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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze10.0ms (0.3%)

Memory

25.4MiB live, 25.4MiB 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)

sample729.0ms (22.3%)

Memory

-13.5MiB live, 874.0MiB allocated

Samples

513.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 284.0ms

ival-add: 205.0ms (72.1% of total)

ival-div: 71.0ms (25% of total)

ival-true: 5.0ms (1.8% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain155.0ms (4.7%)

Memory

3.9MiB live, 79.4MiB 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

127.0ms

512×

valid

Compiler

Compiled 60 to 24 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-add: 5.0ms (57.3% of total)

ival-div: 3.0ms (34.4% of total)

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

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

preprocess88.0ms (2.7%)

Memory

1.0MiB live, 38.0MiB allocated

Algorithm

1×	egg-herbie

Rules

856×	`times-frac`
820×	`distribute-lft-in`
772×	`distribute-rgt-in`
636×	`div-sub`
544×	`associate-/r*`

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 y x) (+.f64 y y))

Compiler

Compiled 9 to 5 computations (44.4% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify4.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

10×	`lower-/.f32`
8×	`lower-/.f64`
6×	`lower-+.f32`
4×	`lift-+.f64`
4×	`lower-*.f64`

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

localize28.0ms (0.9%)

Memory

-1.4MiB live, 37.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y y)
accuracy	0	(+.f64 x y)
accuracy	0.0234375	(/.f64 (+.f64 x y) (+.f64 y y))

Samples

24.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-div: 8.0ms (74.8% of total)

ival-add: 2.0ms (18.7% of total)

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

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

series6.0ms (0.2%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

3 → 60

Calls

Call 1

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

Inputs

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

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

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))

simplify140.0ms (4.3%)

Memory

-31.4MiB live, 137.2MiB allocated

Algorithm

1×	egg-herbie

Rules

4 752×	`lower-fma.f64`
4 752×	`lower-fma.f32`
2 808×	`lower-*.f64`
2 808×	`lower-*.f32`
1 714×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	240
1	95	240
2	195	240
3	532	240
4	2458	240
5	4857	240
6	6132	240
7	7089	240
8	7601	240
0	8038	222

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 54

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)
x
(+ x y)
(+ x y)
(+ 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
(* 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 (/ 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
(* 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)))

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))
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
#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
(* 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 (/ 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
(* 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)

rewrite47.0ms (1.4%)

Memory

21.1MiB live, 59.2MiB allocated

Rules

150×	`lower-/.f32`
148×	`lower-/.f64`
128×	`lower-*.f64`
128×	`lower-*.f32`
76×	`lower-+.f32`

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

Outputs
(*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 (+.f64 y x) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (+.f64 y y) (+.f64 y x)))
(*.f64 (neg.f64 (+.f64 y x)) (+.f64 y y))
(*.f64 (+.f64 y y) (+.f64 y x))
(*.f64 (+.f64 y x) (+.f64 y y))
(pow.f64 (/.f64 (+.f64 y y) (+.f64 y x)) #s(literal -1 binary64))
(/.f64 (/.f64 (+.f64 y x) #s(literal 2 binary64)) y)
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 y y)) (-.f64 x y))
(/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (+.f64 y y)) (fma.f64 y (-.f64 y x) (*.f64 x x)))
(/.f64 (*.f64 (+.f64 y x) #s(literal 1 binary64)) (+.f64 y y))
(/.f64 (neg.f64 (neg.f64 (+.f64 y x))) (+.f64 y y))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1 binary64)) (*.f64 (-.f64 x y) (+.f64 y y)))
(/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) #s(literal 1 binary64)) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (+.f64 y y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 y y) (+.f64 y x))))
(/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (+.f64 y y) (-.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 y y) (+.f64 y x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) (+.f64 y x)))
(/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (+.f64 y y) (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 y x)) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 y y))
(neg.f64 (*.f64 (+.f64 y y) (+.f64 y x)))
(.f64 (.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (-.f64 y x))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 y (-.f64 y x) (.f64 x x))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 x y))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (*.f64 (+.f64 y x) (-.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))))
(/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (fma.f64 y y (-.f64 (.f64 x x) (*.f64 y x))))
(/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (fma.f64 y (-.f64 y x) (.f64 x x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))
(+.f64 y x)
(+.f64 x y)
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) y)
(*.f64 #s(literal -1 binary64) (+.f64 y y))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 #s(literal 1 binary64) (+.f64 y y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 y #s(literal 2 binary64))
(pow.f64 (+.f64 y y) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(neg.f64 (+.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)

eval22.0ms (0.7%)

Memory: -20.0MiB live, 18.4MiB allocated
Compiler: Compiled 1 183 to 159 computations (86.6% saved)

prune11.0ms (0.3%)

Memory

19.6MiB live, 19.6MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	4	116

Accuracy

100.0%

Counts

116 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.5%	(*.f64 (+.f64 y y) (+.f64 y x))
▶	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	44.2%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
▶	57.1%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Compiler

Compiled 30 to 18 computations (40% saved)

simplify8.0ms (0.2%)

Memory

7.7MiB live, 7.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

114×	`lower-fma.f32`
112×	`lower-fma.f64`
84×	`lower-+.f32`
80×	`lower-+.f64`
78×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	75
0	24	75
1	44	75
2	72	75
3	113	75
4	147	75
5	180	75
0	180	75

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize67.0ms (2.1%)

