64 x #s(literal -4370447970442389/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 #s(literal 1/2 binary64) x)) (if (<=.f64 x #s(literal 7090649168385425/70906491683854249133971333415503528601229677279443476631916611638829262598057001759775558209235971002092300595769547131083230268742795262708226708464736682213924924871800416657575912944521796077262840069882938251784694133132833485038618990914757637167551284096438594475925700608 binary64)) #s(approx (+ ( (- x y) 1/2) x) (.f64 #s(literal -1/2 binary64) y)) (if (<=.f64 x #s(literal 4676805239458889/187072209578355573530071658587684226515959365500928 binary64)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ ( (- x y) 1/2) x) (*.f64 #s(literal 3/2 binary64) x)))))
(if (<=.f64 y #s(literal -55948864096101/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704 binary64)) #s(approx (+ (* (- x y) 1/2) x) (.f64 #s(literal -1/2 binary64) y)) (if (<=.f64 y #s(literal 2450000000000000073786195968 binary64)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 #s(literal 1/2 binary64) x)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 y #s(literal 1/2 binary64))))))
(if (<=.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1876879207201175/469219801800293764373197355969328553831984974596843971042368711922664472663701981746713137411270711303034626199044091413698918166643890203860091306664994072502482932661931411083539271868071588269998735494868914134645646190292788569954038367952474854129664 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 #s(literal 1/2 binary64) x)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 y #s(literal 1/2 binary64)))))
#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 y #s(literal 1/2 binary64))))

