Metrics for Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample931.0ms (11.1%)

Memory

-122.6MiB live, 994.2MiB allocated

Samples

381.0ms	7 626×	0	valid
26.0ms	272×	1	valid
25.0ms	155×	3	valid
21.0ms	203×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 240.0ms

ival-div: 112.0ms (46.7% of total)

ival-sub: 59.0ms (24.6% of total)

ival-add: 45.0ms (18.8% of total)

adjust: 11.0ms (4.6% of total)

exact: 5.0ms (2.1% of total)

ival-true: 5.0ms (2.1% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

preprocess78.0ms (0.9%)

Memory

-2.4MiB live, 78.1MiB allocated

Algorithm

2×	egg-herbie

Rules

560×	`accelerator-lowering-fma.f32`
560×	`accelerator-lowering-fma.f64`
208×	`-lowering-.f32`
208×	`-lowering-.f64`
182×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	51	42
2	153	42
3	406	42
4	715	42
5	909	42
6	951	42
0	6	7
1	12	7
2	23	7
3	44	7
4	83	7
5	154	7
6	278	7
7	435	7
8	543	7
9	604	7
10	608	7
0	608	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

Inputs
(+ x (/ (- x y) 2))
(+ (neg x) (/ (- (neg x) y) 2))
(+ x (/ (- x (neg y)) 2))
(neg (+ (neg x) (/ (- (neg x) y) 2)))
(neg (+ x (/ (- x (neg y)) 2)))
(+ y (/ (- y x) 2))

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

explain70.0ms (0.8%)

Memory

-15.2MiB live, 143.1MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(/.f64 (-.f64 x y) #s(literal 2 binary64))`
-	-	`y`
-	-	`#s(literal 2 binary64)`
-	-	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`
-	-	`(-.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

21.0ms	456×	0	valid
3.0ms	22×	2	valid
2.0ms	28×	1	valid
1.0ms	6×	3	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

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

ival-div: 4.0ms (32.9% of total)

ival-sub: 3.0ms (24.7% of total)

ival-add: 3.0ms (24.7% of total)

adjust: 1.0ms (8.2% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify28.0ms (0.3%)

Memory

18.7MiB live, 57.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 x y)
✓	cost-diff	192	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))
✓	cost-diff	320	(/.f64 (-.f64 x y) #s(literal 2 binary64))

Rules

560×	`accelerator-lowering-fma.f32`
560×	`accelerator-lowering-fma.f64`
208×	`-lowering-.f32`
208×	`-lowering-.f64`
128×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	12	18
2	23	18
3	44	18
4	83	18
5	154	18
6	278	18
7	435	18
8	543	18
9	604	18
10	608	18
0	608	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize35.0ms (0.4%)

Memory

-6.1MiB live, 30.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 (-.f64 x y) #s(literal 2 binary64))
✓	accuracy	100.0%	(-.f64 x y)
✓	accuracy	99.8%	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))

Samples

25.0ms	228×	0	valid
1.0ms	11×	2	valid
1.0ms	14×	1	valid
0.0ms	3×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-div: 2.0ms (32.8% of total)

ival-sub: 2.0ms (32.8% of total)

ival-add: 1.0ms (16.4% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

3 → 72

Calls

Call 1

Inputs
#<alt (/ (- x y) 2)>
#<alt (+ x (/ (- x y) 2))>
#<alt (- x y)>

Outputs
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 1/2 x))>
#<alt (+ (* -1/2 y) (* 1/2 x))>
#<alt (+ (* -1/2 y) (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 1/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 1/2 (* -1/2 (/ y x))))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1/2)))>
#<alt (* 1/2 x)>
#<alt (+ (* -1/2 y) (* 1/2 x))>
#<alt (+ (* -1/2 y) (* 1/2 x))>
#<alt (+ (* -1/2 y) (* 1/2 x))>
#<alt (* -1/2 y)>
#<alt (* y (- (* 1/2 (/ x y)) 1/2))>
#<alt (* y (- (* 1/2 (/ x y)) 1/2))>
#<alt (* y (- (* 1/2 (/ x y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1/2 (/ x y)))))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (+ x (* 1/2 x))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (* -1/2 y)>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt x>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (* -1 y)>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>