Memory

-0.8MiB live, 76.6MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y y)
accuracy	0	(+.f64 y x)
accuracy	0.00390625	(*.f64 (+.f64 y y) (+.f64 y x))
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)))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	0.2265625	(*.f64 (/.f64 #s(literal 1/2 binary64) y) x)
accuracy	35.64133061510062	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
accuracy	27.432907068436442	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Samples

58.0ms

256×

valid

Compiler

Compiled 63 to 15 computations (76.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-add: 33.0ms (70.6% of total)

ival-div: 9.0ms (19.2% of total)

ival-mult: 4.0ms (8.6% of total)

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

exact: 0.0ms (0% of total)

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

series17.0ms (0.5%)

Memory

-3.2MiB live, 33.8MiB allocated

Counts

10 → 216

Calls

Call 1

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

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

Calls

6 calls:

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

simplify131.0ms (4%)

Memory

-9.4MiB live, 151.8MiB allocated

Algorithm

1×	egg-herbie

Rules

5 472×	`lower-fma.f64`
5 472×	`lower-fma.f32`
3 286×	`lower-*.f64`
3 286×	`lower-*.f32`
1 342×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	1056
1	176	1056
2	395	1056
3	1161	1056
4	2732	1056
5	5988	1056
0	8104	984

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 210

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

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

rewrite57.0ms (1.7%)

Memory

0.4MiB live, 75.1MiB allocated

Rules

412×	`lower-/.f32`
408×	`lower-/.f64`
398×	`lower-*.f32`
394×	`lower-*.f64`
266×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	66
0	24	66
1	106	66
0	840	66

