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

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 9 computations (10% saved)

sample1.2s (16.9%)

Memory

0.4MiB live, 1 062.7MiB allocated

Samples

686.0ms	7 954×	0	valid
154.0ms	146×	1	valid
17.0ms	53×	3	valid
15.0ms	103×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 425.0ms

ival-div: 201.0ms (47.3% of total)

ival-sub: 69.0ms (16.2% of total)

ival-fabs: 68.0ms (16% of total)

ival-add: 63.0ms (14.8% of total)

adjust: 8.0ms (1.9% of total)

ival-true: 6.0ms (1.4% of total)

exact: 5.0ms (1.2% of total)

ival-assert: 4.0ms (0.9% of total)

Bogosity

explain169.0ms (2.5%)

Memory

-10.4MiB live, 152.4MiB 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

28.0ms	484×	0	valid
4.0ms	14×	1	valid
2.0ms	12×	2	valid
0.0ms	2×	3	valid

Compiler

Compiled 60 to 25 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-div: 6.0ms (35.6% of total)

ival-sub: 3.0ms (17.8% of total)

ival-fabs: 3.0ms (17.8% of total)

ival-add: 3.0ms (17.8% of total)

adjust: 1.0ms (5.9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess39.0ms (0.6%)

Memory

22.9MiB live, 61.7MiB allocated

Algorithm

1×	egg-herbie

Rules

192×	`lower-fma.f64`
192×	`lower-fma.f32`
112×	`lower-*.f64`
112×	`lower-*.f32`
94×	`sub-neg`

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

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB 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)

simplify18.0ms (0.3%)

Memory

-25.3MiB live, 17.8MiB 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))

Rules

192×	`lower-fma.f64`
192×	`lower-fma.f32`
112×	`lower-*.f64`
112×	`lower-*.f32`
64×	`lower-+.f32`

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)

localize47.0ms (0.7%)

Memory

-1.1MiB live, 38.4MiB 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	0.0625	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Samples

12.0ms	242×	0	valid
1.0ms	6×	2	valid
1.0ms	7×	1	valid
0.0ms	1×	3	valid

Compiler

Compiled 26 to 9 computations (65.4% saved)

Precisions

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

ival-div: 2.0ms (29.4% of total)

ival-sub: 2.0ms (29.4% of total)

ival-fabs: 1.0ms (14.7% of total)

ival-add: 1.0ms (14.7% 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)

series5.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB 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))

simplify131.0ms (1.9%)

Memory

-14.5MiB live, 140.9MiB allocated

Algorithm

1×	egg-herbie

Rules

3 132×	`lower-/.f32`
3 132×	`lower-/.f64`
2 520×	`lower-fma.f64`
2 520×	`lower-fma.f32`
2 222×	`lower-*.f64`

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)

rewrite166.0ms (2.4%)

Memory

16.5MiB live, 259.1MiB allocated

Rules

4 906×	`lower-fma.f64`
4 906×	`lower-fma.f32`
4 404×	`lower-*.f64`
4 404×	`lower-*.f32`
2 206×	`lower-/.f32`

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>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<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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eval49.0ms (0.7%)

Memory: -13.8MiB live, 108.1MiB allocated
Compiler: Compiled 6 166 to 927 computations (85% saved)

prune15.0ms (0.2%)

Memory

15.7MiB live, 55.4MiB allocated

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	320	10	330
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	321	10	331

Accuracy

100.0%

Counts

331 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(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)
	54.1%	(/.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))
	99.7%	(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y)) x) #s(literal -1 binary64)))
▶	99.4%	(+.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)))
▶	55.3%	(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) #s(literal 2 binary64)))
	55.5%	(+.f64 x (/.f64 (.f64 (fabs.f64 (fma.f64 (neg.f64 x) x (.f64 y y))) #s(literal 1/2 binary64)) (fabs.f64 (+.f64 x y))))
	29.9%	(+.f64 x (/.f64 (fabs.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (+.f64 x y) (fma.f64 x x (.f64 y y))))) #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)))
▶	49.4%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)))

Compiler

Compiled 300 to 212 computations (29.3% saved)

simplify189.0ms (2.8%)

Memory

-24.6MiB live, 217.8MiB 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	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	128	(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) #s(literal 2 binary64)))
cost-diff	384	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) #s(literal 2 binary64))
cost-diff	960	(/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))))
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)

Rules

9 858×	`lower-fma.f32`
9 854×	`lower-fma.f64`
3 270×	`lower-*.f32`
3 260×	`lower-*.f64`
1 856×	`lower-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	275
0	65	190
1	100	190
2	166	188
3	395	187
4	1485	180
5	4126	180
0	8437	180

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

localize144.0ms (2.1%)

