Metrics for Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze13.0ms (0.4%)

Memory

-10.4MiB live, 24.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample740.0ms (20.9%)

Memory

-19.9MiB live, 1 029.0MiB allocated

Samples

522.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 200.0ms

ival-add: 116.0ms (57.9% of total)

ival-div: 74.0ms (37% of total)

ival-true: 7.0ms (3.5% of total)

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

Bogosity

explain83.0ms (2.3%)

Memory

27.2MiB live, 111.2MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 y y)`
-	-	`(/.f64 (+.f64 x y) (+.f64 y y))`
-	-	`y`
-	-	`(+.f64 x y)`
-	-	`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

24.0ms

512×

valid

Compiler

Compiled 56 to 24 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-add: 5.0ms (50.5% of total)

ival-div: 4.0ms (40.4% of total)

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

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

preprocess90.0ms (2.5%)

Memory

-15.5MiB live, 57.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	42	35
2	106	35
3	310	35
4	1262	35
5	2388	35
6	3252	35
7	3801	35
8	4253	35
9	4303	35
10	4335	35
11	4411	35
12	4595	35
0	5	7
0	8	7
1	11	7
2	14	7
3	16	7
0	16	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (+.f64 x y) (+.f64 y y))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-384	(/.f64 (+.f64 x y) (+.f64 y y))
cost-diff	-128	(+.f64 y y)
cost-diff	0	(+.f64 x y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	11	15
2	14	15
3	16	15
0	16	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize24.0ms (0.7%)

Memory

-10.5MiB live, 35.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y y)
accuracy	0	(+.f64 x y)
accuracy	0.0078125	(/.f64 (+.f64 x y) (+.f64 y y))

Samples

20.0ms

256×

valid

Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions

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

ival-div: 11.0ms (77.8% of total)

ival-add: 2.0ms (14.2% of total)

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

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

series6.0ms (0.2%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

3 → 60

Calls

Call 1

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

Inputs

#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())

#s(alt (+.f64 y y) (patch (+.f64 y y) #<representation binary64>) () ())

#s(alt (/.f64 (+.f64 x y) (+.f64 y y)) (patch (/.f64 (+.f64 x y) (+.f64 y y)) #<representation binary64>) () ())

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

Calls

6 calls:

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

simplify117.0ms (3.3%)

Memory

12.3MiB live, 85.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	240
1	95	240
2	195	240
3	532	240
4	2484	240
5	4892	240
6	6155	240
7	7112	240
8	7634	240
0	8014	222

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 54

Calls

Call 1

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

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

rewrite72.0ms (2%)

Memory

6.9MiB live, 83.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	38	13
0	305	13

Stop Event

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

Counts

3 → 61

Calls

Call 1

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

Outputs
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eval47.0ms (1.3%)

Memory: -14.0MiB live, 22.6MiB allocated
Compiler: Compiled 1 133 to 170 computations (85% saved)

prune38.0ms (1.1%)

Memory

-7.8MiB live, 26.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Accuracy

100.0%

Counts

116 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.2%	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
▶	4.3%	(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
▶	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	48.5%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
▶	52.4%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Compiler

Compiled 60 to 58 computations (3.3% saved)

simplify145.0ms (4.1%)

Memory

6.8MiB live, 104.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	19	97
0	29	97
1	57	97
2	116	96
3	319	96
4	539	96
5	725	96
6	1338	93
7	3062	93
8	3609	93
9	3707	93
10	3762	93
11	3795	93
12	3795	93
13	3795	93
0	3795	93

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize77.0ms (2.2%)

Memory

13.6MiB live, 90.7MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.19140625	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	32.908640771724194	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
accuracy	0	(+.f64 y x)
accuracy	0	(*.f64 #s(literal -2 binary64) y)
accuracy	0	(neg.f64 (+.f64 y x))
accuracy	0.015625	(.f64 (neg.f64 (+.f64 y x)) (.f64 #s(literal -2 binary64) y))
accuracy	0	(+.f64 y x)
accuracy	0	(*.f64 #s(literal -2 binary64) y)
accuracy	0.015625	(.f64 (+.f64 y x) (.f64 #s(literal -2 binary64) y))
accuracy	30.495847478922066	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
accuracy	0	(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	0	(/.f64 x y)
accuracy	0	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Samples