Outputs
(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
(fma.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64) x)
(if (<=.f64 x #s(literal -5609391926349049/24388660549343689307668728357759111763660922989570087116087163747073216709529418907189891430183531024686147899385989241370687309994439728955392 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 (+.f64 y x) #s(literal 1/2 binary64))) (if (<=.f64 x #s(literal 2151330410151089/46768052394588893382517914646921056628989841375232 binary64)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x) #s(approx (+ ( (- x y) 1/2) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))))
(if (<=.f64 x #s(literal -5609391926349049/24388660549343689307668728357759111763660922989570087116087163747073216709529418907189891430183531024686147899385989241370687309994439728955392 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (+.f64 y x) #s(literal 1/2 binary64))) (if (<=.f64 x #s(literal 2151330410151089/46768052394588893382517914646921056628989841375232 binary64)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)))
(if (<=.f64 x #s(literal -4370447970442389/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 (+.f64 y x) #s(literal 1/2 binary64))) (if (<=.f64 x #s(literal 2151330410151089/46768052394588893382517914646921056628989841375232 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64))) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)))
(if (<=.f64 y #s(literal -6339534373627983/528294531135665246352339784916516606518847326036121522127960709026673902556724859474417255887657187894674394993257128678882347559502685537250538978462939576908386683999005084168731517676426441053024232908211188404148028292751561738838396898767036476489538580897737998336 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (-.f64 x y) #s(literal 1/2 binary64))) (if (<=.f64 y #s(literal 404468599105957/2379227053564452900476899997039840896210016322655031134489234974905505051456646997672269303193850160943677958064308756880727336392871849132465328929763831401252753344715935798308298255734876378992382713251762299529708397931004608141051358304557852932819272168726630260518024558103494656 binary64)) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))))
(if (<=.f64 y #s(literal -6339534373627983/528294531135665246352339784916516606518847326036121522127960709026673902556724859474417255887657187894674394993257128678882347559502685537250538978462939576908386683999005084168731517676426441053024232908211188404148028292751561738838396898767036476489538580897737998336 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (if (<=.f64 y #s(literal 404468599105957/2379227053564452900476899997039840896210016322655031134489234974905505051456646997672269303193850160943677958064308756880727336392871849132465328929763831401252753344715935798308298255734876378992382713251762299529708397931004608141051358304557852932819272168726630260518024558103494656 binary64)) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))))
(if (<=.f64 y #s(literal -3110598199326797/67621699985365151533099492469314125634412457732623554832378970755414259527260782012725408753620120050518322559136912470896940487616343748768068989243256265844273495551872650773597634262582584454787101812251032115730947621472199902571314803042180668990660938354910463787008 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (-.f64 x y) #s(literal 1/2 binary64))) (if (<=.f64 y #s(literal 5752618031559411/46020944252475287237870212884199033180620210660923048261998100776379565006208246561973370194536329221406749153247076699560650180816490655358168942243705375840708580716765564230733368217919000094579989235733761476822566574679670497657321756298451772713817730735254092349426494960250807374037851220383801379127296 binary64)) #s(approx (+ ( (- x y) 1/2) x) (.f64 #s(literal 3/2 binary64) x)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))))
(if (<=.f64 y #s(literal -3110598199326797/67621699985365151533099492469314125634412457732623554832378970755414259527260782012725408753620120050518322559136912470896940487616343748768068989243256265844273495551872650773597634262582584454787101812251032115730947621472199902571314803042180668990660938354910463787008 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (if (<=.f64 y #s(literal 5752618031559411/46020944252475287237870212884199033180620210660923048261998100776379565006208246561973370194536329221406749153247076699560650180816490655358168942243705375840708580716765564230733368217919000094579989235733761476822566574679670497657321756298451772713817730735254092349426494960250807374037851220383801379127296 binary64)) #s(approx (+ ( (- x y) 1/2) x) (.f64 #s(literal 3/2 binary64) x)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (*.f64 (+.f64 y x) #s(literal 1/2 binary64)))))
(if (<=.f64 y #s(literal 2450000000000000073786195968 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (-.f64 x y) #s(literal 1/2 binary64))) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 y #s(literal 1/2 binary64)))))
(if (<=.f64 y #s(literal 2450000000000000073786195968 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 #s(literal 1/2 binary64) y))))
(if (<=.f64 x #s(literal -4370447970442389/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 #s(literal 1/2 binary64) x)) (if (<=.f64 x #s(literal 7090649168385425/70906491683854249133971333415503528601229677279443476631916611638829262598057001759775558209235971002092300595769547131083230268742795262708226708464736682213924924871800416657575912944521796077262840069882938251784694133132833485038618990914757637167551284096438594475925700608 binary64)) #s(approx (+ ( (- x y) 1/2) x) (.f64 #s(literal -1/2 binary64) y)) (if (<=.f64 x #s(literal 4676805239458889/187072209578355573530071658587684226515959365500928 binary64)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (.f64 y #s(literal 1/2 binary64)))) #s(approx (+ ( (- x y) 1/2) x) (*.f64 #s(literal 3/2 binary64) x)))))
(if (<=.f64 x #s(literal -4370447970442389/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 #s(literal 1/2 binary64) x)) (if (<=.f64 x #s(literal 7090649168385425/70906491683854249133971333415503528601229677279443476631916611638829262598057001759775558209235971002092300595769547131083230268742795262708226708464736682213924924871800416657575912944521796077262840069882938251784694133132833485038618990914757637167551284096438594475925700608 binary64)) #s(approx (+ ( (- x y) 1/2) x) (.f64 #s(literal -1/2 binary64) y)) (if (<=.f64 x #s(literal 4676805239458889/187072209578355573530071658587684226515959365500928 binary64)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (.f64 #s(literal 1/2 binary64) y))) #s(approx (+ ( (- x y) 1/2) x) (*.f64 #s(literal 3/2 binary64) x)))))
(if (<=.f64 y #s(literal -55948864096101/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704 binary64)) #s(approx (+ (* (- x y) 1/2) x) (.f64 #s(literal -1/2 binary64) y)) (if (<=.f64 y #s(literal 2450000000000000073786195968 binary64)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 #s(literal 1/2 binary64) x)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 y #s(literal 1/2 binary64))))))
(if (<=.f64 y #s(literal -55948864096101/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704 binary64)) #s(approx (+ (* (- x y) 1/2) x) (.f64 #s(literal -1/2 binary64) y)) (if (<=.f64 y #s(literal 2450000000000000073786195968 binary64)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 #s(literal 1/2 binary64) x)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 #s(literal 1/2 binary64) y)))))
(if (<=.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))) #s(literal 1876879207201175/469219801800293764373197355969328553831984974596843971042368711922664472663701981746713137411270711303034626199044091413698918166643890203860091306664994072502482932661931411083539271868071588269998735494868914134645646190292788569954038367952474854129664 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 #s(literal 1/2 binary64) x)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 y #s(literal 1/2 binary64)))))
(if (<=.f64 (+.f64 (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)) x) #s(literal 1876879207201175/469219801800293764373197355969328553831984974596843971042368711922664472663701981746713137411270711303034626199044091413698918166643890203860091306664994072502482932661931411083539271868071588269998735494868914134645646190292788569954038367952474854129664 binary64)) #s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) (.f64 #s(literal 1/2 binary64) x)) #s(approx (+ ( (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 y #s(literal 1/2 binary64))))
#s(approx (+ (* (sqrt (* (* 1/2 (- x y)) (- x y))) (sqrt 1/2)) x) #s(approx (* (+ (* (/ 1/2 x) y) 1/2) x) (*.f64 #s(literal 1/2 binary64) y)))

soundness2.1s (27.4%)