Calls

18 calls:

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

rewrite331.0ms (3.9%)

Memory

-3.1MiB live, 592.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 050×	`accelerator-lowering-fma.f32`
4 050×	`accelerator-lowering-fma.f64`
3 870×	`-lowering-.f32`
3 870×	`-lowering-.f64`
2 640×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	45	15
2	397	15
3	5077	15
0	8178	14

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 353

Calls

Call 1

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

Outputs
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 y #s(literal -1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (*.f64 y #s(literal -1/2 binary64))))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) y)))
(+.f64 (.f64 y #s(literal -1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) y)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (-.f64 #s(literal 0 binary64) (log.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (-.f64 #s(literal 0 binary64) (log.f64 (*.f64 (-.f64 x y) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 (-.f64 x y) #s(literal -1/2 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (.f64 y (+.f64 x y)))) #s(literal 2 binary64)) (/.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 x x (.f64 y (+.f64 x y)))) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 x x) (+.f64 x y)) #s(literal 2 binary64)) (/.f64 (/.f64 (.f64 y y) (+.f64 x y)) #s(literal 2 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 2 binary64) (fma.f64 x x (.f64 y (+.f64 x y))))) (/.f64 (.f64 y (.f64 y y)) (.f64 #s(literal 2 binary64) (fma.f64 x x (.f64 y (+.f64 x y))))))
(-.f64 (/.f64 (.f64 x x) (.f64 #s(literal 2 binary64) (+.f64 x y))) (/.f64 (.f64 y y) (.f64 #s(literal 2 binary64) (+.f64 x y))))
(-.f64 (/.f64 (.f64 x #s(literal 2 binary64)) #s(literal 4 binary64)) (/.f64 (.f64 y #s(literal 2 binary64)) #s(literal 4 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (fma.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (+.f64 x y)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (/.f64 (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)) (fma.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (+.f64 x y)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (+.f64 x y))) (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (+.f64 x y))))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 y #s(literal -1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal 1 binary64) (.f64 y #s(literal -1/2 binary64))))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) y)))
(fma.f64 y #s(literal -1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 y #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (*.f64 y #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) y)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 y #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal 1 binary64) (.f64 y #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) y)))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64) (*.f64 y #s(literal -1/2 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64) (.f64 #s(literal 1 binary64) (.f64 y #s(literal -1/2 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) y)))
(neg.f64 (*.f64 (-.f64 x y) #s(literal -1/2 binary64)))
(neg.f64 (.f64 (.f64 (-.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 x y) #s(literal 2 binary64))
(/.f64 (-.f64 y x) #s(literal -2 binary64))
(/.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (.f64 #s(literal 2 binary64) (fma.f64 x x (*.f64 y (+.f64 x y)))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 y (+.f64 x y))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 x y)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (fma.f64 x #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (+.f64 x y)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x y)) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x y)) (.f64 (-.f64 x y) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (.f64 (fma.f64 x (.f64 x x) (.f64 y (*.f64 y y))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x y) (.f64 (+.f64 x y) (.f64 (-.f64 x y) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (.f64 #s(literal 2 binary64) (+.f64 x y)))
(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x y))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) (-.f64 x y)))
(/.f64 (fma.f64 x #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) y)) #s(literal 4 binary64))
(/.f64 (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 y x)) (neg.f64 (.f64 #s(literal 2 binary64) (fma.f64 x x (.f64 y (+.f64 x y))))))
(/.f64 (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 y x)) (.f64 #s(literal -2 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))))
(/.f64 (.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (-.f64 y x)) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 y (+.f64 x y))))))
(/.f64 (.f64 (+.f64 x y) (-.f64 y x)) (neg.f64 (.f64 #s(literal 2 binary64) (+.f64 x y))))
(/.f64 (.f64 (+.f64 x y) (-.f64 y x)) (.f64 #s(literal -2 binary64) (+.f64 x y)))
(/.f64 (.f64 (+.f64 x y) (-.f64 y x)) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x y))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))) (fma.f64 (.f64 y (.f64 y y)) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (fma.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (+.f64 x y)) (.f64 (.f64 x x) #s(literal 1/4 binary64))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y)))) (.f64 (.f64 #s(literal 2 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))) (fma.f64 x (.f64 x x) (.f64 y (*.f64 y y)))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (fma.f64 x (.f64 x x) (.f64 y (.f64 y y)))) (.f64 (.f64 #s(literal 2 binary64) (+.f64 x y)) (fma.f64 (.f64 y y) (fma.f64 x x (.f64 y y)) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x y)) (.f64 (-.f64 x y) #s(literal 1/2 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 x y)))
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simplify311.0ms (3.7%)