65.0ms

256×

valid

Compiler

Compiled 161 to 35 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-div: 26.0ms (49% of total)

ival-add: 18.0ms (33.9% of total)

ival-mult: 8.0ms (15.1% of total)

ival-neg: 1.0ms (1.9% of total)

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

exact: 0.0ms (0% of total)

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

series47.0ms (1.3%)

Memory

0.5MiB live, 38.6MiB allocated

Counts

12 → 264

Calls

Call 1

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

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

Calls

6 calls:

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

simplify186.0ms (5.3%)

Memory

4.3MiB live, 148.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	1296
1	226	1296
2	570	1296
3	1581	1296
4	4021	1296
5	6167	1296
0	8032	1224

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 258

Calls

Call 1

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

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

rewrite107.0ms (3%)

Memory

-30.8MiB live, 95.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	78
0	29	77
1	119	77
0	823	77

Stop Event

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

Counts

12 → 306

Calls

Call 1

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

Outputs
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eval104.0ms (2.9%)

Memory: 31.6MiB live, 109.9MiB allocated
Compiler: Compiled 6 476 to 694 computations (89.3% saved)

prune66.0ms (1.9%)

Memory

-21.9MiB live, 53.8MiB allocated

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	645	5	650
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	647	8	655

Accuracy

100.0%

Counts

655 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	32.5%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
▶	48.6%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	48.5%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
▶	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	52.4%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
▶	1.8%	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
▶	3.4%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))

Compiler

Compiled 77 to 76 computations (1.3% saved)

simplify151.0ms (4.3%)

Memory

-11.8MiB live, 89.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	121
0	37	121
1	69	121
2	140	120
3	328	120
4	521	120
5	743	120
6	1414	120
7	3051	120
8	3495	120
9	3640	120
10	3694	120
11	3706	120
12	3708	120
13	3708	120
14	3748	120
15	3776	120
16	3776	120
0	3776	117

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize59.0ms (1.7%)

Memory

25.4MiB live, 101.9MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) y)
accuracy	43.223826748774044	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (*.f64 #s(literal 2 binary64) y) x #s(literal 1/2 binary64)))
accuracy	0	(*.f64 y y)
accuracy	0.01171875	(.f64 (.f64 y y) #s(literal -2 binary64))
accuracy	25.25509395280022	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
accuracy	0	(*.f64 y y)
accuracy	0.01171875	(.f64 (.f64 y y) #s(literal 2 binary64))
accuracy	25.25509395280022	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 (+.f64 y y) x)
accuracy	61.51711554451038	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.00390625	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
accuracy	32.908640771724194	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Samples

45.0ms

256×

valid

Compiler

Compiled 178 to 43 computations (75.8% saved)

Precisions

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

ival-mult: 22.0ms (67.2% of total)

ival-add: 5.0ms (15.3% of total)

ival-div: 4.0ms (12.2% of total)

ival-neg: 1.0ms (3.1% of total)

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

exact: 0.0ms (0% of total)

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

series21.0ms (0.6%)

Memory

-34.5MiB live, 47.6MiB allocated

Counts

14 → 264

Calls

Call 1

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

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

Calls

6 calls:

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

simplify110.0ms (3.1%)

Memory

8.9MiB live, 123.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	1396
1	197	1396
2	497	1396
3	1110	1396
4	2633	1396
5	5008	1396
6	6828	1396
0	8113	1324

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

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

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

rewrite71.0ms (2%)

Memory

26.3MiB live, 69.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	105
0	37	102
1	126	96
0	808	96

Stop Event

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

Counts

14 → 257

Calls

Call 1

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

Outputs
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eval67.0ms (1.9%)

Memory: -14.6MiB live, 100.3MiB allocated
Compiler: Compiled 4 220 to 519 computations (87.7% saved)

prune48.0ms (1.3%)

Memory

-19.0MiB live, 63.4MiB allocated

Pruning

12 alts after pruning (5 fresh and 7 done)

	Pruned	Kept	Total
New	532	5	537
Fresh	0	0	0
Picked	1	4	5
Done	0	3	3
Total	533	12	545

Accuracy

100.0%

Counts

545 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	32.5%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	48.6%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	48.5%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
✓	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
▶	2.7%	#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (*.f64 y y) #s(literal 2 binary64)) x))
▶	3.0%	#s(approx (/ (+ x y) (+ y y)) (*.f64 #s(literal -2 binary64) y))
✓	52.4%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
▶	3.3%	#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
▶	2.9%	#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
✓	1.8%	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
✓	3.4%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))