Stop Event

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

Counts

10 → 255

Calls

Call 1

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

Outputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y))
(.f64 #s(literal 2 binary64) (.f64 y x))
(*.f64 (+.f64 y y) x)
(*.f64 (/.f64 x y) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 x y))
(*.f64 x (+.f64 y y))
(/.f64 (*.f64 (neg.f64 x) #s(literal 1/2 binary64)) (neg.f64 y))
(/.f64 (*.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) x) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) x) (+.f64 y y))
(/.f64 (*.f64 #s(literal -1/2 binary64) x) (neg.f64 y))
(/.f64 (*.f64 x #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 x (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 x)) (neg.f64 y))
(/.f64 (*.f64 x #s(literal 1 binary64)) (+.f64 y y))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) (neg.f64 y))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x)) (neg.f64 y))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(/.f64 #s(literal 1 binary64) (/.f64 y (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal 1/2 binary64) (/.f64 y x))
(/.f64 x (+.f64 y y))
(fma.f64 y x (*.f64 y x))
(fma.f64 x y (*.f64 y x))
(+.f64 (.f64 y x) (.f64 y x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) y)
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(*.f64 #s(literal -1 binary64) (+.f64 y y))
(.f64 #s(literal 2 binary64) (.f64 y y))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 y y))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(*.f64 (+.f64 y y) y)
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) y))
(*.f64 y #s(literal 2 binary64))
(*.f64 y (+.f64 y y))
(pow.f64 (+.f64 y y) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 y (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 y y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 (neg.f64 y) #s(literal -1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 y #s(literal 1/2 binary64))
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))
(neg.f64 (+.f64 y y))
(fma.f64 #s(literal -1 binary64) y (neg.f64 y))
(fma.f64 y y (*.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 y y))
(+.f64 (.f64 y y) (.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x y)) #s(literal 1/2 binary64))
(.f64 (fma.f64 (.f64 (+.f64 y y) x) (*.f64 (+.f64 y y) x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x)) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 (+.f64 y y) x) #s(literal 1/2 binary64))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x))) (-.f64 #s(literal 1/2 binary64) (.f64 (+.f64 y y) x)))
(/.f64 (neg.f64 (fma.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x)) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (+.f64 y y) x) #s(literal 1/2 binary64))))))
(/.f64 (fma.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x) #s(literal -1/4 binary64)) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64)) (fma.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (+.f64 y y) x) #s(literal 1/2 binary64)))) (fma.f64 (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x)) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x)) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x)) (.f64 (*.f64 (+.f64 y y) x) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x)) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64)) (fma.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (+.f64 y y) x) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 x #s(literal 2 binary64)) y #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64))
(fma.f64 (+.f64 y y) x #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))
(fma.f64 x (+.f64 y y) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 (.f64 (+.f64 y y) x) (*.f64 (+.f64 y y) x)) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))))
(+.f64 (*.f64 (+.f64 y y) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y y) x))
(*.f64 (/.f64 #s(literal 1 binary64) y) x)
(*.f64 #s(literal 1 binary64) (/.f64 x y))
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(*.f64 x (/.f64 #s(literal 1 binary64) y))
(pow.f64 (/.f64 y x) #s(literal -1 binary64))
(/.f64 (*.f64 x #s(literal 1 binary64)) y)
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 y x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 y x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 y x))
(/.f64 (neg.f64 x) (neg.f64 y))
(/.f64 x y)
(neg.f64 (/.f64 (neg.f64 x) y))
(neg.f64 (/.f64 x (neg.f64 y)))
(*.f64 (/.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 (+.f64 y x) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(.f64 (.f64 (+.f64 y x) #s(literal 2 binary64)) y)
(.f64 #s(literal 2 binary64) (.f64 y (+.f64 y x)))
(.f64 #s(literal 1 binary64) (.f64 (+.f64 y y) (+.f64 y x)))
(*.f64 (neg.f64 (+.f64 y x)) (+.f64 y y))
(*.f64 (+.f64 y y) (+.f64 y x))
(*.f64 (+.f64 y x) (+.f64 y y))
(pow.f64 (/.f64 (+.f64 y y) (+.f64 y x)) #s(literal -1 binary64))
(/.f64 (/.f64 (+.f64 y x) #s(literal 2 binary64)) y)
(/.f64 (*.f64 #s(literal 0 binary64) (+.f64 y x)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (+.f64 y x)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 y x)) (+.f64 y y)) (-.f64 y x))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (+.f64 y y)) (-.f64 x y))
(/.f64 (.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (+.f64 y y)) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (+.f64 y y)) (fma.f64 y (-.f64 y x) (*.f64 x x)))
(/.f64 (*.f64 (+.f64 y x) #s(literal 1 binary64)) (+.f64 y y))
(/.f64 (.f64 (+.f64 y y) (.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x))
(/.f64 (.f64 (+.f64 y y) (.f64 (+.f64 y x) (-.f64 x y))) (-.f64 x y))
(/.f64 (.f64 (+.f64 y y) (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (.f64 (+.f64 y y) (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))) (fma.f64 y (-.f64 y x) (*.f64 x x)))
(/.f64 (*.f64 (+.f64 y x) #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 (+.f64 y x) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x))) (-.f64 (+.f64 y y) (*.f64 (+.f64 y y) x)))
(/.f64 (+.f64 (pow.f64 (+.f64 y y) #s(literal 3 binary64)) (.f64 (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x)) (.f64 (+.f64 y y) x))) (fma.f64 (+.f64 y y) (+.f64 y y) (-.f64 (.f64 (.f64 (+.f64 y y) x) (.f64 (+.f64 y y) x)) (.f64 (+.f64 y y) (.f64 (+.f64 y y) x)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 y x))) (+.f64 y y))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1 binary64)) (*.f64 (-.f64 y x) (+.f64 y y)))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 1 binary64)) (*.f64 (-.f64 x y) (+.f64 y y)))
(/.f64 (.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) #s(literal 1 binary64)) (.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) (+.f64 y y)))
(/.f64 (.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) #s(literal 1 binary64)) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (+.f64 y y)))
(/.f64 (.f64 #s(literal 0 binary64) (.f64 (+.f64 y x) (-.f64 y x))) (*.f64 #s(literal 0 binary64) (-.f64 y x)))
(/.f64 (.f64 #s(literal 0 binary64) (.f64 (+.f64 y x) (-.f64 x y))) (*.f64 #s(literal 0 binary64) (-.f64 x y)))
(/.f64 (.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))) (.f64 #s(literal 0 binary64) (fma.f64 x (-.f64 x y) (.f64 y y))))
(/.f64 (.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))) (.f64 #s(literal 0 binary64) (fma.f64 y (-.f64 y x) (.f64 x x))))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (.f64 (+.f64 y x) (-.f64 y x))) (.f64 (fma.f64 y y #s(literal 0 binary64)) (-.f64 y x)))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (.f64 (+.f64 y x) (-.f64 x y))) (.f64 (fma.f64 y y #s(literal 0 binary64)) (-.f64 x y)))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))) (.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))) (.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal 0 binary64)) (*.f64 (-.f64 y x) #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 y x)) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (.f64 (-.f64 y x) (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) #s(literal 0 binary64)) (*.f64 (-.f64 x y) #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (.f64 (-.f64 x y) (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (.f64 (fma.f64 y (-.f64 y x) (*.f64 x x)) (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) #s(literal 0 binary64)) (.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) #s(literal 0 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) #s(literal 0 binary64)) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 y y) (+.f64 y x))))
(/.f64 (.f64 (+.f64 y x) (-.f64 y x)) (.f64 (+.f64 y y) (-.f64 y x)))
(/.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (+.f64 y y) (-.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 y y) (+.f64 y x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) (+.f64 y x)))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (.f64 (+.f64 y y) (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (.f64 (+.f64 y y) (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 y x)) (+.f64 y y))
(/.f64 (+.f64 y x) (+.f64 y y))
(neg.f64 (*.f64 (+.f64 y y) (+.f64 y x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)) (.f64 (+.f64 y y) x))
(fma.f64 (*.f64 x #s(literal 2 binary64)) y (+.f64 y y))
(fma.f64 #s(literal -2 binary64) y (*.f64 (+.f64 y y) x))
(fma.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64) (*.f64 (+.f64 y y) x))
(fma.f64 #s(literal -1 binary64) (+.f64 y y) (*.f64 (+.f64 y y) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) y) (+.f64 y y))
(fma.f64 #s(literal 2 binary64) (*.f64 y x) (+.f64 y y))
(fma.f64 #s(literal 2 binary64) (.f64 y y) (.f64 (+.f64 y y) x))
(fma.f64 #s(literal 2 binary64) (neg.f64 y) (*.f64 (+.f64 y y) x))
(fma.f64 #s(literal 2 binary64) y (*.f64 (+.f64 y y) x))
(fma.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) (*.f64 (+.f64 y y) x))
(fma.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64) (*.f64 (+.f64 y y) x))
(fma.f64 #s(literal 1 binary64) (+.f64 y y) (*.f64 (+.f64 y y) x))
(fma.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))) (.f64 (+.f64 y y) x))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 y)) (*.f64 (+.f64 y y) x))
(fma.f64 (+.f64 y y) y (*.f64 (+.f64 y y) x))
(fma.f64 (+.f64 y y) x (+.f64 y y))
(fma.f64 (/.f64 x y) #s(literal 1/2 binary64) (+.f64 y y))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) y) (*.f64 (+.f64 y y) x))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) (+.f64 y y))
(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) y))
(fma.f64 y #s(literal 2 binary64) (*.f64 (+.f64 y y) x))
(fma.f64 y (+.f64 y y) (*.f64 (+.f64 y y) x))
(fma.f64 y (+.f64 y x) (*.f64 y (+.f64 y x)))
(fma.f64 x (+.f64 y y) (+.f64 y y))
(+.f64 (.f64 y (+.f64 y x)) (.f64 y (+.f64 y x)))
(+.f64 (.f64 (+.f64 y x) y) (.f64 (+.f64 y x) y))
(+.f64 (*.f64 (+.f64 y y) x) (+.f64 y y))
(+.f64 (+.f64 y y) (*.f64 (+.f64 y y) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) y)
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(*.f64 #s(literal -1 binary64) (+.f64 y y))
(.f64 #s(literal 2 binary64) (.f64 y y))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 y y))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(*.f64 (+.f64 y y) y)
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) y))
(*.f64 y #s(literal 2 binary64))
(*.f64 y (+.f64 y y))
(pow.f64 (+.f64 y y) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 y (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 y y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 (neg.f64 y) #s(literal -1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 y #s(literal 1/2 binary64))
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))
(neg.f64 (+.f64 y y))
(fma.f64 #s(literal -1 binary64) y (neg.f64 y))
(fma.f64 y y (*.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 y y))
(+.f64 (.f64 y y) (.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)
(.f64 (.f64 (+.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (-.f64 y x)))
(.f64 (.f64 (+.f64 y x) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y))))
(.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 y x) (*.f64 x x))))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))) (neg.f64 (fma.f64 x (-.f64 x y) (.f64 y y))))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))) (neg.f64 (fma.f64 y (-.f64 y x) (.f64 x x))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (-.f64 y x))
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 x y))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (*.f64 (+.f64 y x) (-.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (*.f64 (+.f64 y x) (-.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y))))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (fma.f64 x (-.f64 x y) (.f64 y y)))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (fma.f64 y (-.f64 y x) (.f64 x x)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))
(+.f64 y x)
(+.f64 x y)