Memory

-1.8MiB live, 290.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (-.f64 x y))
accuracy	0.01953125	(pow.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 x y))) #s(literal 1/2 binary64))
accuracy	0.0625	(+.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	0.4296875	(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	0.0234375	(pow.f64 (+.f64 x y) #s(literal -1 binary64))
accuracy	0.02734375	(.f64 (+.f64 x y) (.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64))))
accuracy	0.0625	(+.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	0.15625	(*.f64 (-.f64 y x) (pow.f64 (+.f64 x y) #s(literal -1 binary64)))
accuracy	0.0625	(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))) #s(literal 2 binary64)))
accuracy	0.1484375	(/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))))
accuracy	2.249975228450042	(fma.f64 (neg.f64 x) x (*.f64 y y))
accuracy	28.331240075456922	(/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))))
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	32.38199162465716	#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	0.0625	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)

Samples

64.0ms	226×	0	valid
31.0ms	13×	2	valid
6.0ms	12×	1	valid
5.0ms	5×	3	valid

Compiler

Compiled 277 to 38 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

adjust: 18.0ms (23.6% of total)

ival-div: 15.0ms (19.6% of total)

ival-mult: 12.0ms (15.7% of total)

ival-add: 10.0ms (13.1% of total)

ival-fabs: 7.0ms (9.2% of total)

ival-pow: 4.0ms (5.2% of total)

ival-pow2: 3.0ms (3.9% of total)

ival-sub: 3.0ms (3.9% of total)

ival-sqrt: 2.0ms (2.6% of total)

exact: 1.0ms (1.3% of total)

ival-neg: 1.0ms (1.3% of total)

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

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

series46.0ms (0.7%)

Memory

22.3MiB live, 140.0MiB allocated

Counts

21 → 504

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 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (.f64 y y))))) #<representation binary64>) () ())
#s(alt (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (.f64 y y)))) (patch (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (.f64 y y)))) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (.f64 y y))))) #s(literal 2 binary64)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (.f64 y y))))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (.f64 y y))))) #s(literal 2 binary64))) (patch (+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 x y)) (fabs.f64 (fma.f64 (neg.f64 x) x (.f64 y y))))) #s(literal 2 binary64))) #<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 (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 (fma.f64 (neg.f64 x) x (.f64 y y)) (patch (fma.f64 (neg.f64 x) x (.f64 y 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>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	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) (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y)))) (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2) (+ x (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2)) (* (- 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 (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))) (+ (* (neg x) x) (* y y)) (pow (+ x y) -1))
6.0ms	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) (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y)))) (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2) (+ x (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2)) (* (- 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 (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))) (+ (* (neg x) x) (* y y)) (pow (+ x y) -1))
5.0ms	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) (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y)))) (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2) (+ x (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2)) (* (- 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 (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))) (+ (* (neg x) x) (* y y)) (pow (+ x y) -1))
5.0ms	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) (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y)))) (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2) (+ x (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2)) (* (- 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 (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))) (+ (* (neg x) x) (* y y)) (pow (+ x y) -1))
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) (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y)))) (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2) (+ x (/ (/ 1 (/ (fabs (+ x y)) (fabs (+ (* (neg x) x) (* y y))))) 2)) (* (- 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 (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))) (+ (* (neg x) x) (* y y)) (pow (+ x y) -1))

simplify169.0ms (2.5%)

Memory

-14.7MiB live, 296.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 138×	`lower-fma.f64`
9 138×	`lower-fma.f32`
3 356×	`lower-*.f64`
3 356×	`lower-*.f32`
2 820×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	329	4401
1	940	4307
2	2385	4213
3	7337	4213
0	8056	4066

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 485

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

rewrite180.0ms (2.6%)

Memory

24.2MiB live, 391.4MiB allocated

Rules

4 992×	`lower-fma.f32`
4 988×	`lower-fma.f64`
4 186×	`lower-/.f32`
4 180×	`lower-/.f64`
3 530×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	210
0	65	133
1	263	125
2	1897	125
0	8363	125

Stop Event

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

Counts

21 → 1 413

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

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

eval303.0ms (4.4%)

Memory: -0.7MiB live, 734.7MiB allocated
Compiler: Compiled 45 573 to 5 268 computations (88.4% saved)

prune65.0ms (1%)

Memory

23.8MiB live, 182.6MiB allocated

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	2 174	11	2 185
Fresh	5	0	5
Picked	3	2	5
Done	0	0	0
Total	2 182	13	2 195