Compiler

Compiled 93 to 93 computations (0% saved)

simplify6.0ms (0.2%)

Memory

11.5MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	106
0	31	106
1	45	106
2	86	106
3	139	106
4	147	106
0	147	106

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize65.0ms (1.8%)

Memory

7.7MiB live, 85.7MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0.01171875	(.f64 (.f64 y y) #s(literal 2 binary64))
accuracy	7.5160890045846145	(.f64 (.f64 (*.f64 y y) #s(literal 2 binary64)) x)
accuracy	62.243180092410306	#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (*.f64 y y) #s(literal 2 binary64)) x))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	62.31842956906241	#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
accuracy	0	(*.f64 #s(literal -2 binary64) y)
accuracy	62.07824853212263	#s(approx (/ (+ x y) (+ y y)) (*.f64 #s(literal -2 binary64) y))
accuracy	0	(+.f64 y y)
accuracy	61.27975951337161	#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
accuracy	0	(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
accuracy	0	(+.f64 y y)
accuracy	43.223826748774044	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))

Samples

43.0ms

256×

valid

Compiler

Compiled 153 to 36 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 21.0ms (66.7% of total)

ival-add: 6.0ms (19.1% of total)

ival-div: 4.0ms (12.7% of total)

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

exact: 0.0ms (0% of total)

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

series30.0ms (0.9%)

Memory

-12.7MiB live, 32.4MiB allocated

Counts

12 → 228

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	y	@	0	((/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (+ y y) (* (+ y x) (* -2 y)) (/ (+ x y) (+ y y)) (* -2 y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (* (* y y) 2) x) (* (* y y) 2) (* y y))
2.0ms	y	@	inf	((/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (+ y y) (* (+ y x) (* -2 y)) (/ (+ x y) (+ y y)) (* -2 y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (* (* y y) 2) x) (* (* y y) 2) (* y y))
2.0ms	y	@	-inf	((/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (+ y y) (* (+ y x) (* -2 y)) (/ (+ x y) (+ y y)) (* -2 y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (* (* y y) 2) x) (* (* y y) 2) (* y y))
1.0ms	x	@	0	((/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (+ y y) (* (+ y x) (* -2 y)) (/ (+ x y) (+ y y)) (* -2 y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (* (* y y) 2) x) (* (* y y) 2) (* y y))
1.0ms	x	@	inf	((/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (+ y y) (* (+ y x) (* -2 y)) (/ (+ x y) (+ y y)) (* -2 y) (* (+ y x) (* -2 y)) (/ 1/2 y) (/ (+ x y) (+ y y)) (* (* (* y y) 2) x) (* (* y y) 2) (* y y))

simplify132.0ms (3.7%)

Memory

12.9MiB live, 130.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	1264
1	173	1264
2	404	1264
3	871	1264
4	1700	1264
5	3572	1264
6	6560	1264
0	8240	1192

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

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

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

rewrite59.0ms (1.7%)

Memory

-14.9MiB live, 66.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	92
0	31	92
1	103	92
0	698	92

Stop Event

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

Counts

12 → 147

Calls

Call 1

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

Outputs
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eval82.0ms (2.3%)

Memory: 18.2MiB live, 94.1MiB allocated
Compiler: Compiled 3 275 to 352 computations (89.3% saved)

prune21.0ms (0.6%)

Memory

8.3MiB live, 51.1MiB allocated

Pruning

12 alts after pruning (1 fresh and 11 done)

	Pruned	Kept	Total
New	422	1	423
Fresh	0	0	0
Picked	1	4	5
Done	0	7	7
Total	423	12	435

Accuracy

100.0%

Counts

435 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
✓	32.5%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	48.6%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	48.5%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
✓	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
	2.7%	#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 x y) (*.f64 #s(literal 2 binary64) y)))
✓	3.0%	#s(approx (/ (+ x y) (+ y y)) (*.f64 #s(literal -2 binary64) y))
✓	52.4%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
✓	3.3%	#s(approx (* (+ y x) (* -2 y)) (/.f64 #s(literal 1/2 binary64) y))
✓	2.9%	#s(approx (* (+ y x) (* -2 y)) (+.f64 y y))
✓	1.8%	#s(approx (* (+ y x) (* -2 y)) (.f64 (.f64 y y) #s(literal -2 binary64)))
✓	3.4%	#s(approx (* (neg (+ y x)) (* -2 y)) (.f64 (.f64 y y) #s(literal 2 binary64)))