Memory

-2.4MiB live, 450.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 504×	`accelerator-lowering-fma.f32`
7 504×	`accelerator-lowering-fma.f64`
2 794×	`-lowering-.f32`
2 794×	`-lowering-.f64`
1 196×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	351
1	176	351
2	487	351
3	1348	315
4	2968	315
5	4585	315
6	6569	315
7	7592	315
0	8078	297

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

eval86.0ms (1%)

Memory: -8.7MiB live, 105.4MiB allocated
Compiler: Compiled 9 026 to 1 113 computations (87.7% saved)

prune57.0ms (0.7%)

Memory

23.0MiB live, 140.2MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	409	16	425
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	410	16	426

Accuracy

100.0%

Counts

426 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	19.5%	(fma.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (/.f64 #s(literal 1/2 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))) x)
▶	49.8%	(fma.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (/.f64 (-.f64 x y) (.f64 #s(literal 2 binary64) (fma.f64 x x (*.f64 y (+.f64 x y))))) x)
	54.4%	(fma.f64 (pow.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) x)
	51.0%	(fma.f64 (/.f64 (.f64 x x) (fma.f64 (-.f64 y x) (.f64 #s(literal 1/4 binary64) (-.f64 x y)) (.f64 x x))) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x) (neg.f64 (/.f64 (.f64 (-.f64 x y) (*.f64 #s(literal 1/4 binary64) (-.f64 x y))) (fma.f64 (-.f64 x y) #s(literal -1/2 binary64) x))))
	99.8%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
	53.9%	(fma.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (/.f64 #s(literal 1/2 binary64) (+.f64 x y)) x)
	55.2%	(fma.f64 x #s(literal 3/2 binary64) #s(literal 0 binary64))
▶	99.8%	(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x))
▶	45.5%	(fma.f64 #s(literal -1/2 binary64) y #s(literal 0 binary64))
	53.4%	(/.f64 (fma.f64 (-.f64 y x) (.f64 #s(literal 1/4 binary64) (-.f64 x y)) (.f64 x x)) (fma.f64 (-.f64 x y) #s(literal -1/2 binary64) x))
▶	51.4%	(/.f64 (-.f64 (.f64 (-.f64 x y) (.f64 #s(literal 1/4 binary64) (-.f64 x y))) (.f64 x x)) (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))
▶	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)))
	53.6%	(+.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 x y) (+.f64 x y)))) (+.f64 x y)))
	88.4%	(+.f64 x (/.f64 (-.f64 (.f64 x (/.f64 #s(literal 2 binary64) y)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) y))))
	99.7%	(+.f64 x (/.f64 (.f64 (+.f64 x y) (.f64 (-.f64 x y) (/.f64 #s(literal 1 binary64) (+.f64 x y)))) #s(literal 2 binary64)))
	99.6%	(+.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 x y))))

Compiler

Compiled 554 to 290 computations (47.7% saved)

simplify489.0ms (5.8%)