Accuracy

100.0%

Counts

2 195 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.5%	(fma.f64 (/.f64 (*.f64 (+.f64 y x) (fabs.f64 (-.f64 y x))) (+.f64 y x)) #s(literal 1/2 binary64) x)
	99.3%	(fma.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 y x))) (sqrt.f64 (fabs.f64 (-.f64 y x)))) #s(literal 1/2 binary64) x)
	55.3%	(fma.f64 (sqrt.f64 (.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) (fabs.f64 (-.f64 y x)))) (sqrt.f64 #s(literal 1/2 binary64)) x)
	99.3%	(fma.f64 (sqrt.f64 (.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1/2 binary64))) (sqrt.f64 (fabs.f64 (-.f64 y x))) x)
	99.4%	(fma.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))) x)
▶	55.3%	(fma.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (neg.f64 y)) (*.f64 (+.f64 y x) (-.f64 x y))))) #s(literal 1/2 binary64) x)
✓	99.9%	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
▶	88.6%	(fma.f64 (fabs.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))) #s(literal 1/2 binary64) x)
	54.4%	(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)
	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)) x)))
▶	99.7%	#s(approx (+ (* (fabs (- x y)) 1/2) x) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) (fabs.f64 (-.f64 y x)) x))
✓	49.4%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)))
▶	7.8%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))

Compiler

Compiled 302 to 215 computations (28.8% saved)

simplify118.0ms (1.7%)

Memory

-35.9MiB live, 136.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (neg.f64 y)) (*.f64 (+.f64 y x) (-.f64 x y))))) #s(literal 1/2 binary64) x)
cost-diff	128	(-.f64 x (neg.f64 y))
cost-diff	704	(/.f64 (-.f64 x (neg.f64 y)) (*.f64 (+.f64 y x) (-.f64 x y)))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (neg.f64 y)) (*.f64 (+.f64 y x) (-.f64 x y))))
cost-diff	0	(+.f64 y x)
cost-diff	0	(*.f64 (+.f64 y x) (fabs.f64 (-.f64 y x)))
cost-diff	0	(fma.f64 (/.f64 (*.f64 (+.f64 y x) (fabs.f64 (-.f64 y x))) (+.f64 y x)) #s(literal 1/2 binary64) x)
cost-diff	1408	(/.f64 (*.f64 (+.f64 y x) (fabs.f64 (-.f64 y x))) (+.f64 y x))
cost-diff	0	#s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))
cost-diff	0	(fabs.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
cost-diff	0	(fma.f64 (fabs.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))) #s(literal 1/2 binary64) x)
cost-diff	1024	(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
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 1/2 binary64) x)
cost-diff	0	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) (fabs.f64 (-.f64 y x)) x)
cost-diff	0	#s(approx (+ (* (fabs (- x y)) 1/2) x) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) (fabs.f64 (-.f64 y x)) x))
cost-diff	1024	(*.f64 (/.f64 #s(literal 1/2 binary64) x) x)

Rules

7 524×	`lower-fma.f32`
7 518×	`lower-fma.f64`
4 228×	`lower-*.f32`
4 220×	`lower-*.f64`
2 296×	`lower-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	280
0	71	266
1	120	265
2	248	218
3	689	218
4	2487	194
5	6303	194
0	8076	194

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

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

localize124.0ms (1.8%)

Memory

15.7MiB live, 216.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (neg.f64 y)) (*.f64 (+.f64 y x) (-.f64 x y)))))
accuracy	0.0625	(fma.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (neg.f64 y)) (*.f64 (+.f64 y x) (-.f64 x y))))) #s(literal 1/2 binary64) x)
accuracy	0.1484375	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (neg.f64 y)) (*.f64 (+.f64 y x) (-.f64 x y))))
accuracy	28.331240075456922	(/.f64 (-.f64 x (neg.f64 y)) (*.f64 (+.f64 y x) (-.f64 x y)))
accuracy	0	(*.f64 (+.f64 y x) (fabs.f64 (-.f64 y x)))
accuracy	0	(fabs.f64 (-.f64 y x))
accuracy	0.0625	(fma.f64 (/.f64 (*.f64 (+.f64 y x) (fabs.f64 (-.f64 y x))) (+.f64 y x)) #s(literal 1/2 binary64) x)
accuracy	28.222770397030818	(/.f64 (*.f64 (+.f64 y x) (fabs.f64 (-.f64 y x))) (+.f64 y x))
accuracy	0	(fabs.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
accuracy	0	#s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))
accuracy	0.0625	(fma.f64 (fabs.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))) #s(literal 1/2 binary64) x)
accuracy	7.107032811906042	(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)
accuracy	0	(neg.f64 x)
accuracy	0	(fabs.f64 #s(approx (- y x) (neg.f64 x)))
accuracy	28.1434016661222	#s(approx (- y x) (neg.f64 x))
accuracy	32.38199162465716	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))
accuracy	0	(fabs.f64 (-.f64 y x))
accuracy	0	#s(approx (+ (* (fabs (- x y)) 1/2) x) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) (fabs.f64 (-.f64 y x)) x))
accuracy	0.0625	(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) x) (fabs.f64 (-.f64 y x)) x)
accuracy	0.1796875	(*.f64 (/.f64 #s(literal 1/2 binary64) x) x)