eval55.0ms (1.7%)

Memory: 29.6MiB live, 105.3MiB allocated
Compiler: Compiled 4 794 to 503 computations (89.5% saved)

prune72.0ms (2.2%)

Memory

-19.1MiB live, 110.7MiB allocated

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	459	6	465
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	460	9	469

Accuracy

100.0%

Counts

469 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	3.9%	(fma.f64 (+.f64 y y) x (+.f64 y y))
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
▶	28.7%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
▶	28.7%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64)))
▶	44.3%	#s(approx (/ (+ x y) (+ y y)) (/.f64 x (+.f64 y y)))
✓	44.2%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
▶	4.2%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	57.1%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
▶	3.7%	#s(approx (* (+ y y) (+ y x)) (.f64 (.f64 y y) #s(literal 2 binary64)))

Compiler

Compiled 125 to 69 computations (44.8% saved)

simplify9.0ms (0.3%)

Memory

8.2MiB live, 8.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

126×	`lower-fma.f32`
122×	`lower-fma.f64`
88×	`lower-+.f32`
86×	`lower-+.f64`
62×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	122
0	32	122
1	47	122
2	70	122
3	107	122
4	143	122
5	176	122
0	176	122

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize173.0ms (5.3%)

Memory

-4.5MiB live, 103.8MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y x)
accuracy	0.00390625	(fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64))
accuracy	45.61277675132126	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64)))
accuracy	0	(.f64 (.f64 y y) #s(literal 2 binary64))
accuracy	0	(*.f64 y y)
accuracy	22.247098560552487	#s(approx (* (+ y y) (+ y x)) (.f64 (.f64 y y) #s(literal 2 binary64)))
accuracy	0	(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
accuracy	0	(+.f64 y y)
accuracy	45.61277675132126	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 (+.f64 y y) x)
accuracy	61.300317755171825	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
accuracy	0	(/.f64 x (+.f64 y y))
accuracy	0	(+.f64 y y)
accuracy	35.64133061510062	#s(approx (/ (+ x y) (+ y y)) (/.f64 x (+.f64 y y)))

Samples

53.0ms

256×

valid

Compiler

Compiled 94 to 19 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-add: 27.0ms (69.2% of total)

ival-mult: 8.0ms (20.5% of total)

ival-div: 3.0ms (7.7% of total)

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

exact: 0.0ms (0% of total)

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

series21.0ms (0.7%)