Memory

10.7MiB live, 687.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	(*.f64 y (+.f64 x y))
✓	cost-diff	0	(fma.f64 x x (*.f64 y (+.f64 x y)))
✓	cost-diff	2880	(fma.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (/.f64 (-.f64 x y) (.f64 #s(literal 2 binary64) (fma.f64 x x (*.f64 y (+.f64 x y))))) x)
✓	cost-diff	0	(-.f64 x y)
✓	cost-diff	0	(-.f64 (.f64 (-.f64 x y) (.f64 #s(literal 1/4 binary64) (-.f64 x y))) (*.f64 x x))
✓	cost-diff	192	(-.f64 (*.f64 (-.f64 x y) #s(literal 1/2 binary64)) x)
✓	cost-diff	192	(/.f64 (-.f64 (.f64 (-.f64 x y) (.f64 #s(literal 1/4 binary64) (-.f64 x y))) (.f64 x x)) (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))
✓	cost-diff	0	(-.f64 x y)
✓	cost-diff	0	(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)))
✓	cost-diff	0	(fma.f64 #s(literal -1/2 binary64) y #s(literal 0 binary64))
✓	cost-diff	0	(fma.f64 y #s(literal -1/2 binary64) x)
✓	cost-diff	192	(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x))

Rules

15 018×	`accelerator-lowering-fma.f32`
15 018×	`accelerator-lowering-fma.f64`
5 108×	`-lowering-.f32`
5 108×	`-lowering-.f64`
1 920×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	186
1	83	186
2	223	178
3	666	178
4	2455	174
5	5628	174
0	8388	164

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* x 1/2) (+ (* y -1/2) x))
x
1/2
(+ (* y -1/2) x)
y
-1/2
(+ (* -1/2 y) 0)
-1/2
y
0
(/ 1 (/ 1 (+ (* (- x y) 1/2) x)))
1
(/ 1 (+ (* (- x y) 1/2) x))
(+ (* (- x y) 1/2) x)
(- x y)
x
y
1/2
(/ (- (* (- x y) (* 1/4 (- x y))) (* x x)) (- (* (- x y) 1/2) x))
(- (* (- x y) (* 1/4 (- x y))) (* x x))
(* (- x y) (* 1/4 (- x y)))
(- x y)
x
y
(* 1/4 (- x y))
1/4
(* x x)
(- (* (- x y) 1/2) x)
(* (- x y) 1/2)
1/2
(+ (* (+ (* x x) (* y (+ x y))) (/ (- x y) (* 2 (+ (* x x) (* y (+ x y)))))) x)
(+ (* x x) (* y (+ x y)))
x
(* y (+ x y))
y
(+ x y)
(/ (- x y) (* 2 (+ (* x x) (* y (+ x y)))))
(- x y)
(* 2 (+ (* x x) (* y (+ x y))))
2

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

localize155.0ms (1.8%)

Memory

-27.5MiB live, 217.7MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (fma.f64 x x (.f64 y (+.f64 x y))))
✓	accuracy	96.5%	(fma.f64 x x (*.f64 y (+.f64 x y)))
✓	accuracy	54.2%	(fma.f64 (fma.f64 x x (.f64 y (+.f64 x y))) (/.f64 (-.f64 x y) (.f64 #s(literal 2 binary64) (fma.f64 x x (*.f64 y (+.f64 x y))))) x)
✓	accuracy	54.0%	(/.f64 (-.f64 x y) (.f64 #s(literal 2 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))))
✓	accuracy	100.0%	(-.f64 (*.f64 (-.f64 x y) #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(.f64 (-.f64 x y) (.f64 #s(literal 1/4 binary64) (-.f64 x y)))
✓	accuracy	73.0%	(-.f64 (.f64 (-.f64 x y) (.f64 #s(literal 1/4 binary64) (-.f64 x y))) (*.f64 x x))
✓	accuracy	53.9%	(/.f64 (-.f64 (.f64 (-.f64 x y) (.f64 #s(literal 1/4 binary64) (-.f64 x y))) (.f64 x x)) (-.f64 (.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))
✓	accuracy	100.0%	(-.f64 x y)
✓	accuracy	99.8%	(fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x)))
✓	accuracy	100.0%	(fma.f64 #s(literal -1/2 binary64) y #s(literal 0 binary64))
✓	accuracy	100.0%	(fma.f64 y #s(literal -1/2 binary64) x)
✓	accuracy	99.8%	(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y #s(literal -1/2 binary64) x))

