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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 9 computations (10% saved)

sample967.0ms (21.5%)

Memory

13.8MiB live, 958.1MiB allocated

Samples

632.0ms	7 944×	0	valid
14.0ms	75×	3	valid
13.0ms	144×	1	valid
13.0ms	93×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 255.0ms

ival-sub: 82.0ms (32.1% of total)

ival-div: 61.0ms (23.9% of total)

ival-fabs: 47.0ms (18.4% of total)

ival-add: 41.0ms (16.1% of total)

adjust: 9.0ms (3.5% of total)

ival-true: 6.0ms (2.3% of total)

exact: 5.0ms (2% of total)

ival-assert: 4.0ms (1.6% of total)

Bogosity

explain93.0ms (2.1%)

Memory

20.4MiB live, 115.8MiB 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

25.0ms	488×	0	valid
2.0ms	12×	2	valid
1.0ms	8×	1	valid
1.0ms	4×	3	valid

Compiler

Compiled 60 to 25 computations (58.3% saved)

Precisions

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

ival-div: 4.0ms (27.9% of total)

ival-sub: 3.0ms (20.9% of total)

ival-fabs: 3.0ms (20.9% of total)

ival-add: 3.0ms (20.9% of total)

adjust: 1.0ms (7% of total)

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

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

exact: 0.0ms (0% of total)

preprocess58.0ms (1.3%)

Memory

-26.3MiB live, 20.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	41	46
2	70	46
3	110	46
4	191	46
5	257	46
6	265	46
7	278	46
8	280	46
0	7	8
0	11	8
1	18	8
2	25	8
3	39	8
4	66	8
5	88	8
6	90	8
7	94	8
8	97	8
0	97	8

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify5.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
0	11	24
1	18	24
2	25	24
3	39	24
4	66	24
5	88	24
6	90	24
7	94	24
8	97	24
0	97	24

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

localize19.0ms (0.4%)

Memory

21.5MiB live, 21.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64))
accuracy	0.0	(-.f64 y x)
accuracy	0.0	(fabs.f64 (-.f64 y x))
accuracy	0.05078125	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Samples

12.0ms	244×	0	valid
1.0ms	6×	2	valid
0.0ms	4×	1	valid
0.0ms	2×	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 (28.9% of total)

ival-sub: 2.0ms (28.9% of total)

ival-fabs: 1.0ms (14.5% of total)

ival-add: 1.0ms (14.5% 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)

series4.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

4 → 19

Calls

Call 1

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

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

Calls

6 calls:

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

simplify196.0ms (4.4%)

Memory

-12.6MiB live, 98.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	84
1	127	84
2	346	84
3	968	84
4	2383	84
5	3739	84
6	6329	84
0	8023	80

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 17

Calls

Call 1

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

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

rewrite357.0ms (7.9%)

Memory

-16.0MiB live, 172.1MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	21
0	11	20
1	47	20
2	323	18
3	4001	18
0	8907	18

Stop Event

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

Counts

4 → 274

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x)) #s(literal 2 binary64))) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x)))
(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64))) (-.f64 (.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64))) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (pow.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 2 binary64)) (pow.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 2 binary64))) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x))
(.f64 (/.f64 (pow.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))))
(.f64 (/.f64 (pow.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x)))
(*.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x)))
(.f64 (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x)) (/.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 2 binary64)) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x)) #s(literal 2 binary64))) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) #s(literal 2 binary64))) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x))
(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 3 binary64))) (/.f64 (pow.f64 (-.f64 y x) #s(literal 6 binary64)) (pow.f64 (.f64 #s(literal -4 binary64) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 2 binary64)) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x)) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x))) (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 2 binary64)) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x)))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x)) (*.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 2 binary64)))) (pow.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x)) (.f64 (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x)) (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x)) #s(literal 2 binary64)))
(/.f64 (pow.f64 (pow.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 3 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 6 binary64))) (.f64 (pow.f64 (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x)) #s(literal 2 binary64)) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 6 binary64))) (.f64 (-.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))))
(/.f64 (+.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (-.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 6 binary64))) (pow.f64 (.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x))))
(/.f64 (pow.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) #s(literal 2 binary64)) (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x)))))
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(.f64 (pow.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 y x)) (*.f64 (+.f64 y x) (-.f64 y x))) #s(literal 1 binary64)) (-.f64 y x))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 y x))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 y x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fabs.f64 (sqrt.f64 (-.f64 y x))) #s(literal 1 binary64)) (pow.f64 (fabs.f64 (sqrt.f64 (-.f64 y x))) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 y x) x (*.f64 y y)))
(.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 y x) x) #s(literal 2 binary64)))) (-.f64 (.f64 y y) (.f64 (+.f64 y x) x)))
(.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 y x) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 y x) x) (-.f64 (.f64 (+.f64 y x) x) (*.f64 y y)) (pow.f64 y #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 y x)) (*.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 y x))) (neg.f64 (sqrt.f64 (-.f64 y x))))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 y x))) (sqrt.f64 (-.f64 y x)))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 y x))) (fabs.f64 (sqrt.f64 (-.f64 y x))))
(*.f64 (fabs.f64 (+.f64 y x)) (pow.f64 (/.f64 (-.f64 y x) (+.f64 y x)) #s(literal 1 binary64)))
(.f64 (fabs.f64 (fma.f64 (+.f64 y x) x (.f64 y y))) (pow.f64 (/.f64 (-.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (-.f64 y x)) (neg.f64 (sqrt.f64 (-.f64 y x))))
(*.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (-.f64 y x)))
(*.f64 (+.f64 y x) (/.f64 (-.f64 y x) (+.f64 y x)))
(.f64 (fma.f64 (+.f64 y x) x (.f64 y y)) (/.f64 (-.f64 y x) (neg.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)))))
(.f64 (fma.f64 (+.f64 y x) x (.f64 y y)) (/.f64 (-.f64 y x) (fma.f64 (+.f64 y x) x (*.f64 y y))))
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 y x))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (sqrt.f64 (-.f64 y x))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 y x) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (-.f64 y x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (-.f64 y x) #s(literal 1 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 y (/.f64 y (+.f64 y x))) #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 x (+.f64 y x))) #s(literal 2 binary64))) (-.f64 y x))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y)))))
(/.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (+.f64 y x) #s(literal 3 binary64))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (+.f64 y x) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 y (/.f64 y (+.f64 y x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 x (/.f64 x (+.f64 y x))) #s(literal 2 binary64)) (.f64 (.f64 y (/.f64 y (+.f64 y x))) (*.f64 x (/.f64 x (+.f64 y x)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (*.f64 y y)))))))
(/.f64 (neg.f64 (*.f64 (fabs.f64 (+.f64 y x)) (-.f64 y x))) (neg.f64 (fabs.f64 (+.f64 y x))))
(/.f64 (neg.f64 (*.f64 (fabs.f64 (+.f64 y x)) (-.f64 y x))) (fabs.f64 (+.f64 y x)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fabs.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fabs.f64 (fma.f64 (+.f64 y x) x (*.f64 y y))))
(/.f64 (-.f64 (.f64 (.f64 y y) (+.f64 y x)) (.f64 (+.f64 y x) (.f64 x x))) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) (.f64 (fma.f64 (+.f64 y x) x (.f64 y y)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)) #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 y x)) (-.f64 y x)) (sqrt.f64 (+.f64 y x)))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (-.f64 y x))) (sqrt.f64 (fma.f64 (+.f64 y x) x (.f64 y y))))
(/.f64 (sqrt.f64 (.f64 (.f64 (+.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (.f64 (+.f64 y x) (fma.f64 (+.f64 y x) x (.f64 y y)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (neg.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (fma.f64 (+.f64 y x) x (*.f64 y y))))
(/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (fma.f64 (.f64 x x) (fma.f64 y y (*.f64 x x)) (pow.f64 y #s(literal 4 binary64))) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (+.f64 y x) x (.f64 y y)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (+.f64 y x) x (.f64 y y))))
(/.f64 (*.f64 (fabs.f64 (+.f64 y x)) (-.f64 y x)) (neg.f64 (fabs.f64 (+.f64 y x))))
(/.f64 (*.f64 (fabs.f64 (+.f64 y x)) (-.f64 y x)) (fabs.f64 (+.f64 y x)))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fabs.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fabs.f64 (fma.f64 (+.f64 y x) x (*.f64 y y))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (+.f64 y x))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (neg.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (+.f64 y x) x (*.f64 y y))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (+.f64 y x) x (*.f64 y y)))
(neg.f64 (-.f64 y x))
(fma.f64 (/.f64 (.f64 y y) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 y x) x (.f64 y y)) (*.f64 x (/.f64 x (+.f64 y x))))
(fma.f64 (/.f64 (.f64 y y) (.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x) (*.f64 x (/.f64 x (+.f64 y x))))
(fma.f64 (neg.f64 y) (/.f64 (neg.f64 y) (+.f64 y x)) (*.f64 x (/.f64 x (+.f64 y x))))
(fma.f64 y (/.f64 y (+.f64 y x)) (*.f64 x (/.f64 x (+.f64 y x))))
(sqrt.f64 (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(-.f64 (.f64 x (/.f64 x (+.f64 y x))) (.f64 y (/.f64 y (+.f64 y x))))
(-.f64 (.f64 y (/.f64 y (+.f64 y x))) (.f64 x (/.f64 x (+.f64 y x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 y x) x (.f64 y y))))
(-.f64 y x)
(-.f64 x y)
(fabs.f64 (-.f64 y x))
(exp.f64 (/.f64 (log.f64 (pow.f64 (-.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (-.f64 y x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 y x))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (-.f64 y x)))
(+.f64 (cosh.f64 (log.f64 (-.f64 y x))) (sinh.f64 (log.f64 (-.f64 y x))))
(+.f64 (.f64 y (/.f64 y (+.f64 y x))) (.f64 x (/.f64 x (+.f64 y x))))

eval60.0ms (1.3%)