Samples

56.0ms	226×	0	valid
13.0ms	13×	2	valid
8.0ms	5×	3	valid
6.0ms	12×	1	valid

Compiler

Compiled 231 to 37 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-mult: 18.0ms (30.6% of total)

ival-div: 11.0ms (18.7% of total)

ival-add: 8.0ms (13.6% of total)

adjust: 7.0ms (11.9% of total)

ival-fabs: 7.0ms (11.9% of total)

ival-sub: 6.0ms (10.2% of total)

ival-neg: 2.0ms (3.4% of total)

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

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

exact: 0.0ms (0% of total)

series31.0ms (0.4%)

Memory

-22.8MiB live, 53.2MiB allocated

Counts

23 → 516

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (* (/ 1/2 x) x) (fabs (- y x))) x) (/ 1/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- (/ x y) 1) y) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (/ (* (+ y x) (fabs (- y x))) (+ y x)) (+ (* (/ (* (+ y x) (fabs (- y x))) (+ y x)) 1/2) x) (* (+ y x) (fabs (- y x))) (+ y x) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (/ (- x (neg y)) (* (+ y x) (- x y))) (- x (neg y)) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (- y x)) (neg x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))))
2.0ms	x	@	-inf	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (* (/ 1/2 x) x) (fabs (- y x))) x) (/ 1/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- (/ x y) 1) y) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (/ (* (+ y x) (fabs (- y x))) (+ y x)) (+ (* (/ (* (+ y x) (fabs (- y x))) (+ y x)) 1/2) x) (* (+ y x) (fabs (- y x))) (+ y x) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (/ (- x (neg y)) (* (+ y x) (- x y))) (- x (neg y)) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (- y x)) (neg x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))))
2.0ms	x	@	inf	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (* (/ 1/2 x) x) (fabs (- y x))) x) (/ 1/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- (/ x y) 1) y) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (/ (* (+ y x) (fabs (- y x))) (+ y x)) (+ (* (/ (* (+ y x) (fabs (- y x))) (+ y x)) 1/2) x) (* (+ y x) (fabs (- y x))) (+ y x) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (/ (- x (neg y)) (* (+ y x) (- x y))) (- x (neg y)) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (- y x)) (neg x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))))
2.0ms	y	@	-inf	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (* (/ 1/2 x) x) (fabs (- y x))) x) (/ 1/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- (/ x y) 1) y) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (/ (* (+ y x) (fabs (- y x))) (+ y x)) (+ (* (/ (* (+ y x) (fabs (- y x))) (+ y x)) 1/2) x) (* (+ y x) (fabs (- y x))) (+ y x) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (/ (- x (neg y)) (* (+ y x) (- x y))) (- x (neg y)) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (- y x)) (neg x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))))
1.0ms	y	@	0	((* (/ 1/2 x) x) (+ (* (fabs (- x y)) 1/2) x) (+ (* (* (/ 1/2 x) x) (fabs (- y x))) x) (/ 1/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- y x)) 1/2) (fabs (- y x)) (- y x) (* (- (/ x y) 1) y) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (/ (* (+ y x) (fabs (- y x))) (+ y x)) (+ (* (/ (* (+ y x) (fabs (- y x))) (+ y x)) 1/2) x) (* (+ y x) (fabs (- y x))) (+ y x) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (/ (- x (neg y)) (* (+ y x) (- x y))) (- x (neg y)) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (- y x)) (neg x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))))

simplify145.0ms (2.1%)

Memory

14.2MiB live, 207.2MiB allocated

Algorithm

1×	egg-herbie

Rules

9 900×	`lower-fma.f64`
9 900×	`lower-fma.f32`
3 614×	`lower-*.f64`
3 614×	`lower-*.f32`
2 028×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	213	2621
1	633	2607
2	1579	2570
3	5215	2562
0	8113	2420

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 480

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

rewrite189.0ms (2.8%)

Memory

19.3MiB live, 343.7MiB allocated

Rules

4 204×	`lower-/.f32`
4 194×	`lower-/.f64`
4 056×	`lower-*.f32`
4 050×	`lower-*.f64`
3 336×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	231
0	71	222
1	281	213
2	2195	150
0	9902	150

Stop Event

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

Counts

23 → 1 036

Calls

Call 1

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

Outputs
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eval393.0ms (5.7%)