Samples

40.0ms	210×	0	valid
16.0ms	17×	2	valid
8.0ms	21×	1	valid
6.0ms	7×	3	valid
1.0ms	1×	5	exit

Compiler

Compiled 195 to 34 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 24.0ms (46.9% of total)

ival-add: 10.0ms (19.6% of total)

ival-div: 8.0ms (15.6% of total)

ival-sub: 4.0ms (7.8% of total)

adjust: 3.0ms (5.9% of total)

exact: 1.0ms (2% of total)

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

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

series28.0ms (0.3%)

Memory

21.2MiB live, 57.4MiB allocated

Counts

17 → 396

Calls

Call 1

Inputs
#<alt (+ (* x 1/2) (+ (* y -1/2) x))>
#<alt (+ (* y -1/2) x)>
#<alt (+ (* -1/2 y) 0)>
#<alt (/ 1 (/ 1 (+ (* (- x y) 1/2) x)))>
#<alt (/ 1 (+ (* (- x y) 1/2) x))>
#<alt (+ (* (- x y) 1/2) x)>
#<alt (- x y)>
#<alt (/ (- (* (- x y) (* 1/4 (- x y))) (* x x)) (- (* (- x y) 1/2) x))>
#<alt (- (* (- x y) 1/2) x)>
#<alt (- (* (- x y) (* 1/4 (- x y))) (* x x))>
#<alt (+ (* (+ (* x x) (* y (+ x y))) (/ (- x y) (* 2 (+ (* x x) (* y (+ x y)))))) x)>
#<alt (+ (* x x) (* y (+ x y)))>
#<alt (* y (+ x y))>
#<alt (+ x y)>
#<alt (* (- x y) (* 1/4 (- x y)))>
#<alt (/ (- x y) (* 2 (+ (* x x) (* y (+ x y)))))>
#<alt (* 2 (+ (* x x) (* y (+ x y))))>