Memory: -4.8MiB live, 40.1MiB allocated
Compiler: Compiled 4 841 to 704 computations (85.5% saved)

prune5.0ms (0.1%)

Memory

16.6MiB live, 16.7MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	179	5	184
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	5	185

Accuracy

100.0%

Counts

185 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	21.5%	(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x))))
▶	51.7%	(fma.f64 (sqrt.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64))) (sqrt.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64))) x)
▶	36.7%	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (/.f64 (-.f64 y x) #s(literal -2 binary64)))
▶	99.9%	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x))
▶	59.1%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64)))

Compiler

Compiled 202 to 102 computations (49.5% saved)

simplify233.0ms (5.2%)

Memory

-18.4MiB live, 174.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x))
cost-diff	0	(/.f64 x (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x)))
cost-diff	0	(*.f64 x x)
cost-diff	18	(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x))))
cost-diff	0	(-.f64 y x)
cost-diff	0	(/.f64 (-.f64 y x) #s(literal -2 binary64))
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)))
cost-diff	7	(fma.f64 (sqrt.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64))) (sqrt.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64))) x)
cost-diff	0	(-.f64 y x)
cost-diff	0	(/.f64 (-.f64 y x) #s(literal -2 binary64))
cost-diff	0	(sqrt.f64 x)
cost-diff	3	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (/.f64 (-.f64 y x) #s(literal -2 binary64)))
cost-diff	0	(-.f64 x y)
cost-diff	0	(fabs.f64 (-.f64 x y))
cost-diff	0	(*.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 x y)) #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)
cost-diff	0	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	251
0	50	241
1	96	225
2	313	221
3	1246	221
4	4267	221
0	8280	221

Stop Event

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

Calls

Call 1

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

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

localize151.0ms (3.4%)

Memory

17.1MiB live, 208.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.078125	(fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x))
accuracy	7.35151392695581	(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (.f64 x x))) (/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x))))
accuracy	8.149457859360206	(/.f64 x (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x)))
accuracy	13.496873459998936	(/.f64 (pow.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)) x) (/.f64 (-.f64 y x) #s(literal -2 binary64)) (*.f64 x x)))
accuracy	0.0	(/.f64 (-.f64 y x) #s(literal -2 binary64))
accuracy	0.0	(-.f64 y x)
accuracy	0.0	(sqrt.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64)))
accuracy	0.10546875	(fma.f64 (sqrt.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64))) (sqrt.f64 (/.f64 (-.f64 y x) #s(literal -2 binary64))) x)
accuracy	0.0	(/.f64 (-.f64 y x) #s(literal -2 binary64))
accuracy	0.0	(-.f64 y x)
accuracy	0.0	(sqrt.f64 x)
accuracy	0.08203125	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (/.f64 (-.f64 y x) #s(literal -2 binary64)))
accuracy	0.0	(-.f64 x y)
accuracy	0.0	(*.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64))
accuracy	0.0	(fabs.f64 (-.f64 x y))
accuracy	12.32172858000278	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64)))
accuracy	0.0	(-.f64 x y)
accuracy	0.0	(fabs.f64 (-.f64 x y))
accuracy	0.0	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x))
accuracy	0.046875	(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)

Samples

56.0ms	162×	0	invalid
37.0ms	11×	1	valid
14.0ms	71×	0	valid
6.0ms	8×	2	valid
4.0ms	4×	3	valid

Compiler

Compiled 247 to 32 computations (87% saved)

Precisions

Click to see histograms. Total time spent on operations: 96.0ms

ival-fabs: 35.0ms (36.5% of total)

ival-div: 25.0ms (26% of total)

ival-add: 10.0ms (10.4% of total)

ival-mult: 9.0ms (9.4% of total)

ival-pow: 5.0ms (5.2% of total)

ival-sub: 4.0ms (4.2% of total)

ival-sqrt: 4.0ms (4.2% of total)

adjust: 2.0ms (2.1% of total)

exact: 1.0ms (1% of total)

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

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

series48.0ms (1.1%)