Memory

-7.9MiB live, 35.2MiB allocated

Counts

13 → 276

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	x	@	inf	((/ (+ x y) (+ y y)) (/ x (+ y y)) (+ y y) (/ (+ x y) (+ y y)) (* (+ y y) x) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (* y y) 2) (* (+ y y) (+ y x)) (* y y) (+ (* 2 (* y x)) 1/2) (/ (+ x y) (+ y y)) (* y x))
2.0ms	y	@	-inf	((/ (+ x y) (+ y y)) (/ x (+ y y)) (+ y y) (/ (+ x y) (+ y y)) (* (+ y y) x) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (* y y) 2) (* (+ y y) (+ y x)) (* y y) (+ (* 2 (* y x)) 1/2) (/ (+ x y) (+ y y)) (* y x))
2.0ms	y	@	inf	((/ (+ x y) (+ y y)) (/ x (+ y y)) (+ y y) (/ (+ x y) (+ y y)) (* (+ y y) x) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (* y y) 2) (* (+ y y) (+ y x)) (* y y) (+ (* 2 (* y x)) 1/2) (/ (+ x y) (+ y y)) (* y x))
2.0ms	y	@	0	((/ (+ x y) (+ y y)) (/ x (+ y y)) (+ y y) (/ (+ x y) (+ y y)) (* (+ y y) x) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (* y y) 2) (* (+ y y) (+ y x)) (* y y) (+ (* 2 (* y x)) 1/2) (/ (+ x y) (+ y y)) (* y x))
1.0ms	x	@	-inf	((/ (+ x y) (+ y y)) (/ x (+ y y)) (+ y y) (/ (+ x y) (+ y y)) (* (+ y y) x) (/ (+ x y) (+ y y)) (+ (* (+ y y) x) 1/2) (* (* y y) 2) (* (+ y y) (+ y x)) (* y y) (+ (* 2 (* y x)) 1/2) (/ (+ x y) (+ y y)) (* y x))

simplify132.0ms (4.1%)

Memory

26.9MiB live, 180.3MiB allocated

Algorithm

1×	egg-herbie

Rules

6 034×	`lower-fma.f64`
6 034×	`lower-fma.f32`
3 620×	`lower-*.f64`
3 620×	`lower-*.f32`
1 424×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	1472
1	167	1472
2	401	1472
3	866	1472
4	1543	1472
5	3742	1472
6	6347	1472
0	8083	1364

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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

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

rewrite55.0ms (1.7%)

Memory

-17.7MiB live, 99.1MiB allocated

Rules

406×	`lower-*.f32`
398×	`lower-*.f64`
364×	`lower-/.f32`
362×	`lower-/.f64`
326×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	103
0	32	101
1	113	99
0	796	99

Stop Event

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

Counts

13 → 187

Calls

Call 1

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

Outputs
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
(*.f64 (/.f64 x #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 x (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) y)
(.f64 (.f64 x #s(literal 2 binary64)) y)
(.f64 #s(literal 1 binary64) (.f64 (+.f64 y y) x))
(*.f64 (neg.f64 x) (+.f64 y y))
(.f64 (.f64 y x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 y x))
(*.f64 (+.f64 y y) x)
(.f64 y (.f64 x #s(literal 2 binary64)))
(*.f64 x (+.f64 y y))
(pow.f64 (/.f64 (+.f64 y y) x) #s(literal -1 binary64))
(/.f64 (/.f64 x #s(literal 2 binary64)) y)
(/.f64 (*.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) x) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (*.f64 x #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 x (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (*.f64 x #s(literal 1 binary64)) (+.f64 y y))
(/.f64 (neg.f64 (neg.f64 x)) (+.f64 y y))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 y y) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 y y) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) x))
(/.f64 (neg.f64 x) (+.f64 y y))
(/.f64 x (+.f64 y y))
(neg.f64 (*.f64 (+.f64 y y) x))
(fma.f64 y x (*.f64 y x))
(fma.f64 x y (*.f64 y x))
(+.f64 (.f64 y x) (.f64 y x))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) y)
(*.f64 #s(literal -1 binary64) (+.f64 y y))
(*.f64 #s(literal 1 binary64) (+.f64 y y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(.f64 #s(literal 2 binary64) (.f64 y y))
(*.f64 #s(literal 2 binary64) y)
(.f64 (.f64 y y) #s(literal 2 binary64))
(*.f64 (+.f64 y y) y)
(*.f64 y #s(literal 2 binary64))
(*.f64 y (+.f64 y y))
(pow.f64 (+.f64 y y) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 y (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal 1/2 binary64) y)
(neg.f64 (+.f64 y y))
(fma.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)) (*.f64 y y))
(fma.f64 y y (*.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 (.f64 y y) (.f64 y y))
(+.f64 y y)
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
(*.f64 (/.f64 x #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 x (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) y)
(.f64 (.f64 x #s(literal 2 binary64)) y)
(.f64 #s(literal 1 binary64) (.f64 (+.f64 y y) x))
(*.f64 (neg.f64 x) (+.f64 y y))
(.f64 (.f64 y x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 y x))
(*.f64 (+.f64 y y) x)
(.f64 y (.f64 x #s(literal 2 binary64)))
(*.f64 x (+.f64 y y))
(pow.f64 (/.f64 (+.f64 y y) x) #s(literal -1 binary64))
(/.f64 (/.f64 x #s(literal 2 binary64)) y)
(/.f64 (*.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) x) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (*.f64 x #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 x (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (*.f64 x #s(literal 1 binary64)) (+.f64 y y))
(/.f64 (neg.f64 (neg.f64 x)) (+.f64 y y))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 y y) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 y y) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) x))
(/.f64 (neg.f64 x) (+.f64 y y))
(/.f64 x (+.f64 y y))
(neg.f64 (*.f64 (+.f64 y y) x))
(fma.f64 y x (*.f64 y x))
(fma.f64 x y (*.f64 y x))
(+.f64 (.f64 y x) (.f64 y x))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
(.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 y x) #s(literal 1 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y y) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (*.f64 y x)) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 y x) #s(literal 1 binary64))))))
(/.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (*.f64 y x)) #s(literal -1/4 binary64)) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (*.f64 y x)) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 y x) #s(literal 1 binary64)))) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (*.f64 y x) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 y x) #s(literal 1 binary64)))))
(fma.f64 (/.f64 x #s(literal 0 binary64)) #s(literal 0 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) y #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 2 binary64)) y #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (+.f64 y y) x) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (+.f64 y y) #s(literal 1/2 binary64))
(fma.f64 (*.f64 y x) #s(literal 2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64))
(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
(fma.f64 y (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (+.f64 y y) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y y) x))
(+.f64 (*.f64 (+.f64 y y) x) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) y)
(*.f64 #s(literal -1 binary64) (+.f64 y y))
(*.f64 #s(literal 1 binary64) (+.f64 y y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(.f64 #s(literal 2 binary64) (.f64 y y))
(*.f64 #s(literal 2 binary64) y)
(.f64 (.f64 y y) #s(literal 2 binary64))
(*.f64 (+.f64 y y) y)
(*.f64 y #s(literal 2 binary64))
(*.f64 y (+.f64 y y))
(pow.f64 (+.f64 y y) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 y (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal 1/2 binary64) y)
(neg.f64 (+.f64 y y))
(fma.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)) (*.f64 y y))
(fma.f64 y y (*.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 (.f64 y y) (.f64 y y))
(+.f64 y y)
#s(approx (/ (+ x y) (+ y y)) (+.f64 y y))
(*.f64 (pow.f64 y #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)))
(*.f64 y y)
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 y x) #s(literal 1 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y y) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (*.f64 y x)) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 y x) #s(literal 1 binary64))))))
(/.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (*.f64 y x)) #s(literal -1/4 binary64)) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (*.f64 y x)) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 y x) #s(literal 1 binary64)))) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (*.f64 y x) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (.f64 (+.f64 y y) x) #s(literal 1/8 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 y x) #s(literal 1 binary64)))))
(fma.f64 (/.f64 x #s(literal 0 binary64)) #s(literal 0 binary64) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) x) y #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 2 binary64)) y #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (+.f64 y y) x) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 x) (+.f64 y y) #s(literal 1/2 binary64))
(fma.f64 (*.f64 y x) #s(literal 2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64))
(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
(fma.f64 y (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(fma.f64 x (+.f64 y y) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 y x) (.f64 y x))) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (+.f64 y y) x #s(literal -1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 y y) x))
(+.f64 (*.f64 (+.f64 y y) x) #s(literal 1/2 binary64))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
(*.f64 y x)
(*.f64 x y)

