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

analyze10.0ms (0.2%)

Memory

25.5MiB live, 25.5MiB 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)

sample893.0ms (19.9%)

Memory

-136.9MiB live, 1 159.8MiB allocated

Samples

668.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 199.0ms

ival-add: 115.0ms (57.7% of total)

ival-div: 75.0ms (37.6% of total)

ival-true: 6.0ms (3% of total)

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

Bogosity

preprocess97.0ms (2.2%)

Memory

-17.2MiB live, 65.3MiB 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))

explain63.0ms (1.4%)

Memory

18.2MiB live, 136.1MiB 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

26.0ms

512×

valid

Compiler

Compiled 52 to 24 computations (53.8% saved)

Precisions

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

ival-add: 6.0ms (55.9% of total)

ival-div: 4.0ms (37.3% of total)

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

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

eval0.0ms (0%)

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

prune2.0ms (0%)

Memory

-36.3MiB live, 1.5MiB 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)

simplify5.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

localize20.0ms (0.4%)

Memory

18.6MiB live, 52.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(/.f64 (+.f64 x y) (+.f64 y y))

Samples

14.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-div: 2.0ms (40.9% of total)

ival-add: 2.0ms (40.9% of total)

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

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

series5.0ms (0.1%)

Memory

14.8MiB live, 14.9MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (/.f64 (+.f64 x y) (+.f64 y y))>
#<alt (+.f64 x y)>
#<alt (+.f64 y y)>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>

Calls

15 calls:

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

simplify190.0ms (4.2%)

Memory

-30.4MiB live, 308.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4 752×	`lower-fma.f64`
4 752×	`lower-fma.f32`
2 672×	`lower-*.f64`
2 672×	`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	539	240
4	2494	240
5	4900	240
6	6147	240
7	7103	240
8	7625	240
0	8012	222

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 54

Calls

Call 1

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

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

rewrite221.0ms (4.9%)

Memory

-2.8MiB live, 77.7MiB allocated

Algorithm

1×	batch-egg-rewrite

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

eval12.0ms (0.3%)

Memory: -4.3MiB live, 34.3MiB allocated
Compiler: Compiled 1 183 to 160 computations (86.5% saved)

prune10.0ms (0.2%)

Memory

-14.9MiB live, 23.8MiB 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
▶	4.4%	(*.f64 (+.f64 y y) (+.f64 x y))
▶	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
▶	46.8%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
▶	54.9%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Compiler

Compiled 30 to 18 computations (40% saved)

simplify10.0ms (0.2%)

Memory

16.1MiB live, 16.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 x y)
✓	cost-diff	(+.f64 y y)
✓	cost-diff	(*.f64 (+.f64 y y) (+.f64 x y))
✓	cost-diff	(/.f64 x y)
✓	cost-diff	(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
✓	cost-diff	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
✓	cost-diff	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	cost-diff	#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	23	75
1	37	75
2	65	75
3	110	75
4	146	75
5	179	75
0	179	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) x) y))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
y
#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 x y)
x
y
(*.f64 (+.f64 y y) (+.f64 x y))
(+.f64 y y)
y
(+.f64 x y)
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) x) y))
#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) y))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
(/.f64 (*.f64 x #s(literal 1/2 binary64)) y)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
y
#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 x (/.f64 #s(literal 1/2 binary64) y) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) y) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 x y)
x
y
(*.f64 (+.f64 y y) (+.f64 x y))
(+.f64 y y)
y
(+.f64 x y)
x

localize44.0ms (1%)

Memory

2.0MiB live, 84.8MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 (+.f64 y y) (+.f64 x y))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 x y)
✓	accuracy	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) x) y)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	46.8%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	accuracy	54.9%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))

Samples

28.0ms

256×

valid

Compiler

Compiled 63 to 14 computations (77.8% saved)

Precisions

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

ival-div: 8.0ms (48.9% of total)

ival-mult: 5.0ms (30.6% of total)

ival-add: 4.0ms (24.5% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.3%)

Memory

-19.7MiB live, 18.6MiB allocated

Counts

10 → 216

Calls

Call 1

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

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 (/ x y))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/2 (/ 1 y)) (* 1/2 (/ 1 x))))>
#<alt (* 1/2 (/ x y))>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (* 2 (* x y))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>

Calls

54 calls:

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

simplify228.0ms (5.1%)