Outputs
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (+ x (* 1/2 x))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (* -1/2 y)>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt x>
#<alt (+ x (* -1/2 y))>
#<alt (+ x (* -1/2 y))>
#<alt (+ x (* -1/2 y))>
#<alt (* -1/2 y)>
#<alt (* y (- (/ x y) 1/2))>
#<alt (* y (- (/ x y) 1/2))>
#<alt (* y (- (/ x y) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ x y)))))>
#<alt (* -1/2 y)>
#<alt (+ x (* -1/2 y))>
#<alt (+ x (* -1/2 y))>
#<alt (+ x (* -1/2 y))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ y x))))>
#<alt (* x (+ 1 (* -1/2 (/ y x))))>
#<alt (* x (+ 1 (* -1/2 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1)))>
#<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 (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (+ x (* 1/2 x))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (* -1/2 y)>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (/ -2 y)>
#<alt (- (* -6 (/ x (pow y 2))) (* 2 (/ 1 y)))>
#<alt (- (* x (- (* -18 (/ x (pow y 3))) (* 6 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))>
#<alt (- (* x (- (* x (- (* -54 (/ x (pow y 4))) (* 18 (/ 1 (pow y 3))))) (* 6 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))>
#<alt (/ 2/3 x)>
#<alt (/ (+ 2/3 (* 2/9 (/ y x))) x)>
#<alt (/ (- (+ 2/3 (* 2/27 (/ (pow y 2) (pow x 2)))) (* -2/9 (/ y x))) x)>
#<alt (/ (- (+ 2/3 (* 2/81 (/ (pow y 3) (pow x 3)))) (+ (* -2/9 (/ y x)) (* -2/27 (/ (pow y 2) (pow x 2))))) x)>
#<alt (/ 2/3 x)>
#<alt (* -1 (/ (- (* -2/9 (/ y x)) 2/3) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 2/27 (/ (pow y 2) x)) (* -2/9 y)) x)) 2/3) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -2/81 (/ (pow y 3) x)) (* 2/27 (pow y 2))) x)) (* -2/9 y)) x)) 2/3) x))>
#<alt (/ 1 (+ x (* 1/2 x)))>
#<alt (+ (* 1/2 (/ y (pow (+ x (* 1/2 x)) 2))) (/ 1 (+ x (* 1/2 x))))>
#<alt (+ (* y (+ (* 1/4 (/ y (pow (+ x (* 1/2 x)) 3))) (* 1/2 (/ 1 (pow (+ x (* 1/2 x)) 2))))) (/ 1 (+ x (* 1/2 x))))>
#<alt (+ (* y (+ (* y (+ (* 1/8 (/ y (pow (+ x (* 1/2 x)) 4))) (* 1/4 (/ 1 (pow (+ x (* 1/2 x)) 3))))) (* 1/2 (/ 1 (pow (+ x (* 1/2 x)) 2))))) (/ 1 (+ x (* 1/2 x))))>
#<alt (/ -2 y)>
#<alt (/ (- (* -4 (/ (+ x (* 1/2 x)) y)) 2) y)>
#<alt (/ (- (* -8 (/ (pow (+ x (* 1/2 x)) 2) (pow y 2))) (+ 2 (* 4 (/ (+ x (* 1/2 x)) y)))) y)>
#<alt (/ (- (* -16 (/ (pow (+ x (* 1/2 x)) 3) (pow y 3))) (+ 2 (+ (* 4 (/ (+ x (* 1/2 x)) y)) (* 8 (/ (pow (+ x (* 1/2 x)) 2) (pow y 2)))))) y)>
#<alt (/ -2 y)>
#<alt (* -1 (/ (+ 2 (* 4 (/ (+ x (* 1/2 x)) y))) y))>
#<alt (* -1 (/ (+ 2 (* -1 (/ (- (* -8 (/ (pow (+ x (* 1/2 x)) 2) y)) (* 4 (+ x (* 1/2 x)))) y))) y))>
#<alt (* -1 (/ (+ 2 (* -1 (/ (- (* -1 (/ (- (* 16 (/ (pow (+ x (* 1/2 x)) 3) y)) (* -8 (pow (+ x (* 1/2 x)) 2))) y)) (* 4 (+ x (* 1/2 x)))) y))) y))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (+ x (* 1/2 x))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (* -1/2 y)>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt x>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (* -1 y)>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (- (+ 3/2 (/ y x)) (* 3/2 (/ y x))))>
#<alt (* x (- (+ 3/2 (+ (* -1/2 (/ (pow y 2) (pow x 2))) (/ y x))) (+ (* 3/2 (/ y x)) (/ (* y (- y (* 3/2 y))) (pow x 2)))))>
#<alt (* x (- (+ 3/2 (+ (* -1 (/ (* y (- (* -1/2 (pow y 2)) (* y (- y (* 3/2 y))))) (pow x 3))) (+ (* -1/2 (/ (pow y 2) (pow x 2))) (/ y x)))) (+ (* 3/2 (/ y x)) (/ (* y (- y (* 3/2 y))) (pow x 2)))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* -1 (/ (- y (* 3/2 y)) x)) 3/2)))>