eval87.0ms (2.7%)

Memory: 9.7MiB live, 88.0MiB allocated
Compiler: Compiled 4 898 to 275 computations (94.4% saved)

prune40.0ms (1.2%)

Memory

4.0MiB live, 78.9MiB allocated

Pruning

11 alts after pruning (4 fresh and 7 done)

	Pruned	Kept	Total
New	555	4	559
Fresh	1	0	1
Picked	1	4	5
Done	0	3	3
Total	557	11	568

Accuracy

100.0%

Counts

568 → 11

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)))
✓	28.7%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	28.7%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64)))
✓	44.3%	#s(approx (/ (+ x y) (+ y y)) (/.f64 x (+.f64 y y)))
▶	3.2%	#s(approx (/ (+ x y) (+ y y)) (+.f64 y y))
✓	44.2%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
✓	4.2%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	57.1%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
▶	3.8%	#s(approx (* (+ y y) (+ y x)) (/.f64 #s(literal 1/2 binary64) y))
▶	3.7%	#s(approx (* (+ y y) (+ y x)) (*.f64 (+.f64 y y) y))
▶	3.0%	#s(approx (* (+ y y) (+ y x)) (*.f64 #s(literal -2 binary64) y))

Compiler

Compiled 81 to 47 computations (42% saved)

simplify7.0ms (0.2%)

Memory

12.6MiB live, 12.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

106×	`lower-fma.f64`
106×	`lower-fma.f32`
76×	`lower-+.f32`
74×	`lower-+.f64`
66×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	69
0	22	69
1	33	69
2	56	69
3	96	69
4	130	69
5	163	69
0	163	69

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize153.0ms (4.7%)

Memory

-23.4MiB live, 44.2MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y y)
accuracy	61.92486620945822	#s(approx (/ (+ x y) (+ y y)) (+.f64 y y))
accuracy	0	(/.f64 #s(literal 1/2 binary64) y)
accuracy	62.348559954905774	#s(approx (* (+ y y) (+ y x)) (/.f64 #s(literal 1/2 binary64) y))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 (+.f64 y y) y)
accuracy	22.247098560552487	#s(approx (* (+ y y) (+ y x)) (*.f64 (+.f64 y y) y))
accuracy	0	(*.f64 #s(literal -2 binary64) y)
accuracy	61.35153655979999	#s(approx (* (+ y y) (+ y x)) (*.f64 #s(literal -2 binary64) y))

Samples

21.0ms

256×

valid

Compiler

Compiled 53 to 14 computations (73.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 5.0ms (40.6% of total)

ival-div: 3.0ms (24.3% of total)

ival-add: 3.0ms (24.3% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.3%)