Memory

27.1MiB live, 261.2MiB allocated

Algorithm

1×	egg-herbie

Rules

5 472×	`lower-fma.f64`
5 472×	`lower-fma.f32`
3 286×	`lower-*.f64`
3 286×	`lower-*.f32`
1 318×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	1056
1	176	1056
2	393	1056
3	1169	1056
4	2718	1056
5	5963	1056
0	8114	984

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 210

Calls

Call 1

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

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

rewrite97.0ms (2.2%)

Memory

-12.2MiB live, 83.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

388×	`lower-*.f32`
384×	`lower-*.f64`
360×	`lower-/.f32`
356×	`lower-/.f64`
316×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	66
0	23	66
1	90	66
0	712	66

Stop Event

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

Counts

10 → 194

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

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

eval68.0ms (1.5%)

Memory: 6.2MiB live, 81.1MiB allocated
Compiler: Compiled 3 928 to 403 computations (89.7% saved)

prune54.0ms (1.2%)

Memory

-9.5MiB live, 73.9MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	399	5	404
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	399	9	408

Accuracy

100.0%

Counts

408 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.0%	(fma.f64 (+.f64 y y) x (+.f64 y y))
▶	3.7%	(fma.f64 #s(literal -2 binary64) y (*.f64 x (+.f64 y y)))
✓	4.4%	(*.f64 (+.f64 y y) (+.f64 x y))
▶	29.8%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
✓	46.8%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
▶	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	54.9%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
▶	3.5%	#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal 2 binary64))))

Compiler

Compiled 120 to 66 computations (45% saved)

simplify41.0ms (0.9%)

Memory

9.6MiB live, 48.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(*.f64 x (+.f64 y y))
✓	cost-diff	192	(fma.f64 #s(literal -2 binary64) y (*.f64 x (+.f64 y y)))
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	64	(fma.f64 (+.f64 y y) x (+.f64 y y))
✓	cost-diff	0	(.f64 y (.f64 y #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal 2 binary64))))
✓	cost-diff	128	(*.f64 y #s(literal 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	(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)))

Rules

594×	`lower-fma.f32`
588×	`lower-fma.f64`
302×	`lower-*.f32`
294×	`lower-*.f64`
192×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	104
0	30	104
1	55	103
2	127	102
3	215	102
4	293	102
5	324	102
6	418	102
7	418	102
8	439	102
9	495	102
10	600	102
11	672	102
12	721	102
13	721	102
0	721	98

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize83.0ms (1.9%)

Memory

4.1MiB live, 84.3MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(*.f64 x (+.f64 y y))
✓	accuracy	100.0%	(fma.f64 #s(literal -2 binary64) y (*.f64 x (+.f64 y y)))
✓	accuracy	100.0%	(fma.f64 (+.f64 y y) x (+.f64 y y))
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(.f64 y (.f64 y #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 y #s(literal 2 binary64))
✓	accuracy	60.0%	#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal 2 binary64))))
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(*.f64 (+.f64 y y) x)
✓	accuracy	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
✓	accuracy	100.0%	(fma.f64 (+.f64 y y) x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	29.8%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))

Samples

40.0ms

256×

valid

Compiler

Compiled 90 to 19 computations (78.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 18.0ms (66.5% of total)

ival-add: 7.0ms (25.9% of total)

ival-div: 2.0ms (7.4% of total)

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

exact: 0.0ms (0% of total)

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

series17.0ms (0.4%)