#<alt (* -1 (* x (- (* -1 (/ (- (+ y (* -1 (/ (- (* 1/2 (pow y 2)) (* -1 (* y (- y (* 3/2 y))))) x))) (* 3/2 y)) x)) 3/2)))>
#<alt (* -1 (* x (- (* -1 (/ (- (+ y (* -1 (/ (- (+ (* -1 (/ (* y (- (* 1/2 (pow y 2)) (* -1 (* y (- y (* 3/2 y)))))) x)) (* 1/2 (pow y 2))) (* -1 (* y (- y (* 3/2 y))))) x))) (* 3/2 y)) x)) 3/2)))>
#<alt (/ (- (* 1/4 (pow x 2)) (pow x 2)) (- (* 1/2 x) x))>
#<alt (- (+ (* 1/4 (/ (pow x 2) (- (* 1/2 x) x))) (* y (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (- (* 1/4 (pow x 2)) (pow x 2)) (pow (- (* 1/2 x) x) 2)))))) (/ (pow x 2) (- (* 1/2 x) x)))>
#<alt (- (+ (* 1/4 (/ (pow x 2) (- (* 1/2 x) x))) (* y (- (+ (* -1/2 (/ x (- (* 1/2 x) x))) (* y (- (* 1/4 (/ 1 (- (* 1/2 x) x))) (* -1/2 (/ (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (- (* 1/4 (pow x 2)) (pow x 2)) (pow (- (* 1/2 x) x) 2)))) (- (* 1/2 x) x)))))) (* -1/2 (/ (- (* 1/4 (pow x 2)) (pow x 2)) (pow (- (* 1/2 x) x) 2)))))) (/ (pow x 2) (- (* 1/2 x) x)))>
#<alt (- (+ (* 1/4 (/ (pow x 2) (- (* 1/2 x) x))) (* y (- (+ (* -1/2 (/ x (- (* 1/2 x) x))) (* y (- (+ (* 1/4 (/ 1 (- (* 1/2 x) x))) (* 1/2 (/ (* y (- (* 1/4 (/ 1 (- (* 1/2 x) x))) (* -1/2 (/ (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (- (* 1/4 (pow x 2)) (pow x 2)) (pow (- (* 1/2 x) x) 2)))) (- (* 1/2 x) x))))) (- (* 1/2 x) x)))) (* -1/2 (/ (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (- (* 1/4 (pow x 2)) (pow x 2)) (pow (- (* 1/2 x) x) 2)))) (- (* 1/2 x) x)))))) (* -1/2 (/ (- (* 1/4 (pow x 2)) (pow x 2)) (pow (- (* 1/2 x) x) 2)))))) (/ (pow x 2) (- (* 1/2 x) x)))>
#<alt (* -1/2 y)>
#<alt (* y (- (* 2 (/ x y)) (+ 1/2 (* 1/2 (/ x y)))))>
#<alt (* y (- (+ (* -2 (/ (- (* 1/4 (pow x 2)) (pow x 2)) (pow y 2))) (* 2 (/ x y))) (+ 1/2 (+ (* -2 (/ (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))) (pow y 2))) (* 1/2 (/ x y))))))>
#<alt (* y (- (+ (* -2 (/ (- (* 1/4 (pow x 2)) (pow x 2)) (pow y 2))) (+ (* 2 (/ x y)) (* 2 (/ (* (- (* -2 (- (* 1/4 (pow x 2)) (pow x 2))) (* -2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))))) (- (* 1/2 x) x)) (pow y 3))))) (+ 1/2 (+ (* -2 (/ (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))) (pow y 2))) (* 1/2 (/ x y))))))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 2 x) (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (+ (* -1 (/ (- (* 2 (- (* 1/4 (pow x 2)) (pow x 2))) (* 2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))))) y)) (* 2 x)) (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (- (* 1/4 (pow x 2)) (pow x 2))) (* 2 (/ (* (- (* 1/2 x) x) (- (* 2 (- (* 1/4 (pow x 2)) (pow x 2))) (* 2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x)))))) y))) (* 2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))))) y)) (* 2 x)) (* 1/2 x)) y)))))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 x) (* -1/2 y))>
#<alt (+ (* -1/2 x) (* -1/2 y))>
#<alt (+ (* -1/2 x) (* -1/2 y))>
#<alt (* -1/2 x)>
#<alt (* x (- (* -1/2 (/ y x)) 1/2))>
#<alt (* x (- (* -1/2 (/ y x)) 1/2))>
#<alt (* x (- (* -1/2 (/ y x)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ y x)))))>
#<alt (- (* 1/2 x) x)>
#<alt (- (+ (* -1/2 y) (* 1/2 x)) x)>
#<alt (- (+ (* -1/2 y) (* 1/2 x)) x)>
#<alt (- (+ (* -1/2 y) (* 1/2 x)) x)>
#<alt (* -1/2 y)>
#<alt (* y (- (* 1/2 (/ x y)) (+ 1/2 (/ x y))))>
#<alt (* y (- (* 1/2 (/ x y)) (+ 1/2 (/ x y))))>
#<alt (* y (- (* 1/2 (/ x y)) (+ 1/2 (/ x y))))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 1/2 x) x) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 1/2 x) x) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 1/2 x) x) y)))))>