Memory

-16.3MiB live, 83.7MiB allocated

Counts

17 → 145

Calls

Call 1

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

Outputs
(* 1/2 (fabs (- y x)))
(+ x (* 1/2 (fabs (- y x))))
(* 1/2 (fabs (- x y)))
(+ x (* 1/2 (fabs (- x y))))
(fabs (- x y))
(* -1 y)
(- x y)
(* -1/2 y)
(+ (* -1/2 y) (* 3/2 x))
(sqrt x)
(+ (* -1/2 y) (* 1/2 x))
y
(+ y (* -1 x))
(* y (pow (sqrt -1/2) 2))
(+ (* x (+ 1 (* -1 (pow (sqrt -1/2) 2)))) (* y (pow (sqrt -1/2) 2)))
(* (sqrt y) (sqrt -1/2))
(+ (* -1/2 (* (* x (sqrt -1/2)) (sqrt (/ 1 y)))) (* (sqrt y) (sqrt -1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt -1/2))) (* -1/8 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (sqrt -1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt -1/2))) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow y 3))) (sqrt -1/2))) (* -1/16 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 5))))))))) (* (sqrt y) (sqrt -1/2)))
(+ (* -1/2 y) (* -1/8 (* x (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y))))))
(+ (* -1/2 y) (* x (+ (* -1/8 (* x (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y)))))) (* -1/8 (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))))))
(+ (* -1/2 y) (* x (+ (* -1/8 (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (* x (+ (* -1/8 (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (* x (+ (* 1/8 (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (pow y 2))) (+ (* 3 (/ (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y))) (pow y 2))) (* 4 (/ 1 (pow y 2)))))) (* 4 (/ 1 (pow y 2))))))))))
(pow x 2)
(* 4 (/ x (pow y 2)))
(* x (+ (* 8 (/ (* x (+ (* -1/2 y) (* 1/2 y))) (pow y 4))) (* 4 (/ 1 (pow y 2)))))
(* x (+ (* x (- (* -1 (* x (+ (* -16 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow y 6))) (* 12 (/ 1 (pow y 4)))))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) (pow y 4))))) (* 4 (/ 1 (pow y 2)))))
(* x (+ (* x (- (* x (- (* -1 (* x (+ (* 2 (/ (* (+ (* -16 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow y 6))) (* 12 (/ 1 (pow y 4)))) (+ (* -1/2 y) (* 1/2 y))) (pow y 2))) (* 24 (/ (+ (* -1/2 y) (* 1/2 y)) (pow y 6)))))) (+ (* -16 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow y 6))) (* 12 (/ 1 (pow y 4)))))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) (pow y 4))))) (* 4 (/ 1 (pow y 2)))))
(* 1/4 (pow y 2))
(+ (* -1/2 (* x (+ (* -1/2 y) (* 1/2 y)))) (* 1/4 (pow y 2)))
(+ (* 1/4 (pow y 2)) (* x (+ (* -1/2 (+ (* -1/2 y) (* 1/2 y))) (* 3/4 x))))
(+ (* -1/2 y) (* x (+ (* -1/8 (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (* x (+ (* -1/8 (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (* 1/8 (* x (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (pow y 2))) (+ (* 3 (/ (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y))) (pow y 2))) (* 4 (/ 1 (pow y 2))))))))))))
x
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(* x (+ 1 (* 1/2 (/ (fabs (- x y)) x))))
(* x (+ 1 (* -1 (/ y x))))
(* 3/2 x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(* 1/2 x)
(* x (+ 1/2 (* -1/2 (/ y x))))
(* -1 x)
(* x (- (/ y x) 1))
(* x (+ 1 (* -1 (pow (sqrt -1/2) 2))))
(* x (+ 1 (+ (* -1 (pow (sqrt -1/2) 2)) (/ (* y (pow (sqrt -1/2) 2)) x))))
(* (sqrt x) (* (sqrt -1) (sqrt -1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (* y (sqrt -1/2)) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (* (pow y 2) (sqrt -1/2)) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (* y (sqrt -1/2)) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (* (pow y 2) (sqrt -1/2)) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (* (pow y 3) (sqrt -1/2)) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (* y (sqrt -1/2)) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))))
(* x (- (+ 3/2 (* -1/8 (/ (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x))) (* -8/9 (/ (+ (* -1/2 y) (* 1/2 y)) x))))
(* x (- (+ 3/2 (+ (* -1/8 (/ (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x)) (* -1/8 (/ (- (* 4/3 (+ (* -2 (pow y 2)) (* -1 (pow y 2)))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* -4/9 (pow y 2)))) (pow x 2))))) (+ (* -8/9 (/ (+ (* -1/2 y) (* 1/2 y)) x)) (+ (* -16/27 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow x 2))) (* 4/9 (/ (pow y 2) (pow x 2)))))))
(* x (- (+ 3/2 (+ (* -1/8 (/ (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x)) (+ (* -1/8 (/ (- (* 4/3 (+ (* -2 (pow y 2)) (* -1 (pow y 2)))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* -4/9 (pow y 2)))) (pow x 2))) (* -1/8 (/ (- (* 4/3 (pow y 3)) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ (* -2 (pow y 2)) (* -1 (pow y 2)))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* -4/9 (pow y 2)))))) (* 1/3 (* (pow y 2) (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))))))) (pow x 3)))))) (+ (* -8/9 (/ (+ (* -1/2 y) (* 1/2 y)) x)) (+ (* -16/27 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow x 2))) (+ (* 8/27 (/ (* (pow y 2) (+ (* -1/2 y) (* 1/2 y))) (pow x 3))) (+ (* 4/9 (/ (pow y 2) (pow x 2))) (* 2/3 (/ (* (+ (* -16/27 (pow (+ (* -1/2 y) (* 1/2 y)) 2)) (* 4/9 (pow y 2))) (+ (* -1/2 y) (* 1/2 y))) (pow x 3)))))))))
(/ 4/3 x)
(/ (+ 4/3 (* 8/9 (/ (+ (* -1/2 y) (* 1/2 y)) x))) x)
(/ (- (+ 4/3 (* -1 (/ (+ (* -16/27 (pow (+ (* -1/2 y) (* 1/2 y)) 2)) (* 4/9 (pow y 2))) (pow x 2)))) (* -8/9 (/ (+ (* -1/2 y) (* 1/2 y)) x))) x)
(/ (- (+ 4/3 (* -1 (/ (+ (* 8/27 (* (pow y 2) (+ (* -1/2 y) (* 1/2 y)))) (* 2/3 (* (+ (* -16/27 (pow (+ (* -1/2 y) (* 1/2 y)) 2)) (* 4/9 (pow y 2))) (+ (* -1/2 y) (* 1/2 y))))) (pow x 3)))) (+ (* -8/9 (/ (+ (* -1/2 y) (* 1/2 y)) x)) (+ (* -16/27 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow x 2))) (* 4/9 (/ (pow y 2) (pow x 2)))))) x)
(* 3/4 (pow x 2))
(* (pow x 2) (+ 3/4 (* -1/2 (/ (+ (* -1/2 y) (* 1/2 y)) x))))
(* (pow x 2) (+ 3/4 (+ (* -1/2 (/ (+ (* -1/2 y) (* 1/2 y)) x)) (* 1/4 (/ (pow y 2) (pow x 2))))))
(* 1/6 x)
(* x (+ 1/6 (* -1/8 (/ (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x))))
(* x (+ 1/6 (+ (* -1/8 (/ (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x)) (* -1/8 (/ (- (* 4/3 (+ (* -2 (pow y 2)) (* -1 (pow y 2)))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* -4/9 (pow y 2)))) (pow x 2))))))
(* x (+ 1/6 (+ (* -1/8 (/ (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x)) (+ (* -1/8 (/ (- (* 4/3 (+ (* -2 (pow y 2)) (* -1 (pow y 2)))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* -4/9 (pow y 2)))) (pow x 2))) (* -1/8 (/ (- (* 4/3 (pow y 3)) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ (* -2 (pow y 2)) (* -1 (pow y 2)))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* -4/9 (pow y 2)))))) (* 1/3 (* (pow y 2) (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))))))) (pow x 3)))))))
(* -1 (* x (- (* -1/2 (/ (fabs (+ y (* -1 x))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (fabs (neg (+ y (* -1 x)))) x)) 1)))
(fabs (neg (+ y (* -1 x))))
(* -1 (* x (- (/ y x) 1)))
(* 1/2 (fabs (neg (+ y (* -1 x)))))
(* -1 (* x (- (pow (sqrt -1) 2) 1/2)))
(* -1 (* x (- (+ (* 1/2 (/ y x)) (pow (sqrt -1) 2)) 1/2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* 1/2 (/ y x)) 1/2)))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (- (pow (sqrt -1/2) 2) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt -1/2) 2)) x)) (pow (sqrt -1/2) 2)) 1)))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (* (sqrt -1) (sqrt -1/2))))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (* (sqrt -1) (sqrt -1/2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (* (sqrt -1) (sqrt -1/2))))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (* (sqrt -1) (sqrt -1/2))))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (* (sqrt -1) (sqrt -1/2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (* (sqrt -1) (sqrt -1/2))))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2))))))))
(* -1 (* x (- (* -1 (/ (+ (* -8/9 (+ (* -1/2 y) (* 1/2 y))) (* -1/8 (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))))) x)) 3/2)))
(* -1 (* x (- (* -1 (/ (+ (* -1 (/ (+ (* -16/27 (pow (+ (* -1/2 y) (* 1/2 y)) 2)) (+ (* -1/8 (- (* 4/3 (+ (* 2 (pow y 2)) (pow y 2))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* 4/9 (pow y 2))))) (* 4/9 (pow y 2)))) x)) (+ (* -8/9 (+ (* -1/2 y) (* 1/2 y))) (* -1/8 (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y))))))) x)) 3/2)))
(* -1 (* x (- (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (- (* 4/3 (pow y 3)) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ (* 2 (pow y 2)) (pow y 2))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* 4/9 (pow y 2)))))) (* 1/3 (* (pow y 2) (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y))))))))) (+ (* 8/27 (* (pow y 2) (+ (* -1/2 y) (* 1/2 y)))) (* 2/3 (* (+ (* -16/27 (pow (+ (* -1/2 y) (* 1/2 y)) 2)) (* 4/9 (pow y 2))) (+ (* -1/2 y) (* 1/2 y)))))) x)) (+ (* -16/27 (pow (+ (* -1/2 y) (* 1/2 y)) 2)) (+ (* -1/8 (- (* 4/3 (+ (* 2 (pow y 2)) (pow y 2))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* 4/9 (pow y 2))))) (* 4/9 (pow y 2))))) x)) (+ (* -8/9 (+ (* -1/2 y) (* 1/2 y))) (* -1/8 (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y))))))) x)) 3/2)))
(* -1 (/ (- (* 8/9 (/ (+ (* -1/2 y) (* 1/2 y)) x)) 4/3) x))
(* -1 (/ (- (* -1 (/ (- (+ (* -4/9 (/ (pow y 2) x)) (* 16/27 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) x))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x)) 4/3) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (+ (* -8/27 (/ (* (pow y 2) (+ (* -1/2 y) (* 1/2 y))) x)) (* 2/3 (/ (* (+ (* -1/2 y) (* 1/2 y)) (+ (* -4/9 (pow y 2)) (* 16/27 (pow (+ (* -1/2 y) (* 1/2 y)) 2)))) x))) (+ (* -4/9 (pow y 2)) (* 16/27 (pow (+ (* -1/2 y) (* 1/2 y)) 2)))) x)) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x)) 4/3) x))
(* (pow x 2) (+ 3/4 (* 1/2 (/ (+ (* -1/2 y) (* 1/2 y)) x))))
(* (pow x 2) (+ 3/4 (* -1 (/ (+ (* -1/2 (+ (* -1/2 y) (* 1/2 y))) (* -1/4 (/ (pow y 2) x))) x))))
(* -1 (* x (- (* 1/8 (/ (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))) x)) 1/6)))
(* -1 (* x (- (* -1 (/ (+ (* -1/8 (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y))))) (* 1/8 (/ (- (* 4/3 (+ (* 2 (pow y 2)) (pow y 2))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* 4/9 (pow y 2)))) x))) x)) 1/6)))
(* -1 (* x (- (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (- (* 4/3 (+ (* 2 (pow y 2)) (pow y 2))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* 4/9 (pow y 2))))) (* 1/8 (/ (- (* 4/3 (pow y 3)) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ (* 2 (pow y 2)) (pow y 2))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* 4/9 (pow y 2)))))) (* 1/3 (* (pow y 2) (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))))))) x))) x)) (* -1/8 (- (* 4/3 (+ y (* 2 y))) (* -8/9 (+ (* -1/2 y) (* 1/2 y)))))) x)) 1/6)))
(+ x (* -1 y))
(+ x (* 1/2 x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(- y x)
(+ x (* -1 (* x (pow (sqrt -1/2) 2))))
(+ x (+ (* -1 (* x (pow (sqrt -1/2) 2))) (* y (pow (sqrt -1/2) 2))))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ (* y (sqrt -1/2)) (sqrt -1)))) (* (sqrt x) (* (sqrt -1) (sqrt -1/2))))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ (* y (sqrt -1/2)) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1/2) (sqrt -1)))))) (* (sqrt x) (* (sqrt -1) (sqrt -1/2))))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1/2) (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1/2) (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ (* y (sqrt -1/2)) (pow (sqrt -1) 5)))))))) (* (sqrt x) (* (sqrt -1) (sqrt -1/2))))
(+ (* 1/8 (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))
(+ (* -1/8 (* y (+ (* 2 (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) (+ (* 1/8 (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))
(+ (* 1/8 (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (+ (* y (+ (* -1/8 (+ (* 2 (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (* y (- (* -1/8 (- (+ (* -2 (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (* -1 (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (* -1/4 (/ (pow x 3) (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2))))) (* 1/4 (/ (pow x 3) (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2))))))) (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))
(+ (* 1/8 (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (+ (* y (+ (* -1/8 (+ (* 2 (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (* y (- (+ (* -1/8 (* y (- (/ 1 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))) (* 1/4 (/ (+ (* 2 (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))))) (* -1/8 (- (+ (* -2 (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (* -1 (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (* -1/4 (/ (pow x 3) (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2)))))) (* 1/4 (/ (pow x 3) (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2))))))) (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))
(/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))
(+ (* -1/4 (/ (* x (pow y 2)) (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2))) (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))
(+ (* (pow y 2) (- (* 1/16 (/ (* x (pow y 2)) (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 3))) (* 1/4 (/ x (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2))))) (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))
(+ (* (pow y 2) (- (* (pow y 2) (- (* -1/64 (/ (* x (pow y 2)) (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 4))) (* -1/16 (/ x (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 3))))) (* 1/4 (/ x (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2))))) (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))
(+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))
(+ (* 1/4 (pow y 2)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))
(* 1/8 (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))
(+ (* -1/8 (* y (+ (* 2 (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) (* 1/8 (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))
(+ (* 1/8 (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (* y (+ (* -1/8 (* y (- (+ (* -2 (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (* -1 (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (* -1/4 (/ (pow x 3) (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2)))))) (* -1/8 (+ (* 2 (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))))))
(+ (* 1/8 (/ (pow x 3) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (* y (+ (* -1/8 (+ (* 2 (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (* y (+ (* -1/8 (* y (- (/ 1 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))) (* 1/4 (/ (+ (* 2 (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (/ (pow x 2) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))))) (* -1/8 (- (+ (* -2 (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (* -1 (/ x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (* -1/4 (/ (pow x 3) (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2))))))))))
(* y (- (/ x y) 1))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* y (- (* 1/2 (/ x y)) 1/2))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ (* -1 (/ (* x (pow (sqrt -1/2) 2)) y)) (+ (/ x y) (pow (sqrt -1/2) 2))))
(* y (+ (* -1/2 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (sqrt -1/2))))
(* y (+ (* -1/2 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* (pow x 2) (sqrt -1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt -1/2)))))
(* y (+ (* -1/2 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* (pow x 2) (sqrt -1/2)) (sqrt (/ 1 (pow y 5))))) (+ (* -1/16 (* (* (pow x 3) (sqrt -1/2)) (sqrt (/ 1 (pow y 7))))) (* (sqrt (/ 1 y)) (sqrt -1/2))))))
(* y (- (* -1/2 (/ (+ (* -2 x) (* -1 x)) y)) 1/2))
(* y (- (+ (* -1/2 (/ (+ (* -2 x) (* -1 x)) y)) (* -1/8 (/ (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (pow y 2)))) 1/2))
(* y (- (+ (* -1/2 (/ (+ (* -2 x) (* -1 x)) y)) (+ (* -1/8 (/ (- (* -4 (pow x 3)) (* 16 (* (+ (* -2 x) (* -1 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (pow y 3))) (+ (* -1/8 (/ (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (pow y 2))) (* 4 (/ (pow x 3) (pow y 3)))))) 1/2))
(/ (+ (* -16 (/ (* x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))) (pow y 2))) (* 4 x)) (pow y 2))
(/ (- (+ (* 4 x) (* 64 (/ (* x (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2)) (pow y 4)))) (* 16 (/ (* x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))) (pow y 2)))) (pow y 2))
(/ (- (+ (* -256 (/ (* x (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 3)) (pow y 6))) (* 4 x)) (+ (* -64 (/ (* x (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2)) (pow y 4))) (* 16 (/ (* x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))) (pow y 2))))) (pow y 2))
(* (pow y 2) (+ 1/4 (+ (* 1/2 (/ (* x (- (* 1/2 x) x)) (pow y 2))) (/ (pow x 2) (pow y 2)))))
(* y (- (+ (* -1/2 (/ (+ (* -2 x) (* -1 x)) y)) (+ (* -1/8 (/ (- (* -4 (pow x 3)) (* 16 (* (+ (* -2 x) (* -1 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (pow y 3))) (* -1/8 (/ (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (pow y 2))))) 1/2))
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(fabs (+ x (* -1 y)))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* 1/2 (fabs (+ x (* -1 y))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (pow (sqrt 1/2) 2)))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* (sqrt y) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* y (+ (* 1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))))
(* -1 (* y (+ 1/2 (* -1/2 (/ (+ x (* 2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1/8 (/ (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) y)) (* 1/2 (+ x (* 2 x)))) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (- (* 4 (pow x 3)) (* 16 (* (+ x (* 2 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) (* 4 (pow x 3))) y)) (* 1/8 (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) y)) (* 1/2 (+ x (* 2 x)))) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (- (* 4 (pow x 3)) (* 16 (* (+ x (* 2 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) y)) (* 1/8 (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) y)) (* 1/2 (+ x (* 2 x)))) y)))))