Memory

-27.9MiB live, 10.1MiB allocated

Counts

11 → 228

Calls

Call 1

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

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (* x y)))>
#<alt (+ 1/2 (* 2 (* x y)))>
#<alt (+ 1/2 (* 2 (* x y)))>
#<alt (* 2 (* x y))>
#<alt (* y (+ (* 2 x) (* 1/2 (/ 1 y))))>
#<alt (* y (+ (* 2 x) (* 1/2 (/ 1 y))))>
#<alt (* y (+ (* 2 x) (* 1/2 (/ 1 y))))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* y (- (* -2 x) (* 1/2 (/ 1 y)))))>
#<alt (* -1 (* y (- (* -2 x) (* 1/2 (/ 1 y)))))>
#<alt (* -1 (* y (- (* -2 x) (* 1/2 (/ 1 y)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (* x y)))>
#<alt (+ 1/2 (* 2 (* x y)))>
#<alt (+ 1/2 (* 2 (* x y)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 y) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 2 y) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 2 y) (* 1/2 (/ 1 x))))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (- (* -2 y) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* -2 y) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* -2 y) (* 1/2 (/ 1 x)))))>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 (* x y))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* y (+ 2 (* 2 x)))>
#<alt (* y (+ 2 (* 2 x)))>
#<alt (* y (+ 2 (* 2 x)))>
#<alt (* y (+ 2 (* 2 x)))>
#<alt (* y (+ 2 (* 2 x)))>
#<alt (* y (+ 2 (* 2 x)))>
#<alt (* y (+ 2 (* 2 x)))>
#<alt (* y (+ 2 (* 2 x)))>
#<alt (* -1 (* y (- (* -2 x) 2)))>
#<alt (* -1 (* y (- (* -2 x) 2)))>
#<alt (* -1 (* y (- (* -2 x) 2)))>
#<alt (* -1 (* y (- (* -2 x) 2)))>
#<alt (* 2 y)>
#<alt (+ (* 2 y) (* 2 (* x y)))>
#<alt (+ (* 2 y) (* 2 (* x y)))>
#<alt (+ (* 2 y) (* 2 (* x y)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 y) (* 2 (/ y x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ y x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ y x))))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ y x)))))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* -1 (* y (+ 2 (* -2 x))))>
#<alt (* -1 (* y (+ 2 (* -2 x))))>
#<alt (* -1 (* y (+ 2 (* -2 x))))>
#<alt (* -1 (* y (+ 2 (* -2 x))))>
#<alt (* -2 y)>
#<alt (+ (* -2 y) (* 2 (* x y)))>
#<alt (+ (* -2 y) (* 2 (* x y)))>
#<alt (+ (* -2 y) (* 2 (* x y)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* -2 (/ y x)) (* 2 y)))>
#<alt (* x (+ (* -2 (/ y x)) (* 2 y)))>
#<alt (* x (+ (* -2 (/ y x)) (* 2 y)))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>

Calls

57 calls:

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

simplify232.0ms (5.2%)

Memory

38.1MiB live, 192.0MiB allocated

Algorithm

1×	egg-herbie

Rules

4 586×	`lower-fma.f64`
4 586×	`lower-fma.f32`
2 968×	`lower-*.f64`
2 968×	`lower-*.f32`
1 594×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	1284
1	252	1284
2	652	1284
3	1361	1284
4	3001	1284
5	6798	1284
0	8069	1188

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

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

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

rewrite97.0ms (2.2%)

Memory

-4.1MiB live, 122.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 340×	`lower-fma.f32`
1 334×	`lower-fma.f64`
406×	`lower-*.f32`
398×	`lower-*.f64`
344×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	83
0	30	79
1	121	77
0	1101	77

Stop Event

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

Counts

11 → 780

Calls

Call 1

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

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

eval233.0ms (5.2%)

Memory: 19.8MiB live, 360.3MiB allocated
Compiler: Compiled 16 487 to 1 198 computations (92.7% saved)

prune247.0ms (5.5%)

Memory

-11.4MiB live, 352.1MiB allocated

Pruning

22 alts after pruning (17 fresh and 5 done)

	Pruned	Kept	Total
New	1 395	17	1 412
Fresh	0	0	0
Picked	3	2	5
Done	1	3	4
Total	1 399	22	1 421

Accuracy

100.0%

Counts

1 421 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	29.8%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
✓	46.8%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
✓	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
▶	3.9%	#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) x))
✓	54.9%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
▶	3.7%	#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64))))
	3.0%	#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y #s(literal -2 binary64)))
	3.2%	#s(approx (* (+ y y) (+ x y)) (fma.f64 (+.f64 y y) #s(literal 2 binary64) (+.f64 y y)))
	3.5%	#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal 1/2 binary64) y))
	3.6%	#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal -1 binary64) (+.f64 y y)))
▶	3.2%	#s(approx (* (+ y y) (+ x y)) (+.f64 y y))
▶	3.5%	#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) y))
	3.2%	#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) #s(literal 2 binary64)))
	3.0%	#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) #s(literal -2 binary64)))
	2.6%	#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal 8 binary64)))
	2.4%	#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal -8 binary64)))
	3.5%	#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y y) #s(literal 4 binary64)))
▶	54.8%	#s(approx (* (+ y y) (+ x y)) (*.f64 y (/.f64 #s(literal 1/2 binary64) y)))
	2.6%	#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 (+.f64 y y) y)))
	1.9%	#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 (+.f64 y y) #s(literal -2 binary64))))
	1.9%	#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal -2 binary64))))

Compiler

Compiled 326 to 192 computations (41.1% saved)

simplify19.0ms (0.4%)