Memory: -8.6MiB live, 533.1MiB allocated
Compiler: Compiled 35 171 to 3 744 computations (89.4% saved)

prune116.0ms (1.7%)

Memory

14.6MiB live, 213.5MiB allocated

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	1 777	4	1 781
Fresh	3	3	6
Picked	3	2	5
Done	0	2	2
Total	1 783	11	1 794

Accuracy

100.0%

Counts

1 794 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	35.3%	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (-.f64 x y) x) x)
▶	56.1%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
▶	51.5%	(fma.f64 (*.f64 (-.f64 x y) (/.f64 #s(literal 1/2 binary64) x)) x x)
	55.3%	(fma.f64 (sqrt.f64 (.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) (fabs.f64 (-.f64 y x)))) (sqrt.f64 #s(literal 1/2 binary64)) x)
	99.3%	(fma.f64 (sqrt.f64 (.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))) #s(literal 1/2 binary64))) (sqrt.f64 (fabs.f64 (-.f64 y x))) x)
▶	99.4%	(fma.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))) x)
✓	99.9%	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
▶	54.4%	(fma.f64 (fabs.f64 #s(approx (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg.f64 y))) #s(literal 1/2 binary64) x)
✓	88.6%	(fma.f64 (fabs.f64 #s(approx (- x y) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))) #s(literal 1/2 binary64) x)
✓	49.4%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)))
✓	7.8%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))

Compiler

Compiled 195 to 139 computations (28.7% saved)

simplify125.0ms (1.8%)

Memory

-3.7MiB live, 188.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x y)
cost-diff	0	(*.f64 (-.f64 x y) x)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	1024	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (-.f64 x y) x) x)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(-.f64 x y)
cost-diff	128	(*.f64 (-.f64 x y) (/.f64 #s(literal 1/2 binary64) x))
cost-diff	896	(fma.f64 (*.f64 (-.f64 x y) (/.f64 #s(literal 1/2 binary64) x)) x x)
cost-diff	0	(neg.f64 y)
cost-diff	0	#s(approx (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg.f64 y))
cost-diff	0	(fabs.f64 #s(approx (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg.f64 y)))
cost-diff	0	(fma.f64 (fabs.f64 #s(approx (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg.f64 y))) #s(literal 1/2 binary64) x)
cost-diff	0	(-.f64 y x)
cost-diff	0	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
cost-diff	0	(fabs.f64 (-.f64 y x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
cost-diff	2240	(fma.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))) x)

Rules

10 274×	`lower-fma.f32`
10 264×	`lower-fma.f64`
3 216×	`lower-*.f32`
3 210×	`lower-*.f64`
2 938×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	162
0	48	146
1	90	143
2	192	119
3	621	113
4	2126	113
5	5257	113
0	8265	111

Stop Event

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

Calls

Call 1

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

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

localize314.0ms (4.6%)

Memory

-11.2MiB live, 245.8MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0	(-.f64 x y)
accuracy	0.01171875	(*.f64 (-.f64 x y) x)
accuracy	21.72502233093963	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (-.f64 x y) x) x)
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0	(-.f64 x y)
accuracy	0.2265625	(*.f64 (-.f64 x y) (/.f64 #s(literal 1/2 binary64) x))
accuracy	7.371998372155075	(fma.f64 (*.f64 (-.f64 x y) (/.f64 #s(literal 1/2 binary64) x)) x x)
accuracy	0	(neg.f64 y)
accuracy	0	(fabs.f64 #s(approx (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg.f64 y)))
accuracy	0.0625	(fma.f64 (fabs.f64 #s(approx (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg.f64 y))) #s(literal 1/2 binary64) x)
accuracy	34.531442211021286	#s(approx (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg.f64 y))
accuracy	0	(-.f64 y x)
accuracy	0.09375	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
accuracy	0	(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))
accuracy	0	(fabs.f64 (-.f64 y x))
accuracy	0.01953125	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x))))
accuracy	0.34375	(fma.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))) x)

Samples

207.0ms	18×	1	valid
60.0ms	209×	0	valid
19.0ms	20×	2	valid
7.0ms	8×	3	valid
1.0ms	1×	5	exit

Compiler

Compiled 160 to 32 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 268.0ms

ival-sub: 202.0ms (75.5% of total)

ival-mult: 35.0ms (13.1% of total)

ival-add: 8.0ms (3% of total)

adjust: 7.0ms (2.6% of total)

ival-div: 6.0ms (2.2% of total)

ival-fabs: 5.0ms (1.9% of total)

ival-sqrt: 2.0ms (0.7% of total)

ival-neg: 1.0ms (0.4% of total)

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

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

exact: 0.0ms (0% of total)

series30.0ms (0.4%)