Memory

-19.0MiB live, 1 020.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	479
1	115	479
2	264	479
3	775	479
4	2401	479
5	3216	479
6	4243	479
7	5084	479
8	5657	479
9	6145	479
10	7847	479
0	8326	458
0	34	179
0	59	138
1	239	136
2	1711	121
0	8775	121
0	424	4608
1	1337	4329
2	3671	4090
0	8065	3788
0	526	4603
1	1607	4426
2	4371	4361
0	8281	4086
0	141	2205
1	405	1642
2	1121	1642
3	3562	1642
0	8066	1534
0	7	21
0	11	21
1	51	21
2	380	21
3	5345	21
0	8350	20

Stop Event

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

Compiler

Compiled 883 to 605 computations (31.5% saved)

preprocess100.0ms (1.3%)

Memory: 10.4MiB live, 126.4MiB allocated
Compiler: Compiled 474 to 166 computations (65% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	19	48
1	46	40
2	127	40
3	248	40
4	352	40
5	419	40
6	463	40
7	501	40
8	513	40
9	518	40
10	521	40
11	523	40
0	7	8
0	11	8
1	16	8
2	23	8
3	31	8
4	50	8
5	97	8
6	155	8
7	184	8
8	229	8
9	265	8
10	301	8
11	313	8
12	319	8
13	322	8
14	324	8
0	324	7

Iter	Nodes	Cost
0	7	24
0	11	24
1	16	24
2	23	24
3	31	24
4	50	24
5	97	24
6	155	24
7	184	24
8	229	24
9	265	24
10	301	24
11	313	24
12	319	24
13	322	24
14	324	24
0	324	23

Iter	Nodes	Cost
0	19	48
1	46	40
2	127	40
3	248	40
4	352	40
5	419	40
6	463	40
7	501	40
8	513	40
9	518	40
10	521	40
11	523	40
0	7	8
0	11	8
1	16	8
2	23	8
3	31	8
4	50	8
5	97	8
6	155	8
7	184	8
8	229	8
9	265	8
10	301	8
11	313	8
12	319	8
13	322	8
14	324	8
0	324	7

Iter	Nodes	Cost
0	7	24
0	11	24
1	16	24
2	23	24
3	31	24
4	50	24
5	97	24
6	155	24
7	184	24
8	229	24
9	265	24
10	301	24
11	313	24
12	319	24
13	322	24
14	324	24
0	324	23

start0.0ms (0%)

analyze0.0ms (0%)

sample1.0s (13.3%)

explain126.0ms (1.6%)

preprocess40.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify12.0ms (0.2%)

localize23.0ms (0.3%)

series6.0ms (0.1%)

simplify122.0ms (1.6%)

rewrite162.0ms (2.1%)

eval40.0ms (0.5%)

prune13.0ms (0.2%)

simplify140.0ms (1.8%)

localize110.0ms (1.4%)

series51.0ms (0.7%)

simplify232.0ms (3%)

rewrite227.0ms (2.9%)

eval558.0ms (7.2%)

prune74.0ms (0.9%)

simplify118.0ms (1.5%)

localize311.0ms (4%)

series43.0ms (0.6%)

simplify190.0ms (2.4%)

rewrite190.0ms (2.4%)

eval340.0ms (4.4%)

prune38.0ms (0.5%)

simplify168.0ms (2.2%)

localize145.0ms (1.9%)

series26.0ms (0.3%)

simplify201.0ms (2.6%)

rewrite277.0ms (3.6%)

eval94.0ms (1.2%)

prune23.0ms (0.3%)

regimes42.0ms (0.5%)

regimes25.0ms (0.3%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes40.0ms (0.5%)

regimes4.0ms (0.1%)

regimes9.0ms (0.1%)

regimes30.0ms (0.4%)

regimes6.0ms (0.1%)

regimes4.0ms (0%)

regimes7.0ms (0.1%)

bsearch52.0ms (0.7%)

bsearch2.0ms (0%)

bsearch13.0ms (0.2%)

bsearch45.0ms (0.6%)

bsearch38.0ms (0.5%)

bsearch18.0ms (0.2%)

bsearch25.0ms (0.3%)

bsearch11.0ms (0.1%)

bsearch0.0ms (0%)

simplify30.0ms (0.4%)

soundness2.1s (27.4%)

preprocess100.0ms (1.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	19	48
1	46	40
2	127	40
3	248	40
4	352	40
5	419	40
6	463	40
7	501	40
8	513	40
9	518	40
10	521	40
11	523	40
0	7	8
0	11	8
1	16	8
2	23	8
3	31	8
4	50	8
5	97	8
6	155	8
7	184	8
8	229	8
9	265	8
10	301	8
11	313	8
12	319	8
13	322	8
14	324	8
0	324	7

Iter	Nodes	Cost
0	7	24
0	11	24
1	16	24
2	23	24
3	31	24
4	50	24
5	97	24
6	155	24
7	184	24
8	229	24
9	265	24
10	301	24
11	313	24
12	319	24
13	322	24
14	324	24
0	324	23