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	y	@	0	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt x) (sqrt x)) (/ (- y x) -2)) (sqrt x) (/ (- y x) -2) (- y x) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (sqrt (/ (- y x) -2)) (+ (* (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))))
10.0ms	x	@	inf	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt x) (sqrt x)) (/ (- y x) -2)) (sqrt x) (/ (- y x) -2) (- y x) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (sqrt (/ (- y x) -2)) (+ (* (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))))
6.0ms	x	@	-inf	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt x) (sqrt x)) (/ (- y x) -2)) (sqrt x) (/ (- y x) -2) (- y x) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (sqrt (/ (- y x) -2)) (+ (* (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))))
6.0ms	x	@	0	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt x) (sqrt x)) (/ (- y x) -2)) (sqrt x) (/ (- y x) -2) (- y x) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (sqrt (/ (- y x) -2)) (+ (* (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))))
5.0ms	y	@	inf	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt x) (sqrt x)) (/ (- y x) -2)) (sqrt x) (/ (- y x) -2) (- y x) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (sqrt (/ (- y x) -2)) (+ (* (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)))) (* x x) (/ x (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x)) (/ (pow (/ (- y x) -2) 3) (+ (* (- (/ (- y x) -2) x) (/ (- y x) -2)) (* x x))))

simplify167.0ms (3.7%)

Memory

25.1MiB live, 260.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	814	4595
1	2809	4040
0	8980	3776

Stop Event

1×	iter limit
1×	node limit

Counts

145 → 143

Calls

Call 1

Inputs
(* 1/2 (fabs (- y x)))
(+ x (* 1/2 (fabs (- y x))))
(* 1/2 (fabs (- x y)))
(+ x (* 1/2 (fabs (- x y))))
(fabs (- x y))
(* -1 y)
(- x y)
(* -1/2 y)
(+ (* -1/2 y) (* 3/2 x))
(sqrt x)
(+ (* -1/2 y) (* 1/2 x))
y
(+ y (* -1 x))
(* y (pow (sqrt -1/2) 2))
(+ (* x (+ 1 (* -1 (pow (sqrt -1/2) 2)))) (* y (pow (sqrt -1/2) 2)))
(* (sqrt y) (sqrt -1/2))
(+ (* -1/2 (* (* x (sqrt -1/2)) (sqrt (/ 1 y)))) (* (sqrt y) (sqrt -1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt -1/2))) (* -1/8 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (sqrt -1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt -1/2))) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow y 3))) (sqrt -1/2))) (* -1/16 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 5))))))))) (* (sqrt y) (sqrt -1/2)))
(+ (* -1/2 y) (* -1/8 (* x (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y))))))
(+ (* -1/2 y) (* x (+ (* -1/8 (* x (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y)))))) (* -1/8 (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))))))
(+ (* -1/2 y) (* x (+ (* -1/8 (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (* x (+ (* -1/8 (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (* x (+ (* 1/8 (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (pow y 2))) (+ (* 3 (/ (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y))) (pow y 2))) (* 4 (/ 1 (pow y 2)))))) (* 4 (/ 1 (pow y 2))))))))))
(pow x 2)
(* 4 (/ x (pow y 2)))
(* x (+ (* 8 (/ (* x (+ (* -1/2 y) (* 1/2 y))) (pow y 4))) (* 4 (/ 1 (pow y 2)))))
(* x (+ (* x (- (* -1 (* x (+ (* -16 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow y 6))) (* 12 (/ 1 (pow y 4)))))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) (pow y 4))))) (* 4 (/ 1 (pow y 2)))))
(* x (+ (* x (- (* x (- (* -1 (* x (+ (* 2 (/ (* (+ (* -16 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow y 6))) (* 12 (/ 1 (pow y 4)))) (+ (* -1/2 y) (* 1/2 y))) (pow y 2))) (* 24 (/ (+ (* -1/2 y) (* 1/2 y)) (pow y 6)))))) (+ (* -16 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow y 6))) (* 12 (/ 1 (pow y 4)))))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) (pow y 4))))) (* 4 (/ 1 (pow y 2)))))
(* 1/4 (pow y 2))
(+ (* -1/2 (* x (+ (* -1/2 y) (* 1/2 y)))) (* 1/4 (pow y 2)))
(+ (* 1/4 (pow y 2)) (* x (+ (* -1/2 (+ (* -1/2 y) (* 1/2 y))) (* 3/4 x))))
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(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* (sqrt y) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* y (+ (* 1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))))
(* -1 (* y (+ 1/2 (* -1/2 (/ (+ x (* 2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1/8 (/ (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) y)) (* 1/2 (+ x (* 2 x)))) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (- (* 4 (pow x 3)) (* 16 (* (+ x (* 2 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) (* 4 (pow x 3))) y)) (* 1/8 (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) y)) (* 1/2 (+ x (* 2 x)))) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (- (* 4 (pow x 3)) (* 16 (* (+ x (* 2 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) y)) (* 1/8 (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) y)) (* 1/2 (+ x (* 2 x)))) y)))))