Memory

-22.6MiB live, 15.7MiB allocated

Counts

8 → 144

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	0	((* (+ y y) (+ y x)) (* -2 y) (* (+ y y) (+ y x)) (* (+ y y) y) (+ y y) (* (+ y y) (+ y x)) (/ 1/2 y) (/ (+ x y) (+ y y)))
1.0ms	y	@	inf	((* (+ y y) (+ y x)) (* -2 y) (* (+ y y) (+ y x)) (* (+ y y) y) (+ y y) (* (+ y y) (+ y x)) (/ 1/2 y) (/ (+ x y) (+ y y)))
1.0ms	y	@	-inf	((* (+ y y) (+ y x)) (* -2 y) (* (+ y y) (+ y x)) (* (+ y y) y) (+ y y) (* (+ y y) (+ y x)) (/ 1/2 y) (/ (+ x y) (+ y y)))
0.0ms	x	@	-inf	((* (+ y y) (+ y x)) (* -2 y) (* (+ y y) (+ y x)) (* (+ y y) y) (+ y y) (* (+ y y) (+ y x)) (/ 1/2 y) (/ (+ x y) (+ y y)))
0.0ms	x	@	inf	((* (+ y y) (+ y x)) (* -2 y) (* (+ y y) (+ y x)) (* (+ y y) y) (+ y y) (* (+ y y) (+ y x)) (/ 1/2 y) (/ (+ x y) (+ y y)))

simplify124.0ms (3.8%)

Memory

2.4MiB live, 120.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6 008×	`lower-fma.f64`
6 008×	`lower-fma.f32`
3 016×	`lower-*.f64`
3 016×	`lower-*.f32`
1 802×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	780
1	123	780
2	286	780
3	592	780
4	1180	780
5	2809	780
6	5088	780
7	7579	780
0	8031	762

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

rewrite64.0ms (2%)

Memory

29.1MiB live, 102.5MiB allocated

Rules

298×	`lower-/.f32`
296×	`lower-/.f64`
294×	`lower-*.f32`
290×	`lower-*.f64`
148×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	60
0	22	56
1	76	56
0	617	56

Stop Event

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

Counts

8 → 180

Calls

Call 1

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

Outputs
#s(approx (/ (+ x y) (+ y y)) (+.f64 y y))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -1 binary64) (+.f64 y y))
(.f64 #s(literal 2 binary64) (.f64 y y))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 y y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) y))
(*.f64 (+.f64 y y) y)
(*.f64 #s(literal -2 binary64) y)
(*.f64 y #s(literal 2 binary64))
(*.f64 y (+.f64 y y))
(*.f64 y #s(literal -2 binary64))
(pow.f64 (+.f64 y y) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 y (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 y) #s(literal -1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 y #s(literal 1/2 binary64))
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))
(neg.f64 (+.f64 y y))
(fma.f64 #s(literal -1 binary64) y (neg.f64 y))
(fma.f64 y y (*.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 y y))
(+.f64 (.f64 y y) (.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)
#s(approx (/ (+ x y) (+ y y)) (+.f64 y y))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -1 binary64) (+.f64 y y))
(.f64 #s(literal 2 binary64) (.f64 y y))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 y y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) y))
(*.f64 (+.f64 y y) y)
(*.f64 #s(literal -2 binary64) y)
(*.f64 y #s(literal 2 binary64))
(*.f64 y (+.f64 y y))
(*.f64 y #s(literal -2 binary64))
(pow.f64 (+.f64 y y) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 y (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 y) #s(literal -1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 y #s(literal 1/2 binary64))
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))
(neg.f64 (+.f64 y y))
(fma.f64 #s(literal -1 binary64) y (neg.f64 y))
(fma.f64 y y (*.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 y y))
(+.f64 (.f64 y y) (.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -1 binary64) (+.f64 y y))
(.f64 #s(literal 2 binary64) (.f64 y y))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 y y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) y))
(*.f64 (+.f64 y y) y)
(*.f64 #s(literal -2 binary64) y)
(*.f64 y #s(literal 2 binary64))
(*.f64 y (+.f64 y y))
(*.f64 y #s(literal -2 binary64))
(pow.f64 (+.f64 y y) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 y (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 y) #s(literal -1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 y #s(literal 1/2 binary64))
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))
(neg.f64 (+.f64 y y))
(fma.f64 #s(literal -1 binary64) y (neg.f64 y))
(fma.f64 y y (*.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 y y))
(+.f64 (.f64 y y) (.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)
#s(approx (/ (+ x y) (+ y y)) (+.f64 y y))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(*.f64 #s(literal -1 binary64) (+.f64 y y))
(.f64 #s(literal 2 binary64) (.f64 y y))
(*.f64 #s(literal 2 binary64) (neg.f64 y))
(*.f64 #s(literal 2 binary64) y)
(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 y y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 y)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) y))
(*.f64 (+.f64 y y) y)
(*.f64 #s(literal -2 binary64) y)
(*.f64 y #s(literal 2 binary64))
(*.f64 y (+.f64 y y))
(*.f64 y #s(literal -2 binary64))
(pow.f64 (+.f64 y y) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) y) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 y (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 y) #s(literal -1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (neg.f64 y))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 y)))
(/.f64 #s(literal 1/2 binary64) y)
(/.f64 y #s(literal 1/2 binary64))
(neg.f64 (/.f64 #s(literal -1/2 binary64) y))
(neg.f64 (+.f64 y y))
(fma.f64 #s(literal -1 binary64) y (neg.f64 y))
(fma.f64 y y (*.f64 y y))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 y y))
(+.f64 (.f64 y y) (.f64 y y))
(+.f64 (neg.f64 y) (neg.f64 y))
(+.f64 y y)
#s(approx (/ (+ x y) (+ y y)) (+.f64 y y))

eval53.0ms (1.6%)