Memory

-11.0MiB live, 28.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) x)
✓	cost-diff	0	#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) x))
✓	cost-diff	192	(*.f64 (+.f64 y y) #s(literal 2 binary64))
✓	cost-diff	0	(fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64))
✓	cost-diff	0	(*.f64 y (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64)))
✓	cost-diff	0	#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64))))
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(*.f64 (+.f64 y y) y)
✓	cost-diff	0	#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) y))
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	#s(approx (* (+ y y) (+ x y)) (+.f64 y y))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	0	#s(approx (* (+ y y) (+ x y)) (*.f64 y (/.f64 #s(literal 1/2 binary64) y)))
✓	cost-diff	1024	(*.f64 y (/.f64 #s(literal 1/2 binary64) y))

Rules

210×	`lower-fma.f32`
208×	`lower-fma.f64`
134×	`lower-*.f32`
130×	`lower-+.f32`
128×	`lower-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	123
0	36	130
1	65	118
2	116	118
3	176	106
4	239	106
5	273	106
6	287	106
0	287	106

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize69.0ms (1.5%)

Memory

9.2MiB live, 130.7MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(*.f64 (+.f64 y y) #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) x)
✓	accuracy	3.9%	#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) x))
✓	accuracy	100.0%	(fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64))
✓	accuracy	100.0%	#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64))))
✓	accuracy	100.0%	(*.f64 y (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64)))
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(*.f64 (+.f64 y y) y)
✓	accuracy	60.0%	#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) y))
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	4.1%	#s(approx (* (+ y y) (+ x y)) (+.f64 y y))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) y)
✓	accuracy	99.8%	(*.f64 y (/.f64 #s(literal 1/2 binary64) y))
✓	accuracy	4.0%	#s(approx (* (+ y y) (+ x y)) (*.f64 y (/.f64 #s(literal 1/2 binary64) y)))

Samples

43.0ms

256×

valid

Compiler

Compiled 96 to 22 computations (77.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 18.0ms (67.5% of total)

ival-add: 5.0ms (18.8% of total)

ival-div: 3.0ms (11.3% of total)

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

exact: 0.0ms (0% of total)

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

series34.0ms (0.8%)

Memory

-18.4MiB live, 20.9MiB allocated

Counts

13 → 240

Calls

Call 1

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

Outputs
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt (* 2 (* x y))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (/ 1/2 y)>
#<alt (* 2 (* x y))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 (* x y))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* y (+ (* 2 x) (* 2 y)))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* 2 (pow y 2))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* x (+ (* 2 y) (* 2 (/ (pow y 2) x))))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -2 (/ (pow y 2) x)))))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* 2 (pow y 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* -1 (* y (+ 2 (* -2 x))))>
#<alt (* -1 (* y (+ 2 (* -2 x))))>
#<alt (* -1 (* y (+ 2 (* -2 x))))>
#<alt (* -1 (* y (+ 2 (* -2 x))))>
#<alt (* -2 y)>
#<alt (+ (* -2 y) (* 2 (* x y)))>
#<alt (+ (* -2 y) (* 2 (* x y)))>
#<alt (+ (* -2 y) (* 2 (* x y)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* -2 (/ y x)) (* 2 y)))>
#<alt (* x (+ (* -2 (/ y x)) (* 2 y)))>
#<alt (* x (+ (* -2 (/ y x)) (* 2 y)))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* y (- (* 2 x) 2))>
#<alt (* -2 y)>
#<alt (+ (* -2 y) (* 2 (* x y)))>
#<alt (+ (* -2 y) (* 2 (* x y)))>
#<alt (+ (* -2 y) (* 2 (* x y)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* -2 (/ y x)) (* 2 y)))>
#<alt (* x (+ (* -2 (/ y x)) (* 2 y)))>
#<alt (* x (+ (* -2 (/ y x)) (* 2 y)))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))>
#<alt -2>
#<alt (- (* 2 x) 2)>
#<alt (- (* 2 x) 2)>
#<alt (- (* 2 x) 2)>
#<alt (* 2 x)>
#<alt (* x (- 2 (* 2 (/ 1 x))))>
#<alt (* x (- 2 (* 2 (/ 1 x))))>
#<alt (* x (- 2 (* 2 (/ 1 x))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 2)))>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 2)))>
#<alt (* -1 (* x (- (* 2 (/ 1 x)) 2)))>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* x (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 y))))>
#<alt (* 1/2 (/ x y))>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt (/ (+ (* 1/2 x) (* 1/2 y)) y)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (+ 1/2 (* 1/2 (/ x y)))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>
#<alt (* 4 (* x y))>