Outputs
(* 1/2 (fabs (- y x)))
(*.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64))
(+ x (* 1/2 (fabs (- y x))))
(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
(* 1/2 (fabs (- x y)))
(*.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64))
(+ x (* 1/2 (fabs (- x y))))
(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
(fabs (- x y))
(fabs.f64 (-.f64 x y))
(* -1 y)
(neg.f64 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))
(sqrt x)
(sqrt.f64 x)
(+ (* -1/2 y) (* 1/2 x))
(*.f64 #s(literal -1/2 binary64) (-.f64 y x))
y
(+ y (* -1 x))
(-.f64 y x)
(* y (pow (sqrt -1/2) 2))
(*.f64 #s(literal -1/2 binary64) y)
(+ (* x (+ 1 (* -1 (pow (sqrt -1/2) 2)))) (* y (pow (sqrt -1/2) 2)))
(fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y))
(* (sqrt y) (sqrt -1/2))
(*.f64 (sqrt.f64 y) (sqrt.f64 #s(literal -1/2 binary64)))
(+ (* -1/2 (* (* x (sqrt -1/2)) (sqrt (/ 1 y)))) (* (sqrt y) (sqrt -1/2)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1/2 binary64)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 (sqrt.f64 y) (sqrt.f64 #s(literal -1/2 binary64))))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt -1/2))) (* -1/8 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (sqrt -1/2)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal -1/2 binary64)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) x (*.f64 (sqrt.f64 y) (sqrt.f64 #s(literal -1/2 binary64))))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt -1/2))) (* x (+ (* -1/8 (* (sqrt (/ 1 (pow y 3))) (sqrt -1/2))) (* -1/16 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 5))))))))) (* (sqrt y) (sqrt -1/2)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 #s(literal -1/2 binary64)) (.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (.f64 (sqrt.f64 #s(literal -1/2 binary64)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1/2 binary64))) #s(literal -1/8 binary64))) x)) x (*.f64 (sqrt.f64 y) (sqrt.f64 #s(literal -1/2 binary64))))
(+ (* -1/2 y) (* -1/8 (* x (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) x) (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) (*.f64 #s(literal -1/2 binary64) y))
(+ (* -1/2 y) (* x (+ (* -1/8 (* x (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y)))))) (* -1/8 (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) (fma.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 #s(literal 3 binary64) y) y)) (fma.f64 (.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) (.f64 y y))) #s(literal -2 binary64) (/.f64 #s(literal 12 binary64) y))) x (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)))) x (.f64 #s(literal -1/2 binary64) y))
(+ (* -1/2 y) (* x (+ (* -1/8 (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (* x (+ (* -1/8 (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (* x (+ (* 1/8 (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (pow y 2))) (+ (* 3 (/ (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y))) (pow y 2))) (* 4 (/ 1 (pow y 2)))))) (* 4 (/ 1 (pow y 2))))))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 #s(literal 3 binary64) y) y)) (fma.f64 (.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) (.f64 y y))) #s(literal -2 binary64) (/.f64 #s(literal 12 binary64) y))) y) (/.f64 #s(literal 0 binary64) y)) #s(literal -2 binary64) (/.f64 (fma.f64 #s(literal 3 binary64) (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) #s(literal 4 binary64)) (.f64 y y))) #s(literal 1/8 binary64) (/.f64 #s(literal 4 binary64) (.f64 y y))) x (.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 #s(literal 3 binary64) y) y)) (fma.f64 (.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) (.f64 y y))) #s(literal -2 binary64) (/.f64 #s(literal 12 binary64) y))) #s(literal -1/8 binary64))) x (.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) #s(literal -1/8 binary64))) x (.f64 #s(literal -1/2 binary64) y))
(pow x 2)
(*.f64 x x)
(* 4 (/ x (pow y 2)))
(.f64 (/.f64 x (.f64 y y)) #s(literal 4 binary64))
(* x (+ (* 8 (/ (* x (+ (* -1/2 y) (* 1/2 y))) (pow y 4))) (* 4 (/ 1 (pow y 2)))))
(.f64 (fma.f64 (.f64 x (/.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) #s(literal 8 binary64) (/.f64 #s(literal 4 binary64) (*.f64 y y))) x)
(* x (+ (* x (- (* -1 (* x (+ (* -16 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow y 6))) (* 12 (/ 1 (pow y 4)))))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) (pow y 4))))) (* 4 (/ 1 (pow y 2)))))
(.f64 (fma.f64 (-.f64 (.f64 (neg.f64 x) (+.f64 (/.f64 #s(literal 12 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 6 binary64))))) (/.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) x (/.f64 #s(literal 4 binary64) (*.f64 y y))) x)
(* x (+ (* x (- (* x (- (* -1 (* x (+ (* 2 (/ (* (+ (* -16 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow y 6))) (* 12 (/ 1 (pow y 4)))) (+ (* -1/2 y) (* 1/2 y))) (pow y 2))) (* 24 (/ (+ (* -1/2 y) (* 1/2 y)) (pow y 6)))))) (+ (* -16 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow y 6))) (* 12 (/ 1 (pow y 4)))))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) (pow y 4))))) (* 4 (/ 1 (pow y 2)))))
(.f64 (fma.f64 (-.f64 (.f64 (-.f64 (.f64 (neg.f64 x) (fma.f64 (.f64 (+.f64 (/.f64 #s(literal 12 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 6 binary64)))) (/.f64 #s(literal 0 binary64) (.f64 y y))) #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 6 binary64))))) (+.f64 (/.f64 #s(literal 12 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 6 binary64))))) x) (/.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 4 binary64)))) x (/.f64 #s(literal 4 binary64) (.f64 y y))) x)
(* 1/4 (pow y 2))
(.f64 #s(literal 1/4 binary64) (.f64 y y))
(+ (* -1/2 (* x (+ (* -1/2 y) (* 1/2 y)))) (* 1/4 (pow y 2)))
(fma.f64 #s(literal 1/4 binary64) (.f64 y y) (.f64 (*.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64)))
(+ (* 1/4 (pow y 2)) (* x (+ (* -1/2 (+ (* -1/2 y) (* 1/2 y))) (* 3/4 x))))
(fma.f64 (fma.f64 #s(literal 3/4 binary64) x #s(literal 0 binary64)) x (.f64 #s(literal 1/4 binary64) (.f64 y y)))
(+ (* -1/2 y) (* x (+ (* -1/8 (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (* x (+ (* -1/8 (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (* 1/8 (* x (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ y (* 2 y)) (pow y 2))) (+ (* -2 (/ (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y)))) (pow y 2))) (* 12 (/ 1 y))))) (pow y 2))) (+ (* 3 (/ (- (* 4 (/ (+ (* -2 (pow y 2)) (* -1 (pow y 2))) (pow y 2))) (* -8 (/ (+ (* -1/2 y) (* 1/2 y)) y))) (pow y 2))) (* 4 (/ 1 (pow y 2))))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (-.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 #s(literal 3 binary64) y) y)) (fma.f64 (.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) (.f64 y y))) #s(literal -2 binary64) (/.f64 #s(literal 12 binary64) y))) (.f64 (fma.f64 (.f64 (/.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 #s(literal 3 binary64) y) y)) (fma.f64 (.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) (.f64 y y))) #s(literal -2 binary64) (/.f64 #s(literal 12 binary64) y))) y) (/.f64 #s(literal 0 binary64) y)) #s(literal -2 binary64) (/.f64 (fma.f64 #s(literal 3 binary64) (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) #s(literal 4 binary64)) (.f64 y y))) x))) x (.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (.f64 (.f64 y y) #s(literal -3 binary64)) y)) (/.f64 #s(literal 0 binary64) y)) #s(literal -1/8 binary64))) x (.f64 #s(literal -1/2 binary64) y))
x
(* x (+ 1 (* 1/2 (/ (fabs (- y x)) x))))
(*.f64 (fma.f64 (/.f64 (fabs.f64 (-.f64 x y)) x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* 1/2 (/ (fabs (- x y)) x))))
(*.f64 (fma.f64 (/.f64 (fabs.f64 (-.f64 x y)) x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* -1 (/ y x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* 3/2 x)
(*.f64 #s(literal 3/2 binary64) x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 3/2 binary64)) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/2 (/ y x))))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ y x) 1))
(*.f64 (-.f64 (/.f64 y x) #s(literal 1 binary64)) x)
(* x (+ 1 (* -1 (pow (sqrt -1/2) 2))))
(*.f64 #s(literal 3/2 binary64) x)
(* x (+ 1 (+ (* -1 (pow (sqrt -1/2) 2)) (/ (* y (pow (sqrt -1/2) 2)) x))))
(*.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 3/2 binary64)) x)
(* (sqrt x) (* (sqrt -1) (sqrt -1/2)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (* y (sqrt -1/2)) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (.f64 (sqrt.f64 #s(literal -1/2 binary64)) y) (sqrt.f64 #s(literal -1 binary64))) (.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (* (pow y 2) (sqrt -1/2)) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (* y (sqrt -1/2)) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (/.f64 (.f64 (.f64 y y) (sqrt.f64 #s(literal -1/2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (.f64 (sqrt.f64 #s(literal -1/2 binary64)) y) (sqrt.f64 #s(literal -1 binary64))) (.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64))))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (* (pow y 2) (sqrt -1/2)) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (* (pow y 3) (sqrt -1/2)) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (* y (sqrt -1/2)) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (/.f64 (.f64 (.f64 y y) (sqrt.f64 #s(literal -1/2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (/.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) (sqrt.f64 #s(literal -1/2 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (.f64 (sqrt.f64 #s(literal -1/2 binary64)) y) (sqrt.f64 #s(literal -1 binary64))) (.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64)))))) x)
(* x (- (+ 3/2 (* -1/8 (/ (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x))) (* -8/9 (/ (+ (* -1/2 y) (* 1/2 y)) x))))
(.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 #s(literal 3 binary64) y) #s(literal 0 binary64)) #s(literal -1/8 binary64) #s(literal 0 binary64)) x)) x)
(* x (- (+ 3/2 (+ (* -1/8 (/ (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))) x)) (* -1/8 (/ (- (* 4/3 (+ (* -2 (pow y 2)) (* -1 (pow y 2)))) (+ (* -2/3 (* (+ (* -1/2 y) (* 1/2 y)) (- (* 4/3 (+ y (* 2 y))) (* 8/9 (+ (* -1/2 y) (* 1/2 y)))))) (* -4/9 (pow y 2)))) (pow x 2))))) (+ (* -8/9 (/ (+ (* -1/2 y) (* 1/2 y)) x)) (+ (* -16/27 (/ (pow (+ (* -1/2 y) (* 1/2 y)) 2) (pow x 2))) (* 4/9 (/ (pow y 2) (pow x 2)))))))
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(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1/2 binary64)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (.f64 x x) (sqrt.f64 #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal -1/2 binary64))))) y)
(* y (+ (* -1/2 (* (* x (sqrt -1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* (pow x 2) (sqrt -1/2)) (sqrt (/ 1 (pow y 5))))) (+ (* -1/16 (* (* (pow x 3) (sqrt -1/2)) (sqrt (/ 1 (pow y 7))))) (* (sqrt (/ 1 y)) (sqrt -1/2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1/2 binary64)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))) #s(literal -1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal -1/2 binary64)))))) y)
(* y (- (* -1/2 (/ (+ (* -2 x) (* -1 x)) y)) 1/2))
(.f64 (-.f64 (.f64 (/.f64 (*.f64 x #s(literal -3 binary64)) y) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) y)
(* y (- (+ (* -1/2 (/ (+ (* -2 x) (* -1 x)) y)) (* -1/8 (/ (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (pow y 2)))) 1/2))
(.f64 (-.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) #s(literal 4 binary64) (.f64 #s(literal -16 binary64) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)))) (.f64 y y)) #s(literal -1/8 binary64) (.f64 (/.f64 (.f64 x #s(literal -3 binary64)) y) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) y)
(* y (- (+ (* -1/2 (/ (+ (* -2 x) (* -1 x)) y)) (+ (* -1/8 (/ (- (* -4 (pow x 3)) (* 16 (* (+ (* -2 x) (* -1 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (pow y 3))) (+ (* -1/8 (/ (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (pow y 2))) (* 4 (/ (pow x 3) (pow y 3)))))) 1/2))
(.f64 (-.f64 (fma.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (fma.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) #s(literal 4 binary64) (.f64 #s(literal -16 binary64) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)))) (.f64 y y)) (/.f64 (fma.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal -16 binary64) (.f64 (.f64 x #s(literal -3 binary64)) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x))))) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 4 binary64) (.f64 (/.f64 (.f64 x #s(literal -3 binary64)) y) #s(literal -1/2 binary64)))) #s(literal 1/2 binary64)) y)
(/ (+ (* -16 (/ (* x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))) (pow y 2))) (* 4 x)) (pow y 2))
(/.f64 (fma.f64 (/.f64 #s(literal -16 binary64) y) (/.f64 (.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)) x) y) (.f64 #s(literal 4 binary64) x)) (.f64 y y))
(/ (- (+ (* 4 x) (* 64 (/ (* x (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2)) (pow y 4)))) (* 16 (/ (* x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))) (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x) (pow.f64 y #s(literal 4 binary64))) #s(literal 64 binary64) (fma.f64 (/.f64 #s(literal -16 binary64) y) (/.f64 (.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)) x) y) (.f64 #s(literal 4 binary64) x))) (.f64 y y))
(/ (- (+ (* -256 (/ (* x (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 3)) (pow y 6))) (* 4 x)) (+ (* -64 (/ (* x (pow (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)) 2)) (pow y 4))) (* 16 (/ (* x (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))) (pow y 2))))) (pow y 2))
(/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)) #s(literal 3 binary64)) x) (pow.f64 y #s(literal 6 binary64))) #s(literal -256 binary64) (-.f64 (.f64 #s(literal 4 binary64) x) (fma.f64 (/.f64 #s(literal 16 binary64) y) (/.f64 (.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)) x) y) (/.f64 (.f64 #s(literal -64 binary64) (.f64 (pow.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) x)) (pow.f64 y #s(literal 4 binary64)))))) (*.f64 y y))
(* (pow y 2) (+ 1/4 (+ (* 1/2 (/ (* x (- (* 1/2 x) x)) (pow y 2))) (/ (pow x 2) (pow y 2)))))
(.f64 (+.f64 (/.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)) (.f64 y y)) #s(literal 1/4 binary64)) (.f64 y y))
(* y (- (+ (* -1/2 (/ (+ (* -2 x) (* -1 x)) y)) (+ (* -1/8 (/ (- (* -4 (pow x 3)) (* 16 (* (+ (* -2 x) (* -1 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) (pow y 3))) (* -1/8 (/ (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) (pow y 2))))) 1/2))
(.f64 (-.f64 (fma.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (fma.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) #s(literal 4 binary64) (.f64 #s(literal -16 binary64) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)))) (.f64 y y)) (/.f64 (fma.f64 #s(literal -4 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal -16 binary64) (.f64 (.f64 x #s(literal -3 binary64)) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x))))) (pow.f64 y #s(literal 3 binary64)))) (.f64 (/.f64 (.f64 x #s(literal -3 binary64)) y) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) y)
(+ x (* 1/2 (fabs (neg (+ x (* -1 y))))))
(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
(+ x (* 1/2 (fabs (+ x (* -1 y)))))
(fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x)
(fabs (+ x (* -1 y)))
(fabs.f64 (-.f64 x y))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 (neg.f64 y) (-.f64 #s(literal 1 binary64) (/.f64 x y)))
(* 1/2 (fabs (+ x (* -1 y))))
(*.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 (neg.f64 y) (fma.f64 #s(literal -3/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))
(*.f64 (neg.f64 y) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* -1 (* y (- (/ x y) 1)))
(*.f64 (neg.f64 y) (-.f64 (/.f64 x y) #s(literal 1 binary64)))
(* -1 (* y (pow (sqrt 1/2) 2)))
(*.f64 #s(literal -1/2 binary64) y)
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(*.f64 (neg.f64 y) (fma.f64 #s(literal -3/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
(* -1 (* (sqrt y) (* (sqrt -1) (sqrt 1/2))))
(.f64 (.f64 (sqrt.f64 y) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* y (+ (* 1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))))
(* -1 (* y (+ 1/2 (* -1/2 (/ (+ x (* 2 x)) y)))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 (.f64 #s(literal 3 binary64) x) y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1/8 (/ (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))) y)) (* 1/2 (+ x (* 2 x)))) y)))))
(.f64 (neg.f64 y) (-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) #s(literal 4 binary64) (.f64 #s(literal -16 binary64) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)))) y) #s(literal -1/8 binary64) (.f64 (*.f64 #s(literal 3 binary64) x) #s(literal 1/2 binary64))) y)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (- (* 4 (pow x 3)) (* 16 (* (+ x (* 2 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) (* 4 (pow x 3))) y)) (* 1/8 (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) y)) (* 1/2 (+ x (* 2 x)))) y)))))
(.f64 (neg.f64 y) (-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 #s(literal 3 binary64) x) #s(literal 1/2 binary64) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) #s(literal 4 binary64) (.f64 #s(literal -16 binary64) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x)))) #s(literal 1/8 binary64) (/.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4 binary64) (.f64 #s(literal -16 binary64) (.f64 (.f64 #s(literal 3 binary64) x) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x))))) #s(literal 1/8 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4 binary64))) (neg.f64 y))) (neg.f64 y))) y)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (- (* 4 (pow x 3)) (* 16 (* (+ x (* 2 x)) (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2))))) y)) (* 1/8 (- (* 4 (+ (* 2 (pow x 2)) (pow x 2))) (* 16 (+ (* 1/2 (* x (- (* 1/2 x) x))) (pow x 2)))))) y)) (* 1/2 (+ x (* 2 x)))) y)))))
(.f64 (neg.f64 y) (-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 #s(literal 3 binary64) x) #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (-.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4 binary64) (.f64 #s(literal -16 binary64) (.f64 (.f64 #s(literal 3 binary64) x) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (.f64 x x))))) y) (fma.f64 (.f64 #s(literal 3 binary64) (.f64 x x)) #s(literal 4 binary64) (.f64 #s(literal -16 binary64) (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) x) x) #s(literal 1/2 binary64) (*.f64 x x)))))) (neg.f64 y))) y)))