Memory

27.7MiB live, 65.5MiB allocated

Counts

16 → 360

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	x	@	inf	((+ (* (sqrt (* 1/2 (fabs (- y x)))) (sqrt (* 1/2 (fabs (- y x))))) x) (sqrt (* 1/2 (fabs (- y x)))) (* 1/2 (fabs (- y x))) (fabs (- y x)) (+ (* (- y x) -1/2) x) (- y x) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg y) (+ (* (* (- x y) (/ 1/2 x)) x) x) (* (- x y) (/ 1/2 x)) (- x y) (/ 1/2 x) (+ (* (/ 1/2 x) (* (- x y) x)) x) (* (- x y) x))
2.0ms	y	@	inf	((+ (* (sqrt (* 1/2 (fabs (- y x)))) (sqrt (* 1/2 (fabs (- y x))))) x) (sqrt (* 1/2 (fabs (- y x)))) (* 1/2 (fabs (- y x))) (fabs (- y x)) (+ (* (- y x) -1/2) x) (- y x) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg y) (+ (* (* (- x y) (/ 1/2 x)) x) x) (* (- x y) (/ 1/2 x)) (- x y) (/ 1/2 x) (+ (* (/ 1/2 x) (* (- x y) x)) x) (* (- x y) x))
2.0ms	y	@	0	((+ (* (sqrt (* 1/2 (fabs (- y x)))) (sqrt (* 1/2 (fabs (- y x))))) x) (sqrt (* 1/2 (fabs (- y x)))) (* 1/2 (fabs (- y x))) (fabs (- y x)) (+ (* (- y x) -1/2) x) (- y x) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg y) (+ (* (* (- x y) (/ 1/2 x)) x) x) (* (- x y) (/ 1/2 x)) (- x y) (/ 1/2 x) (+ (* (/ 1/2 x) (* (- x y) x)) x) (* (- x y) x))
2.0ms	y	@	-inf	((+ (* (sqrt (* 1/2 (fabs (- y x)))) (sqrt (* 1/2 (fabs (- y x))))) x) (sqrt (* 1/2 (fabs (- y x)))) (* 1/2 (fabs (- y x))) (fabs (- y x)) (+ (* (- y x) -1/2) x) (- y x) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg y) (+ (* (* (- x y) (/ 1/2 x)) x) x) (* (- x y) (/ 1/2 x)) (- x y) (/ 1/2 x) (+ (* (/ 1/2 x) (* (- x y) x)) x) (* (- x y) x))
2.0ms	x	@	-inf	((+ (* (sqrt (* 1/2 (fabs (- y x)))) (sqrt (* 1/2 (fabs (- y x))))) x) (sqrt (* 1/2 (fabs (- y x)))) (* 1/2 (fabs (- y x))) (fabs (- y x)) (+ (* (- y x) -1/2) x) (- y x) (+ (* (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) 1/2) x) (fabs (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y))))) (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg y) (+ (* (* (- x y) (/ 1/2 x)) x) x) (* (- x y) (/ 1/2 x)) (- x y) (/ 1/2 x) (+ (* (/ 1/2 x) (* (- x y) x)) x) (* (- x y) x))

simplify106.0ms (1.5%)

Memory

-19.3MiB live, 175.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6 420×	`lower-fma.f64`
6 420×	`lower-fma.f32`
2 994×	`lower-*.f64`
2 994×	`lower-*.f32`
1 456×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	123	2104
1	357	1816
2	899	1816
3	3028	1816
4	5956	1816
0	8096	1702

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 347

Calls

Call 1

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

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

rewrite197.0ms (2.9%)

Memory

3.5MiB live, 288.5MiB allocated

Rules

4 476×	`lower-fma.f32`
4 466×	`lower-fma.f64`
3 662×	`lower-/.f32`
3 660×	`lower-/.f64`
2 964×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	138
0	48	127
1	208	94
2	1617	87
0	9387	84

Stop Event

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

Counts

16 → 826

Calls

Call 1

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

Outputs
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eval333.0ms (4.9%)

Memory: 5.6MiB live, 464.9MiB allocated
Compiler: Compiled 34 396 to 2 904 computations (91.6% saved)

prune94.0ms (1.4%)

Memory

-18.6MiB live, 128.5MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	1 748	3	1 751
Fresh	2	0	2
Picked	3	2	5
Done	1	3	4
Total	1 754	8	1 762