Calls

60 calls:

Time	Variable		Point	Expression
24.0ms	x	@	inf	(+ (* x 2) -2)
3.0ms	x	@	-inf	(* y (+ (* x 2) -2))
1.0ms	y	@	0	(* y (+ (* x 2) -2))
0.0ms	y	@	inf	(* y (+ (* x 2) -2))
0.0ms	y	@	inf	(* (+ y y) 2)

simplify252.0ms (5.6%)

Memory

-15.3MiB live, 354.0MiB allocated

Algorithm

1×	egg-herbie

Rules

5 214×	`lower-fma.f64`
5 214×	`lower-fma.f32`
3 152×	`lower-*.f64`
3 152×	`lower-*.f32`
2 062×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	1284
1	199	1284
2	493	1284
3	966	1284
4	2287	1284
5	6379	1284
0	8397	1218

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
(* 2 (* x y))
(* y (+ (* 2 x) (* 2 y)))
(* y (+ (* 2 x) (* 2 y)))
(* y (+ (* 2 x) (* 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))
(* (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 (* x y)) (* 2 (pow y 2)))
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(* 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))
(* -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 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(/ 1/2 y)
(* 2 (* x y))
(* y (+ (* 2 x) (* 2 y)))
(* y (+ (* 2 x) (* 2 y)))
(* y (+ (* 2 x) (* 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))
(* (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 (* x y)) (* 2 (pow y 2)))
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(* 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))
(* -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 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 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))
(* (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))
(* (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 (* x y)) (* 2 (pow y 2)))
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(* 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))
(* -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 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* 2 (pow y 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* -1 (* y (+ 2 (* -2 x))))
(* -1 (* y (+ 2 (* -2 x))))
(* -1 (* y (+ 2 (* -2 x))))
(* -1 (* y (+ 2 (* -2 x))))
(* -2 y)
(+ (* -2 y) (* 2 (* x y)))
(+ (* -2 y) (* 2 (* x y)))
(+ (* -2 y) (* 2 (* x y)))
(* 2 (* x y))
(* x (+ (* -2 (/ y x)) (* 2 y)))
(* x (+ (* -2 (/ y x)) (* 2 y)))
(* x (+ (* -2 (/ y x)) (* 2 y)))
(* 2 (* x y))
(* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))
(* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))
(* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* y (- (* 2 x) 2))
(* -2 y)
(+ (* -2 y) (* 2 (* x y)))
(+ (* -2 y) (* 2 (* x y)))
(+ (* -2 y) (* 2 (* x y)))
(* 2 (* x y))
(* x (+ (* -2 (/ y x)) (* 2 y)))
(* x (+ (* -2 (/ y x)) (* 2 y)))
(* x (+ (* -2 (/ y x)) (* 2 y)))
(* 2 (* x y))
(* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))
(* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))
(* -1 (* x (+ (* -2 y) (* 2 (/ y x)))))
-2
(- (* 2 x) 2)
(- (* 2 x) 2)
(- (* 2 x) 2)
(* 2 x)
(* x (- 2 (* 2 (/ 1 x))))
(* x (- 2 (* 2 (/ 1 x))))
(* x (- 2 (* 2 (/ 1 x))))
(* 2 x)
(* -1 (* x (- (* 2 (/ 1 x)) 2)))
(* -1 (* x (- (* 2 (/ 1 x)) 2)))
(* -1 (* x (- (* 2 (/ 1 x)) 2)))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 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))
(* 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) (* 1/2 y)) y)
(/ (+ (* 1/2 x) (* 1/2 y)) y)
(/ (+ (* 1/2 x) (* 1/2 y)) 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)))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))
(* 4 (* x y))

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

rewrite117.0ms (2.6%)

Memory

37.1MiB live, 115.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

550×	`lower-fma.f32`
548×	`lower-fma.f64`
460×	`lower-*.f32`
450×	`lower-*.f64`
342×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	106
0	36	113
1	125	85
0	944	85

Stop Event

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

Counts

13 → 599

Calls

Call 1

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

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

eval247.0ms (5.5%)

Memory: -15.2MiB live, 216.7MiB allocated
Compiler: Compiled 10 090 to 862 computations (91.5% saved)

prune186.0ms (4.1%)

Memory

18.2MiB live, 258.5MiB allocated

Pruning

24 alts after pruning (16 fresh and 8 done)