rewrite145.0ms (3.2%)

Memory

-31.4MiB live, 113.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	198
0	50	149
1	209	149
0	1836	149

Stop Event

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

Counts

17 → 346

Calls

Call 1

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

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

eval124.0ms (2.8%)

Memory: 16.2MiB live, 203.9MiB allocated
Compiler: Compiled 36 038 to 2 473 computations (93.1% saved)

prune16.0ms (0.4%)

Memory

14.3MiB live, 61.5MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	811	5	816
Fresh	0	0	0
Picked	4	1	5
Done	0	0	0
Total	815	6	821

Accuracy

100.0%

Counts

821 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.1%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))
▶	28.5%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal 3/2 binary64) x))
▶	30.3%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal -1/2 binary64) y))
✓	99.9%	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x))
▶	63.5%	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x))
▶	56.4%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64)))

Compiler

Compiled 210 to 138 computations (34.3% saved)

simplify16.0ms (0.3%)

Memory

-21.3MiB live, 26.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	174
0	36	150
1	61	150
2	107	150
3	169	150
4	246	150
5	292	150
6	323	150
7	338	150
8	354	150
9	370	150
10	382	150
11	389	150
12	397	150
13	405	150
14	408	150
0	408	150

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize162.0ms (3.6%)

Memory

20.9MiB live, 171.5MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) y)
accuracy	0.0	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))
accuracy	0.0	(neg.f64 y)
accuracy	0.0	(fabs.f64 #s(approx (- x y) (neg.f64 y)))
accuracy	12.336601060167068	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64)))
accuracy	14.487352015103244	#s(approx (- x y) (neg.f64 y))
accuracy	0.0	(*.f64 #s(literal 3/2 binary64) x)
accuracy	17.934022367093235	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal 3/2 binary64) x))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) y)
accuracy	14.503971437809078	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal -1/2 binary64) y))
accuracy	0.0	(fabs.f64 #s(approx (- x y) (neg.f64 y)))
accuracy	0.0	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x))
accuracy	0.05078125	(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)
accuracy	14.487352015103244	#s(approx (- x y) (neg.f64 y))

Samples

100.0ms	123×	0	invalid
26.0ms	8×	2	valid
16.0ms	110×	0	valid
3.0ms	11×	1	valid
2.0ms	4×	3	valid

Compiler

Compiled 124 to 25 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 118.0ms

ival-div: 95.0ms (80.4% of total)

ival-mult: 6.0ms (5.1% of total)

ival-add: 5.0ms (4.2% of total)

ival-sub: 3.0ms (2.5% of total)

ival-fabs: 3.0ms (2.5% of total)

ival-sqrt: 2.0ms (1.7% of total)

adjust: 2.0ms (1.7% of total)

exact: 1.0ms (0.8% of total)

ival-neg: 1.0ms (0.8% of total)

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

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

series10.0ms (0.2%)