Compiler

Compiled 169 to 109 computations (35.5% saved)

regimes20.0ms (0.6%)

Memory

-30.3MiB live, 47.9MiB allocated

Counts

17 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	(/.f64 (+.f64 x y) (+.f64 y y))
6.0ms	y
6.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes17.0ms (0.5%)

Memory

3.0MiB live, 41.9MiB allocated

Counts

15 → 3

Calls

Call 1

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

Outputs

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

#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

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

Calls

3 calls:

5.0ms	y
5.0ms	x
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
80.3%	3	`x`
78.6%	5	`y`
97.4%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes5.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

14 → 3

Calls

Call 1

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

Outputs

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

#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

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

Calls

1 calls:

4.0ms

(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
97.3%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes16.0ms (0.4%)

Memory

1.8MiB live, 43.5MiB allocated

Accuracy

Total -33.0b remaining (-108.1%)

Threshold costs -33b (-108.1%)

Counts

13 → 1

Calls

Call 1

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

Outputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Calls

3 calls:

6.0ms	x
4.0ms	y
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
52.4%	1	`y`
52.4%	1	`x`
52.4%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5025022432546787	1.626503361804627
0.0ms	-6.471836297830467	0.4931408255150838

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5025022432546787	1.626503361804627
0.0ms	-6.471836297830467	0.4931408255150838

Compiler

Compiled 10 to 10 computations (0% saved)

simplify25.0ms (0.7%)

Memory

-5.0MiB live, 72.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	133
1	33	133

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -5 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y))))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -5 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x))))
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Outputs
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -5 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y))))
(if (<=.f64 (/.f64 (+.f64 y x) (+.f64 y y)) #s(literal -5 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y)) (if (<=.f64 (/.f64 (+.f64 y x) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (/.f64 (.f64 #s(literal 1/2 binary64) x) y))))
(if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal -5 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (if (<=.f64 (/.f64 (+.f64 x y) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x))))
(if (<=.f64 (/.f64 (+.f64 y x) (+.f64 y y)) #s(literal -5 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x)) (if (<=.f64 (/.f64 (+.f64 y x) (+.f64 y y)) #s(literal 1 binary64)) #s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64)) #s(approx (/ (+ x y) (+ y y)) (.f64 (/.f64 #s(literal 1/2 binary64) y) x))))
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

soundness493.0ms (13.9%)

Memory

0.5MiB live, 250.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	240
1	95	240
2	195	240
3	532	240
4	2484	240
5	4892	240
6	6155	240
7	7112	240
8	7634	240
0	8014	222
0	19	78
0	29	77
1	119	77
0	823	77

Stop Event

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

Compiler

Compiled 102 to 54 computations (47.1% saved)

preprocess78.0ms (2.2%)

Memory: -18.4MiB live, 98.4MiB allocated
Compiler: Compiled 182 to 70 computations (61.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze13.0ms (0.4%)

sample740.0ms (20.9%)

explain83.0ms (2.3%)

preprocess90.0ms (2.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize24.0ms (0.7%)

series6.0ms (0.2%)

simplify117.0ms (3.3%)

rewrite72.0ms (2%)

eval47.0ms (1.3%)

prune38.0ms (1.1%)

simplify145.0ms (4.1%)

localize77.0ms (2.2%)

series47.0ms (1.3%)

simplify186.0ms (5.3%)

rewrite107.0ms (3%)

eval104.0ms (2.9%)

prune66.0ms (1.9%)

simplify151.0ms (4.3%)

localize59.0ms (1.7%)

series21.0ms (0.6%)

simplify110.0ms (3.1%)

rewrite71.0ms (2%)

eval67.0ms (1.9%)

prune48.0ms (1.3%)

simplify6.0ms (0.2%)

localize65.0ms (1.8%)

series30.0ms (0.9%)

simplify132.0ms (3.7%)

rewrite59.0ms (1.7%)

eval82.0ms (2.3%)

prune21.0ms (0.6%)

regimes20.0ms (0.6%)

regimes17.0ms (0.5%)

regimes5.0ms (0.1%)

regimes16.0ms (0.4%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify25.0ms (0.7%)

soundness493.0ms (13.9%)

preprocess78.0ms (2.2%)

end0.0ms (0%)

Profiling