	Pruned	Kept	Total
New	1 018	9	1 027
Fresh	5	7	12
Picked	2	3	5
Done	0	5	5
Total	1 025	24	1 049

Accuracy

100.0%

Counts

1 049 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	29.8%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
✓	100.0%	#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
✓	46.8%	#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (fma.f64 #s(literal 4 binary64) y (+.f64 y y)) x))
✓	3.9%	#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
	3.9%	#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (*.f64 #s(literal 4 binary64) y) #s(literal 2 binary64)) x))
	3.9%	#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 #s(literal 4 binary64) y) x))
✓	54.9%	#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
	3.0%	#s(approx (+ (* -2 y) (* x (+ y y))) (.f64 y #s(approx (+ ( x 2) -2) #s(literal -2 binary64))))
	3.2%	#s(approx (* (+ y y) (+ x y)) (fma.f64 #s(literal 4 binary64) y (+.f64 y y)))
	3.5%	#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal 1/2 binary64) y))
	3.6%	#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal -1 binary64) (+.f64 y y)))
✓	3.2%	#s(approx (* (+ y y) (+ x y)) (+.f64 y y))
	3.5%	#s(approx (* (+ y y) (+ x y)) (*.f64 (fma.f64 #s(literal 4 binary64) y (+.f64 y y)) y))
✓	3.5%	#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) y))
	3.0%	#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) #s(literal -2 binary64)))
	2.6%	#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 (+.f64 y y) y) y))
	2.6%	#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal 8 binary64)))
	2.4%	#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal -8 binary64)))
	3.5%	#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y y) #s(literal 4 binary64)))
	1.9%	#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y #s(literal -2 binary64)) y))
✓	54.8%	#s(approx (* (+ y y) (+ x y)) (*.f64 y (/.f64 #s(literal 1/2 binary64) y)))
	1.9%	#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 (+.f64 y y) #s(literal -2 binary64))))
	3.2%	#s(approx (* (+ y y) (+ x y)) (*.f64 #s(literal 4 binary64) y))

Compiler

Compiled 438 to 170 computations (61.2% saved)

regimes42.0ms (0.9%)

Memory

-29.0MiB live, 63.6MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(approx (* (+ y y) (+ x y)) (+.f64 y y))
#s(approx (* (+ y y) (+ x y)) (*.f64 #s(literal 4 binary64) y))
#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y #s(literal -2 binary64)))
#s(approx (+ (* -2 y) (* x (+ y y))) (.f64 y #s(approx (+ ( x 2) -2) #s(literal -2 binary64))))
#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) #s(literal -2 binary64)))
#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) #s(literal 2 binary64)))
#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) y))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
#s(approx (* (+ y y) (+ x y)) (fma.f64 #s(literal 4 binary64) y (+.f64 y y)))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal -2 binary64))))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal 2 binary64))))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y #s(literal -2 binary64)) y))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y y) #s(literal 4 binary64)))
#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 #s(literal 4 binary64) y) x))
#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal 1/2 binary64) y))
#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64))))
(*.f64 (+.f64 y y) (+.f64 x y))
#s(approx (* (+ y y) (+ x y)) (fma.f64 (+.f64 y y) #s(literal 2 binary64) (+.f64 y y)))
(fma.f64 (+.f64 y y) x (+.f64 y y))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 (+.f64 y y) #s(literal -2 binary64))))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 (+.f64 y y) y)))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 (+.f64 y y) y) y))
#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) x))
#s(approx (* (+ y y) (+ x y)) (*.f64 (fma.f64 #s(literal 4 binary64) y (+.f64 y y)) y))
#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal -1 binary64) (+.f64 y y)))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (fma.f64 #s(literal 4 binary64) y (+.f64 y y)) x))
(fma.f64 #s(literal -2 binary64) y (*.f64 x (+.f64 y y)))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal -8 binary64)))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal 8 binary64)))
#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (*.f64 #s(literal 4 binary64) y) #s(literal 2 binary64)) x))
#s(approx (* (+ y y) (+ x y)) (*.f64 y (/.f64 #s(literal 1/2 binary64) y)))
#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 x y) #s(literal 1/2 binary64)))
(/.f64 (+.f64 x y) (+.f64 y y))

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

Calls

3 calls:

18.0ms	y
11.0ms	(/.f64 (+.f64 x y) (+.f64 y y))
11.0ms	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)

regimes32.0ms (0.7%)