Memory

-28.0MiB live, 19.0MiB allocated

Counts

13 → 41

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* -1/2 y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* 3/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* 3/2 x) (* -1/2 y)) (neg y))
2.0ms	y	@	inf	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* -1/2 y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* 3/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* 3/2 x) (* -1/2 y)) (neg y))
1.0ms	y	@	-inf	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* -1/2 y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* 3/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* 3/2 x) (* -1/2 y)) (neg y))
1.0ms	x	@	inf	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* -1/2 y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* 3/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* 3/2 x) (* -1/2 y)) (neg y))
1.0ms	x	@	0	((+ x (/ (fabs (- y x)) 2)) (+ (* (fabs (- x y)) 1/2) x) (fabs (- x y)) (- x y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* -1/2 y) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (* 3/2 x) (+ x (/ (fabs (- y x)) 2)) (* (fabs (- x y)) 1/2) (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* 3/2 x) (* -1/2 y)) (neg y))

simplify115.0ms (2.6%)

Memory

0.6MiB live, 188.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	121	351
1	362	219
2	1142	219
3	3722	219
4	6737	219
0	8225	200

Stop Event

1×	iter limit
1×	node limit

Counts

41 → 40

Calls

Call 1

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

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

rewrite43.0ms (0.9%)

Memory

34.5MiB live, 81.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	143
0	36	119
1	139	119
0	1000	119

Stop Event

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

Counts

13 → 53

Calls

Call 1

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

Outputs
#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y))) x))
(/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64)))) (-.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64)) (.f64 (neg.f64 x) x))) (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64)) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))))))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64)) (.f64 (neg.f64 x) x)) (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64))) (.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64)) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y))))))))
(fma.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y))) x)
(fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))) x)))
(-.f64 x (*.f64 #s(literal -1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))))
(-.f64 x (*.f64 (neg.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y)))) #s(literal 1/2 binary64)))
(+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64)) (.f64 x (-.f64 x (.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64)) (.f64 x (-.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))) x)
(+.f64 x (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))))
(*.f64 (sqrt.f64 #s(approx (- x y) (neg.f64 y))) (sqrt.f64 #s(approx (- x y) (neg.f64 y))))
(pow.f64 (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 #s(approx (- x y) (neg.f64 y)) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (neg.f64 #s(approx (- x y) (neg.f64 y)))))
(fabs.f64 (neg.f64 #s(approx (- x y) (neg.f64 y))))
(fabs.f64 #s(approx (- x y) (neg.f64 y)))
#s(approx (- x y) (neg.f64 y))
#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal -1/2 binary64) y))
(*.f64 #s(literal -1/2 binary64) y)
(*.f64 y #s(literal -1/2 binary64))
#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal 3/2 binary64) x))
(*.f64 #s(literal 3/2 binary64) x)
(*.f64 x #s(literal 3/2 binary64))
#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y)))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- x y) (neg.f64 y))))
(*.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))
(/.f64 (-.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y))) (fma.f64 #s(literal 3/2 binary64) x (.f64 #s(literal 1/2 binary64) y)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 2 binary64)) (.f64 #s(literal 9/4 binary64) (.f64 x x))) (-.f64 (.f64 #s(literal -1/2 binary64) y) (*.f64 #s(literal 3/2 binary64) x)))
(/.f64 (-.f64 (.f64 #s(literal 27/8 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64))) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y) (.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal 1/2 binary64) y)))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 2 binary64)))) (neg.f64 (fma.f64 #s(literal 3/2 binary64) x (.f64 #s(literal 1/2 binary64) y))))
(/.f64 (neg.f64 (fma.f64 #s(literal 27/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 3/2 binary64) x))))))
(/.f64 (-.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 2 binary64))) (fma.f64 #s(literal 3/2 binary64) x (.f64 #s(literal 1/2 binary64) y)))
(/.f64 (fma.f64 #s(literal 27/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (-.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (.f64 (.f64 (*.f64 #s(literal 3/2 binary64) x) #s(literal -1/2 binary64)) y))))
(/.f64 (fma.f64 #s(literal 27/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 3 binary64))) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 3/2 binary64) x)))))
(fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(fma.f64 y #s(literal -1/2 binary64) (*.f64 #s(literal 3/2 binary64) x))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(-.f64 (/.f64 (.f64 #s(literal 9/4 binary64) (.f64 x x)) (fma.f64 #s(literal 3/2 binary64) x (.f64 #s(literal 1/2 binary64) y))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 2 binary64)) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))))
(-.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 (neg.f64 y) #s(literal -1/2 binary64)))
(-.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal 1/2 binary64) y))
(-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal -3/2 binary64) x))
(-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 (neg.f64 x) #s(literal 3/2 binary64)))
(+.f64 (/.f64 (.f64 #s(literal 27/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 3/2 binary64) x))))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 3 binary64)) (fma.f64 #s(literal 9/4 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/2 binary64) y) (-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 3/2 binary64) x))))))
(+.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal -1/2 binary64) y))
(+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 3/2 binary64) x))
(neg.f64 y)

eval24.0ms (0.5%)

Memory: -6.9MiB live, 45.4MiB allocated
Compiler: Compiled 2 006 to 242 computations (87.9% saved)

prune5.0ms (0.1%)

Memory

-34.0MiB live, 13.3MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	75	7	82

Accuracy

100.0%

Counts

82 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.1%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x))
✓	56.1%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))
✓	28.5%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal 3/2 binary64) x))
✓	30.3%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal -1/2 binary64) y))
✓	99.9%	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x))
✓	63.5%	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x))
✓	56.4%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64)))

Compiler

Compiled 135 to 87 computations (35.6% saved)

simplify6.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
0	15	26
1	26	26
2	53	26
3	77	26
4	92	26
5	101	26
6	107	26
7	108	26
8	110	26
9	111	26
10	113	26
11	114	26
12	116	26
0	116	26

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize29.0ms (0.7%)

Memory

17.5MiB live, 64.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 y x)
accuracy	0.0	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x))
accuracy	0.05078125	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)

Samples

9.0ms	123×	0	invalid
9.0ms	110×	0	valid
2.0ms	8×	2	valid
2.0ms	11×	1	valid
1.0ms	4×	3	valid

Compiler

Compiled 30 to 13 computations (56.7% saved)

Precisions

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

ival-mult: 4.0ms (27.8% of total)

ival-add: 3.0ms (20.8% of total)

ival-div: 2.0ms (13.9% of total)

ival-sqrt: 2.0ms (13.9% of total)

ival-sub: 2.0ms (13.9% of total)

adjust: 1.0ms (6.9% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

3 → 28

Calls

Call 1

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

Outputs
(* y (pow (sqrt -1/2) 2))
(+ (* x (+ 1 (* -1 (pow (sqrt -1/2) 2)))) (* y (pow (sqrt -1/2) 2)))
(* -1/2 y)
(+ (* -1/2 y) (* 3/2 x))
y
(+ y (* -1 x))
(* x (+ 1 (* -1 (pow (sqrt -1/2) 2))))
(* x (+ 1 (+ (* -1 (pow (sqrt -1/2) 2)) (/ (* y (pow (sqrt -1/2) 2)) x))))
(* 3/2 x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(* -1 x)
(* x (- (/ y x) 1))
(* -1 (* x (- (pow (sqrt -1/2) 2) 1)))
(* -1 (* x (- (+ (* -1 (/ (* y (pow (sqrt -1/2) 2)) x)) (pow (sqrt -1/2) 2)) 1)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(+ x (* -1 (* x (pow (sqrt -1/2) 2))))
(+ x (+ (* -1 (* x (pow (sqrt -1/2) 2))) (* y (pow (sqrt -1/2) 2))))
(+ x (* 1/2 x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(- y x)
(* y (+ (* -1 (/ (* x (pow (sqrt -1/2) 2)) y)) (+ (/ x y) (pow (sqrt -1/2) 2))))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* y (+ 1 (* -1 (/ x y))))
(* -1 (* y (pow (sqrt 1/2) 2)))
(* -1 (* y (+ (* -1 (/ (+ x (* x (pow (sqrt 1/2) 2))) y)) (pow (sqrt 1/2) 2))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1 (* y (- (/ x y) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* (- y x) -1/2) x) (- y x))
0.0ms	x	@	-inf	((+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* (- y x) -1/2) x) (- y x))
0.0ms	y	@	-inf	((+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* (- y x) -1/2) x) (- y x))
0.0ms	y	@	inf	((+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* (- y x) -1/2) x) (- y x))
0.0ms	x	@	0	((+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (+ (* (- y x) -1/2) x) (- y x))

simplify90.0ms (2%)

Memory

-6.1MiB live, 131.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	276
1	287	129
2	1035	129
3	2753	129
4	5754	129
0	8086	117

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 27

Calls

Call 1

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

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

rewrite86.0ms (1.9%)

Memory

26.3MiB live, 97.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
0	15	23
1	70	23
0	540	23

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

3 → 22

Calls

Call 1

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

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

eval4.0ms (0.1%)

Memory: 13.6MiB live, 13.6MiB allocated
Compiler: Compiled 932 to 123 computations (86.8% saved)

prune61.0ms (1.3%)

Memory

-51.6MiB live, 61.6MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	30	7	37

Accuracy

100.0%

Counts

37 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.1%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x))
✓	56.1%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y)))
✓	28.5%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal 3/2 binary64) x))
✓	30.3%	#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal -1/2 binary64) y))
✓	99.9%	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x))
✓	63.5%	#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x))
✓	56.4%	#s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64)))

Compiler

Compiled 363 to 143 computations (60.6% saved)

regimes12.0ms (0.3%)

Memory

38.7MiB live, 38.7MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes19.0ms (0.4%)

Memory

-25.8MiB live, 18.1MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

13.0ms	y
2.0ms	x
2.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
63.5%	1	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
77.1%	2	`x`
75.0%	2	`y`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes4.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Counts

5 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
73.9%	2	`y`
74.8%	3	`x`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes4.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

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

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes4.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
70.1%	2	`x`
65.8%	3	`y`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes5.0ms (0.1%)

Memory

-37.8MiB live, 10.5MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	x
1.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))
1.0ms	y

Results

Accuracy	Segments	Branch
49.2%	2	`y`
35.8%	3	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
46.4%	2	`x`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes3.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

Outputs
#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) 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	x
1.0ms	y