Accuracy

100.0%

Counts

1 762 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.1%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
✓	99.9%	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
✓	54.4%	(fma.f64 (fabs.f64 #s(approx (/ 1 (/ (- x (neg y)) (* (+ y x) (- x y)))) (neg.f64 y))) #s(literal 1/2 binary64) x)
	56.2%	#s(approx (+ (* (/ 1/2 x) (* (- x y) x)) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))
	36.0%	#s(approx (+ (* (/ 1/2 x) (* (- x y) x)) x) (*.f64 #s(literal 3/2 binary64) x))
	22.6%	#s(approx (+ (* (/ 1/2 x) (* (- x y) x)) x) (*.f64 #s(literal -1/2 binary64) y))
✓	49.4%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64)))
✓	7.8%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- y x) (neg.f64 x))) #s(literal 1/2 binary64)))

Compiler

Compiled 399 to 168 computations (57.9% saved)

regimes32.0ms (0.5%)

Memory

-5.1MiB live, 69.2MiB allocated

Counts

29 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	y
10.0ms	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)

regimes11.0ms (0.2%)

Memory

29.1MiB live, 29.1MiB allocated

Counts

8 → 2

Calls

Call 1

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

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

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
74.5%	2	`x`
74.2%	2	`y`
59.5%	2	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes8.0ms (0.1%)

Memory

-31.8MiB live, 9.8MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
74.4%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes6.0ms (0.1%)

Memory

15.1MiB live, 15.1MiB allocated

Counts

5 → 2

Calls

Call 1

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

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
73.0%	2	`y`
72.1%	3	`x`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes9.0ms (0.1%)

Memory

-13.6MiB live, 23.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
56.1%	1	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
56.1%	1	`x`
56.1%	1	`y`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes6.0ms (0.1%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs

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

#s(approx (+ (* (/ 1/2 x) (* (- x y) x)) 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)))

Outputs

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

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

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

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
46.7%	2	`y`
36.0%	1	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
48.9%	3	`x`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes4.0ms (0.1%)

Memory

16.0MiB live, 16.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
22.6%	1	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
22.6%	1	`y`
22.6%	1	`x`

Compiler

Compiled 10 to 11 computations (-10% saved)

bsearch12.0ms (0.2%)

Memory

-10.3MiB live, 28.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	1.286479245349428e-104	1.0902715614605057e-102

Samples

6.0ms	109×	0	valid
0.0ms	2×	1	valid
0.0ms	1×	2	valid

Compiler

Compiled 109 to 124 computations (-13.8% saved)

Precisions

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

ival-sub: 2.0ms (47.8% of total)

ival-div: 1.0ms (23.9% of total)

ival-fabs: 1.0ms (23.9% 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)

bsearch1.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.286479245349428e-104	1.0902715614605057e-102

Compiler

Compiled 102 to 110 computations (-7.8% saved)

bsearch16.0ms (0.2%)

Memory

5.6MiB live, 42.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	2.3319628599879155e-93	1.4493445852085295e-85

Samples

8.0ms	135×	0	valid
1.0ms	4×	2	valid
0.0ms	5×	1	valid

Compiler

Compiled 128 to 138 computations (-7.8% saved)

Precisions

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

ival-div: 1.0ms (26.5% of total)

ival-sub: 1.0ms (26.5% of total)

ival-add: 1.0ms (26.5% of total)

ival-fabs: 1.0ms (26.5% 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)

bsearch30.0ms (0.4%)

Memory

4.4MiB live, 80.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	1.4871345746348427e-97	1.060165868370096e-96
17.0ms	-7.502673885728112e+113	-1.2383663143235814e+111

Samples

13.0ms

224×

valid

Compiler

Compiled 123 to 180 computations (-46.3% saved)

Precisions

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

ival-add: 4.0ms (51.9% of total)

ival-sub: 1.0ms (13% of total)

ival-div: 1.0ms (13% of total)

ival-fabs: 1.0ms (13% of total)

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

exact: 0.0ms (0% of total)

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

simplify31.0ms (0.5%)

Memory

-38.9MiB live, 88.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	158
1	57	158
2	63	158
3	66	158
4	67	158

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 8069530869021589/40347654345107946713373737062547060536401653012956617387979052445947619094013143666088208645002153616185987062074179584 binary64)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x) #s(approx (+ (* (/ 1/2 x) (* (- x y) x)) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y))))
(if (<=.f64 x #s(literal 8069530869021589/40347654345107946713373737062547060536401653012956617387979052445947619094013143666088208645002153616185987062074179584 binary64)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x))
(if (<=.f64 y #s(literal 4927438432791169/8958978968711216842229769122273777112486581988938598139599956403855167484720643781523509973086428463104 binary64)) (fma.f64 (-.f64 y x) #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 (-.f64 y x) #s(literal -1/2 binary64) x)
(if (<=.f64 x #s(literal -3999999999999999827279090566567263033620417909033513127181584862491530430484445952615771723789729288178995560448 binary64)) #s(approx (+ (* (/ 1/2 x) (* (- x y) x)) x) (.f64 #s(literal 3/2 binary64) x)) (if (<=.f64 x #s(literal 2308711300569989/4809815209520810450717656262224562232065397860164239095208531909697964083434718092213655548692006303809402830848 binary64)) #s(approx (+ ( (/ 1/2 x) (* (- x y) x)) x) (.f64 #s(literal -1/2 binary64) y)) #s(approx (+ ( (/ 1/2 x) (* (- x y) x)) x) (*.f64 #s(literal 3/2 binary64) x))))
#s(approx (+ (* (/ 1/2 x) (* (- x y) x)) x) (*.f64 #s(literal -1/2 binary64) y))