Memory

21.7MiB live, 60.6MiB allocated

Counts

34 → 3

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(approx (* (+ y y) (+ x y)) (+.f64 y y))
#s(approx (* (+ y y) (+ x y)) (*.f64 #s(literal 4 binary64) y))
#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y #s(literal -2 binary64)))
#s(approx (+ (* -2 y) (* x (+ y y))) (.f64 y #s(approx (+ ( x 2) -2) #s(literal -2 binary64))))
#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) #s(literal -2 binary64)))
#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) #s(literal 2 binary64)))
#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) y))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
#s(approx (* (+ y y) (+ x y)) (fma.f64 #s(literal 4 binary64) y (+.f64 y y)))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal -2 binary64))))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal 2 binary64))))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y #s(literal -2 binary64)) y))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y y) #s(literal 4 binary64)))
#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 #s(literal 4 binary64) y) x))
#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal 1/2 binary64) y))
#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64))))
(*.f64 (+.f64 y y) (+.f64 x y))
#s(approx (* (+ y y) (+ x y)) (fma.f64 (+.f64 y y) #s(literal 2 binary64) (+.f64 y y)))
(fma.f64 (+.f64 y y) x (+.f64 y y))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 (+.f64 y y) #s(literal -2 binary64))))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 (+.f64 y y) y)))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 (+.f64 y y) y) y))
#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) x))
#s(approx (* (+ y y) (+ x y)) (*.f64 (fma.f64 #s(literal 4 binary64) y (+.f64 y y)) y))
#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal -1 binary64) (+.f64 y y)))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (fma.f64 #s(literal 4 binary64) y (+.f64 y y)) x))
(fma.f64 #s(literal -2 binary64) y (*.f64 x (+.f64 y y)))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal -8 binary64)))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal 8 binary64)))
#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (*.f64 #s(literal 4 binary64) y) #s(literal 2 binary64)) x))
#s(approx (* (+ y y) (+ x y)) (*.f64 y (/.f64 #s(literal 1/2 binary64) y)))
#s(approx (/ (+ x y) (+ y y)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) y))

Outputs

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

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

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

Calls

3 calls:

11.0ms	y
10.0ms	x
9.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
79.5%	3	`x`
75.2%	3	`y`
98.3%	3	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes35.0ms (0.8%)

Memory

-14.1MiB live, 61.1MiB allocated

Accuracy

Total -34.7b remaining (-120.2%)

Threshold costs -34.7b (-120.2%)

Counts

33 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ x y) (+ y y)) #s(literal 1/2 binary64))
#s(approx (* (+ y y) (+ x y)) (+.f64 y y))
#s(approx (* (+ y y) (+ x y)) (*.f64 #s(literal 4 binary64) y))
#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y #s(literal -2 binary64)))
#s(approx (+ (* -2 y) (* x (+ y y))) (.f64 y #s(approx (+ ( x 2) -2) #s(literal -2 binary64))))
#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) #s(literal -2 binary64)))
#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) #s(literal 2 binary64)))
#s(approx (* (+ y y) (+ x y)) (*.f64 (+.f64 y y) y))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (+.f64 y y) x))
#s(approx (* (+ y y) (+ x y)) (fma.f64 #s(literal 4 binary64) y (+.f64 y y)))
#s(approx (/ (+ x y) (+ y y)) (fma.f64 (+.f64 y y) x #s(literal 1/2 binary64)))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal -2 binary64))))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 y #s(literal 2 binary64))))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y #s(literal -2 binary64)) y))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y y) #s(literal 4 binary64)))
#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 #s(literal 4 binary64) y) x))
#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal 1/2 binary64) y))
#s(approx (+ (* -2 y) (* x (+ y y))) (*.f64 y (fma.f64 x #s(literal 2 binary64) #s(literal -2 binary64))))
(*.f64 (+.f64 y y) (+.f64 x y))
#s(approx (* (+ y y) (+ x y)) (fma.f64 (+.f64 y y) #s(literal 2 binary64) (+.f64 y y)))
(fma.f64 (+.f64 y y) x (+.f64 y y))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 (+.f64 y y) #s(literal -2 binary64))))
#s(approx (* (+ y y) (+ x y)) (.f64 y (.f64 (+.f64 y y) y)))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 (+.f64 y y) y) y))
#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) x))
#s(approx (* (+ y y) (+ x y)) (*.f64 (fma.f64 #s(literal 4 binary64) y (+.f64 y y)) y))
#s(approx (* (+ y y) (+ x y)) (/.f64 #s(literal -1 binary64) (+.f64 y y)))
#s(approx (/ (+ x y) (+ y y)) (*.f64 (fma.f64 #s(literal 4 binary64) y (+.f64 y y)) x))
(fma.f64 #s(literal -2 binary64) y (*.f64 x (+.f64 y y)))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal -8 binary64)))
#s(approx (* (+ y y) (+ x y)) (.f64 (.f64 y (*.f64 y y)) #s(literal 8 binary64)))
#s(approx (/ (+ x y) (+ y y)) (.f64 (.f64 (*.f64 #s(literal 4 binary64) y) #s(literal 2 binary64)) x))
#s(approx (* (+ y y) (+ x y)) (*.f64 y (/.f64 #s(literal 1/2 binary64) y)))