Memory: -6.8MiB live, 74.9MiB allocated
Compiler: Compiled 2 849 to 123 computations (95.7% saved)

prune61.0ms (1.9%)

Memory

4.2MiB live, 77.9MiB allocated

Pruning

12 alts after pruning (1 fresh and 11 done)

	Pruned	Kept	Total
New	379	1	380
Fresh	0	0	0
Picked	0	4	4
Done	0	7	7
Total	379	12	391

Accuracy

100.0%

Counts

391 → 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)))
✓	28.7%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	28.7%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64)))
✓	44.3%	#s(approx (/ (+ x y) (+ y y)) (/.f64 x (+.f64 y y)))
✓	3.2%	#s(approx (/ (+ x y) (+ y y)) (+.f64 y y))
✓	44.2%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
✓	4.2%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	57.1%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
✓	3.8%	#s(approx (* (+ y y) (+ y x)) (/.f64 #s(literal 1/2 binary64) y))
	57.0%	#s(approx (* (+ y y) (+ y x)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) y))
✓	3.7%	#s(approx (* (+ y y) (+ y x)) (*.f64 (+.f64 y y) y))
✓	3.0%	#s(approx (* (+ y y) (+ y x)) (*.f64 #s(literal -2 binary64) y))

Compiler

Compiled 184 to 77 computations (58.2% saved)

regimes18.0ms (0.6%)

Memory

0.2MiB live, 36.7MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(approx (/ (+ x y) (+ y y)) (+.f64 y y))
#s(approx (* (+ y y) (+ y x)) (*.f64 #s(literal -2 binary64) y))
#s(approx (* (+ y y) (+ y x)) (*.f64 (+.f64 y y) 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 (* (+ y y) (+ y x)) (.f64 (.f64 y y) #s(literal 2 binary64)))
#s(approx (* (+ y y) (+ y x)) (/.f64 #s(literal 1/2 binary64) y))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 2 binary64) (*.f64 y x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 y y) (+.f64 y x))
(fma.f64 (+.f64 y y) x (+.f64 y y))
#s(approx (/ (+ x y) (+ y y)) (/.f64 x (+.f64 y y)))
#s(approx (* (+ y y) (+ y x)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) y))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (/.f64 #s(literal 1/2 binary64) y) x))
#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))
5.0ms	y
5.0ms	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 15 to 9 computations (40% saved)

regimes21.0ms (0.6%)

Memory

-12.4MiB live, 32.5MiB allocated

Counts

14 → 3

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	y
5.0ms	x
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
78.3%	3	`x`
77.0%	3	`y`
97.7%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes14.0ms (0.4%)

Memory

-7.3MiB live, 29.9MiB allocated

Accuracy

Total -35.9b remaining (-130.8%)

Threshold costs -35.9b (-130.8%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	y
4.0ms	x
3.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
57.1%	1	`y`
57.1%	1	`x`
57.1%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 15 to 9 computations (40% saved)

bsearch0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.702413415579315	283.9361001193222
0.0ms	-0.8378742949772094	0.49890278938009314

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify6.0ms (0.2%)

Memory

17.1MiB live, 17.1MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	78
1	25	78

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

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

soundness532.0ms (16.3%)

Memory

1.6MiB live, 249.4MiB allocated

Rules

4 752×	`lower-fma.f64`
4 752×	`lower-fma.f32`
2 808×	`lower-*.f64`
2 808×	`lower-*.f32`
1 714×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	240
1	95	240
2	195	240
3	532	240
4	2458	240
5	4857	240
6	6132	240
7	7089	240
8	7601	240
0	8038	222
0	16	66
0	24	66
1	106	66
0	840	66

Stop Event

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

Compiler

Compiled 74 to 36 computations (51.4% saved)

preprocess38.0ms (1.2%)

Memory: -22.9MiB live, 101.7MiB allocated
Compiler: Compiled 126 to 52 computations (58.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze10.0ms (0.3%)

sample729.0ms (22.3%)

explain155.0ms (4.7%)

preprocess88.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize28.0ms (0.9%)

series6.0ms (0.2%)

simplify140.0ms (4.3%)

rewrite47.0ms (1.4%)

eval22.0ms (0.7%)

prune11.0ms (0.3%)

simplify8.0ms (0.2%)

localize67.0ms (2.1%)

series17.0ms (0.5%)

simplify131.0ms (4%)

rewrite57.0ms (1.7%)

eval55.0ms (1.7%)

prune72.0ms (2.2%)

simplify9.0ms (0.3%)

localize173.0ms (5.3%)

series21.0ms (0.7%)

simplify132.0ms (4.1%)

rewrite55.0ms (1.7%)

eval87.0ms (2.7%)

prune40.0ms (1.2%)

simplify7.0ms (0.2%)

localize153.0ms (4.7%)

series10.0ms (0.3%)

simplify124.0ms (3.8%)

rewrite64.0ms (2%)

eval53.0ms (1.6%)

prune61.0ms (1.9%)

regimes18.0ms (0.6%)

regimes21.0ms (0.6%)

regimes14.0ms (0.4%)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

soundness532.0ms (16.3%)

preprocess38.0ms (1.2%)

end0.0ms (0%)

Profiling