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 8069530869021589/40347654345107946713373737062547060536401653012956617387979052445947619094013143666088208645002153616185987062074179584 binary64)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x) #s(approx (+ (* (/ 1/2 x) (* (- x y) x)) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y))))
(if (<=.f64 x #s(literal 8069530869021589/40347654345107946713373737062547060536401653012956617387979052445947619094013143666088208645002153616185987062074179584 binary64)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x))
(if (<=.f64 y #s(literal 4927438432791169/8958978968711216842229769122273777112486581988938598139599956403855167484720643781523509973086428463104 binary64)) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x) #s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64))))
(if (<=.f64 y #s(literal 4927438432791169/8958978968711216842229769122273777112486581988938598139599956403855167484720643781523509973086428463104 binary64)) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x) #s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 y x)))))
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
(if (<=.f64 x #s(literal -3999999999999999827279090566567263033620417909033513127181584862491530430484445952615771723789729288178995560448 binary64)) #s(approx (+ (* (/ 1/2 x) (* (- x y) x)) x) (.f64 #s(literal 3/2 binary64) x)) (if (<=.f64 x #s(literal 2308711300569989/4809815209520810450717656262224562232065397860164239095208531909697964083434718092213655548692006303809402830848 binary64)) #s(approx (+ ( (/ 1/2 x) (* (- x y) x)) x) (.f64 #s(literal -1/2 binary64) y)) #s(approx (+ ( (/ 1/2 x) (* (- x y) x)) x) (*.f64 #s(literal 3/2 binary64) x))))
#s(approx (+ (* (/ 1/2 x) (* (- x y) x)) x) (*.f64 #s(literal -1/2 binary64) y))

soundness1.4s (20.1%)

Memory

23.4MiB live, 867.9MiB allocated

Rules

9 138×	`lower-fma.f64`
9 138×	`lower-fma.f32`
6 420×	`lower-fma.f64`
6 420×	`lower-fma.f32`
4 992×	`lower-fma.f32`

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	37	210
0	65	133
1	263	125
2	1897	125
0	8363	125
0	329	4401
1	940	4307
2	2385	4213
3	7337	4213
0	8056	4066
0	7	21
0	11	21
1	51	21
2	380	21
3	5345	21
0	8350	20
0	123	2104
1	357	1816
2	899	1816
3	3028	1816
4	5956	1816
0	8096	1702
0	42	231
0	71	222
1	281	213
2	2195	150
0	9902	150

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

Compiler

Compiled 272 to 180 computations (33.8% saved)

preprocess105.0ms (1.5%)

Memory: -3.4MiB live, 114.7MiB allocated
Compiler: Compiled 194 to 82 computations (57.7% 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%)

sample1.2s (16.9%)

explain169.0ms (2.5%)

preprocess39.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify18.0ms (0.3%)

localize47.0ms (0.7%)

series5.0ms (0.1%)

simplify131.0ms (1.9%)

rewrite166.0ms (2.4%)

eval49.0ms (0.7%)

prune15.0ms (0.2%)

simplify189.0ms (2.8%)

localize144.0ms (2.1%)

series46.0ms (0.7%)

simplify169.0ms (2.5%)

rewrite180.0ms (2.6%)

eval303.0ms (4.4%)

prune65.0ms (1%)

simplify118.0ms (1.7%)

localize124.0ms (1.8%)

series31.0ms (0.4%)

simplify145.0ms (2.1%)

rewrite189.0ms (2.8%)

eval393.0ms (5.7%)

prune116.0ms (1.7%)

simplify125.0ms (1.8%)

localize314.0ms (4.6%)

series30.0ms (0.4%)

simplify106.0ms (1.5%)

rewrite197.0ms (2.9%)

eval333.0ms (4.9%)

prune94.0ms (1.4%)

regimes32.0ms (0.5%)

regimes11.0ms (0.2%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch12.0ms (0.2%)

bsearch1.0ms (0%)

bsearch16.0ms (0.2%)

bsearch30.0ms (0.4%)

simplify31.0ms (0.5%)

soundness1.4s (20.1%)

preprocess105.0ms (1.5%)

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