Results

Accuracy	Segments	Branch
30.3%	1	`(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) #s(literal 2 binary64)))`
30.3%	1	`x`
30.3%	1	`y`

Compiler

Compiled 10 to 11 computations (-10% saved)

bsearch12.0ms (0.3%)

Memory

21.3MiB live, 21.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	4.8405028806304835e-73	1.7844051614620863e-70

Samples

6.0ms	127×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 339 to 236 computations (30.4% saved)

Precisions

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

ival-div: 1.0ms (31.3% of total)

ival-add: 1.0ms (31.3% of total)

ival-fabs: 1.0ms (31.3% of total)

ival-sub: 1.0ms (31.3% 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)

bsearch37.0ms (0.8%)

Memory

-21.2MiB live, 24.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
35.0ms	2.1989849700288713e-170	5.330740489894525e-170

Samples

27.0ms	77×	0	valid
0.0ms	2×	2	valid
0.0ms	1×	3	valid

Compiler

Compiled 196 to 142 computations (27.6% saved)

Precisions

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

ival-div: 22.0ms (88.6% of total)

ival-sub: 1.0ms (4% of total)

ival-fabs: 1.0ms (4% of total)

ival-add: 1.0ms (4% 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)

bsearch5.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
4.0ms	2.1989849700288713e-170	5.330740489894525e-170

Samples

2.0ms

32×

valid

Compiler

Compiled 211 to 152 computations (28% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

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

exact: 0.0ms (0% of total)

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

bsearch10.0ms (0.2%)

Memory

17.6MiB live, 17.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	4.054432836712902e-40	4.151163046528195e-39

Samples

4.0ms	89×	0	valid
0.0ms	5×	1	valid
0.0ms	2×	2	valid

Compiler

Compiled 233 to 174 computations (25.3% saved)

Precisions

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

ival-div: 1.0ms (36.8% of total)

ival-sub: 1.0ms (36.8% of total)

ival-add: 1.0ms (36.8% of total)

ival-fabs: 1.0ms (36.8% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

bsearch10.0ms (0.2%)

Memory

-35.5MiB live, 14.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	-1.852570369235908e-83	-7.9349837174673685e-84

Samples

4.0ms	73×	0	valid
1.0ms	6×	2	valid
0.0ms	1×	1	valid

Compiler

Compiled 201 to 132 computations (34.3% saved)

Precisions

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

ival-div: 1.0ms (38.7% of total)

ival-sub: 1.0ms (38.7% of total)

ival-fabs: 1.0ms (38.7% 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)

simplify64.0ms (1.4%)

Memory

22.1MiB live, 68.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	192
1	79	192
2	123	192
3	195	192
4	296	192
5	473	192
6	708	192
7	1403	192
8	5852	192

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 5172161658661781/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)) #s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)))
(if (<=.f64 y #s(literal 2515469533980209/67985663080546188632267290438715984298187919069060086169528849689651655662189087070612800289949348565617834174239552129964362155219546526644418557282123181048810402666930332036061200384 binary64)) #s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)) #s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64))))
(if (<=.f64 y #s(literal 5438853046443695/135971326161092377264534580877431968596375838138120172339057699379303311324378174141225600579898697131235668348479104259928724310439093053288837114564246362097620805333860664072122400768 binary64)) #s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)) #s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 1915619426082361/766247770432944429179173513575154591809369561091801088 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64))) #s(approx (+ ( (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal 3/2 binary64) x)))
(if (<=.f64 y #s(literal -861229972883311/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432 binary64)) #s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (.f64 #s(literal -1/2 binary64) y)) #s(approx (+ ( (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal 3/2 binary64) x)))
#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal -1/2 binary64) y))

Outputs
#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64) x))
#s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 5172161658661781/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (fma.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64) x)) #s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)))
(if (<=.f64 y #s(literal 2515469533980209/67985663080546188632267290438715984298187919069060086169528849689651655662189087070612800289949348565617834174239552129964362155219546526644418557282123181048810402666930332036061200384 binary64)) #s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)) #s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 (-.f64 x y)) #s(literal 1/2 binary64))))
(if (<=.f64 y #s(literal 2515469533980209/67985663080546188632267290438715984298187919069060086169528849689651655662189087070612800289949348565617834174239552129964362155219546526644418557282123181048810402666930332036061200384 binary64)) #s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (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 5438853046443695/135971326161092377264534580877431968596375838138120172339057699379303311324378174141225600579898697131235668348479104259928724310439093053288837114564246362097620805333860664072122400768 binary64)) #s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)) #s(approx (+ x (/ (fabs (- y x)) 2)) (*.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 1915619426082361/766247770432944429179173513575154591809369561091801088 binary64)) #s(approx (+ x (/ (fabs (- y x)) 2)) (.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))) #s(literal 1/2 binary64))) #s(approx (+ ( (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal 3/2 binary64) x)))
(if (<=.f64 y #s(literal -861229972883311/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432 binary64)) #s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (.f64 #s(literal -1/2 binary64) y)) #s(approx (+ ( (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal 3/2 binary64) x)))
#s(approx (+ (* (sqrt (/ (- y x) -2)) (sqrt (/ (- y x) -2))) x) (*.f64 #s(literal -1/2 binary64) y))

soundness969.0ms (21.5%)

Memory

-8.1MiB live, 516.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	814	4595
1	2809	4040
0	8980	3776
0	121	351
1	362	219
2	1142	219
3	3722	219
4	6737	219
0	8225	200
0	7	21
0	11	20
1	47	20
2	323	18
3	4001	18
0	8907	18
0	43	84
1	127	84
2	346	84
3	968	84
4	2383	84
5	3739	84
6	6329	84
0	8023	80

Stop Event

1×	done
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

Compiler

Compiled 357 to 169 computations (52.7% saved)

preprocess38.0ms (0.8%)

Memory: 27.2MiB live, 73.3MiB allocated
Compiler: Compiled 512 to 114 computations (77.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	19	48
1	41	46
2	70	46
3	110	46
4	191	46
5	257	46
6	265	46
7	278	46
8	280	46
0	7	8
0	11	8
1	18	8
2	25	8
3	39	8
4	66	8
5	88	8
6	90	8
7	94	8
8	97	8
0	97	8

Iter	Nodes	Cost
0	29	174
0	36	150
1	61	150
2	107	150
3	169	150
4	246	150
5	292	150
6	323	150
7	338	150
8	354	150
9	370	150
10	382	150
11	389	150
12	397	150
13	405	150
14	408	150
0	408	150

Iter	Nodes	Cost
0	12	34
0	15	26
1	26	26
2	53	26
3	77	26
4	92	26
5	101	26
6	107	26
7	108	26
8	110	26
9	111	26
10	113	26
11	114	26
12	116	26
0	116	26

Iter	Nodes	Cost
0	19	48
1	41	46
2	70	46
3	110	46
4	191	46
5	257	46
6	265	46
7	278	46
8	280	46
0	7	8
0	11	8
1	18	8
2	25	8
3	39	8
4	66	8
5	88	8
6	90	8
7	94	8
8	97	8
0	97	8

Iter	Nodes	Cost
0	29	174
0	36	150
1	61	150
2	107	150
3	169	150
4	246	150
5	292	150
6	323	150
7	338	150
8	354	150
9	370	150
10	382	150
11	389	150
12	397	150
13	405	150
14	408	150
0	408	150

Iter	Nodes	Cost
0	12	34
0	15	26
1	26	26
2	53	26
3	77	26
4	92	26
5	101	26
6	107	26
7	108	26
8	110	26
9	111	26
10	113	26
11	114	26
12	116	26
0	116	26

start0.0ms (0%)

analyze0.0ms (0%)

sample967.0ms (21.5%)

explain93.0ms (2.1%)

preprocess58.0ms (1.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize19.0ms (0.4%)

series4.0ms (0.1%)

simplify196.0ms (4.4%)

rewrite357.0ms (7.9%)

eval60.0ms (1.3%)

prune5.0ms (0.1%)

simplify233.0ms (5.2%)

localize151.0ms (3.4%)

series48.0ms (1.1%)

simplify167.0ms (3.7%)

rewrite145.0ms (3.2%)

eval124.0ms (2.8%)

prune16.0ms (0.4%)

simplify16.0ms (0.3%)

localize162.0ms (3.6%)

series10.0ms (0.2%)

simplify115.0ms (2.6%)

rewrite43.0ms (0.9%)

eval24.0ms (0.5%)

prune5.0ms (0.1%)

simplify6.0ms (0.1%)

localize29.0ms (0.7%)

series3.0ms (0.1%)

simplify90.0ms (2%)

rewrite86.0ms (1.9%)

eval4.0ms (0.1%)

prune61.0ms (1.3%)

regimes12.0ms (0.3%)

regimes19.0ms (0.4%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch12.0ms (0.3%)

bsearch37.0ms (0.8%)

bsearch5.0ms (0.1%)

bsearch10.0ms (0.2%)

bsearch10.0ms (0.2%)

simplify64.0ms (1.4%)

soundness969.0ms (21.5%)

preprocess38.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	19	48
1	41	46
2	70	46
3	110	46
4	191	46
5	257	46
6	265	46
7	278	46
8	280	46
0	7	8
0	11	8
1	18	8
2	25	8
3	39	8
4	66	8
5	88	8
6	90	8
7	94	8
8	97	8
0	97	8

Iter	Nodes	Cost
0	29	174
0	36	150
1	61	150
2	107	150
3	169	150
4	246	150
5	292	150
6	323	150
7	338	150
8	354	150
9	370	150
10	382	150
11	389	150
12	397	150
13	405	150
14	408	150
0	408	150

Iter	Nodes	Cost
0	12	34
0	15	26
1	26	26
2	53	26
3	77	26
4	92	26
5	101	26
6	107	26
7	108	26
8	110	26
9	111	26
10	113	26
11	114	26
12	116	26
0	116	26