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

Calls

3 calls:

12.0ms	y
12.0ms	(/.f64 (+.f64 x y) (+.f64 y y))
10.0ms	x

Results

Accuracy	Segments	Branch
54.9%	1	`y`
54.9%	1	`x`
54.9%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 15 to 9 computations (40% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.5000018882334968	9217636.352173796
0.0ms	-5.001486332934084	0.4990986530689326

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify7.0ms (0.2%)

Memory

15.1MiB live, 15.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	78
1	27	78

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

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

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

soundness417.0ms (9.3%)

Memory

-17.0MiB live, 179.5MiB allocated

Rules

4 752×	`lower-fma.f64`
4 752×	`lower-fma.f32`
2 672×	`lower-*.f64`
2 672×	`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	539	240
4	2494	240
5	4900	240
6	6147	240
7	7103	240
8	7625	240
0	8012	222

Stop Event

1×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 66 to 32 computations (51.5% saved)

preprocess32.0ms (0.7%)

Memory: 13.8MiB live, 91.2MiB allocated
Compiler: Compiled 126 to 54 computations (57.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	20	104
0	30	104
1	55	103
2	127	102
3	215	102
4	293	102
5	324	102
6	418	102
7	418	102
8	439	102
9	495	102
10	600	102
11	672	102
12	721	102
13	721	102
0	721	98

Iter	Nodes	Cost
0	25	123
0	36	130
1	65	118
2	116	118
3	176	106
4	239	106
5	273	106
6	287	106
0	287	106

Iter	Nodes	Cost
0	20	104
0	30	104
1	55	103
2	127	102
3	215	102
4	293	102
5	324	102
6	418	102
7	418	102
8	439	102
9	495	102
10	600	102
11	672	102
12	721	102
13	721	102
0	721	98

Iter	Nodes	Cost
0	25	123
0	36	130
1	65	118
2	116	118
3	176	106
4	239	106
5	273	106
6	287	106
0	287	106

analyze10.0ms (0.2%)

sample893.0ms (19.9%)

preprocess97.0ms (2.2%)

explain63.0ms (1.4%)

eval0.0ms (0%)

prune2.0ms (0%)

simplify5.0ms (0.1%)

localize20.0ms (0.4%)

series5.0ms (0.1%)

simplify190.0ms (4.2%)

rewrite221.0ms (4.9%)

eval12.0ms (0.3%)

prune10.0ms (0.2%)

simplify10.0ms (0.2%)

localize44.0ms (1%)

series12.0ms (0.3%)

simplify228.0ms (5.1%)

rewrite97.0ms (2.2%)

eval68.0ms (1.5%)

prune54.0ms (1.2%)

simplify41.0ms (0.9%)

localize83.0ms (1.9%)

series17.0ms (0.4%)

simplify232.0ms (5.2%)

rewrite97.0ms (2.2%)

eval233.0ms (5.2%)

prune247.0ms (5.5%)

simplify19.0ms (0.4%)

localize69.0ms (1.5%)

series34.0ms (0.8%)

simplify252.0ms (5.6%)

rewrite117.0ms (2.6%)

eval247.0ms (5.5%)

prune186.0ms (4.1%)

regimes42.0ms (0.9%)

regimes32.0ms (0.7%)

regimes35.0ms (0.8%)

bsearch0.0ms (0%)

simplify7.0ms (0.2%)

soundness417.0ms (9.3%)

preprocess32.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	20	104
0	30	104
1	55	103
2	127	102
3	215	102
4	293	102
5	324	102
6	418	102
7	418	102
8	439	102
9	495	102
10	600	102
11	672	102
12	721	102
13	721	102
0	721	98

Iter	Nodes	Cost
0	25	123
0	36	130
1	65	118
2	116	118
3	176	106
4	239	106
5	273	106
6	287	106
0	287	106