#<alt (* 1/4 (pow y 2))>
#<alt (+ (* -1/2 (* x y)) (* 1/4 (pow y 2)))>
#<alt (+ (* 1/4 (pow y 2)) (* x (+ (* -3/4 x) (* -1/2 y))))>
#<alt (+ (* 1/4 (pow y 2)) (* x (+ (* -3/4 x) (* -1/2 y))))>
#<alt (* -3/4 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ y x)) 3/4))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2)))) 3/4))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2)))) 3/4))>
#<alt (* -3/4 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ y x)) 3/4))>
#<alt (* (pow x 2) (- (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x)) 3/4))>
#<alt (* (pow x 2) (- (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x)) 3/4))>
#<alt (- (* 1/4 (pow x 2)) (pow x 2))>
#<alt (- (+ (* -1/2 (* x y)) (* 1/4 (pow x 2))) (pow x 2))>
#<alt (- (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y)))) (pow x 2))>
#<alt (- (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y)))) (pow x 2))>
#<alt (* 1/4 (pow y 2))>
#<alt (* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))>
#<alt (* (pow y 2) (- (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))) (/ (pow x 2) (pow y 2))))>
#<alt (* (pow y 2) (- (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))) (/ (pow x 2) (pow y 2))))>
#<alt (* 1/4 (pow y 2))>
#<alt (* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))>
#<alt (* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (- (* 1/4 (pow x 2)) (pow x 2)) y)) (* 1/2 x)) y))))>
#<alt (* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (- (* 1/4 (pow x 2)) (pow x 2)) y)) (* 1/2 x)) y))))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (+ x (* 1/2 x))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (* -1/2 y)>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (pow y 2)>
#<alt (+ (* x y) (pow y 2))>
#<alt (+ (* x (+ x y)) (pow y 2))>
#<alt (+ (* x (+ x y)) (pow y 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y x)))>
#<alt (* (pow x 2) (+ 1 (+ (/ y x) (/ (pow y 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ y x) (/ (pow y 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y x)))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 y) (* -1 (/ (pow y 2) x))) x))))>
#<alt (pow x 2)>
#<alt (+ (* x y) (pow x 2))>
#<alt (+ (* y (+ x y)) (pow x 2))>
#<alt (+ (* y (+ x y)) (pow x 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (/ x y) (/ (pow x 2) (pow y 2)))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) y))) y))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 x) (* -1 (/ (pow x 2) y))) y))))>
#<alt (* x y)>
#<alt (* y (+ x y))>
#<alt (* y (+ x y))>
#<alt (* y (+ x y))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (pow y 2)>
#<alt (+ (* x y) (pow y 2))>
#<alt (+ (* x y) (pow y 2))>
#<alt (+ (* x y) (pow y 2))>
#<alt (* x y)>
#<alt (* x (+ y (/ (pow y 2) x)))>
#<alt (* x (+ y (/ (pow y 2) x)))>
#<alt (* x (+ y (/ (pow y 2) x)))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ (pow y 2) x)))))>
#<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 (* 1/4 (pow y 2))>
#<alt (+ (* -1/2 (* x y)) (* 1/4 (pow y 2)))>
#<alt (+ (* 1/4 (pow y 2)) (* x (+ (* -1/2 y) (* 1/4 x))))>
#<alt (+ (* 1/4 (pow y 2)) (* x (+ (* -1/2 y) (* 1/4 x))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (+ 1/4 (* -1/2 (/ y x))))>
#<alt (* (pow x 2) (+ 1/4 (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/4 (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2))))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (+ 1/4 (* -1/2 (/ y x))))>
#<alt (* (pow x 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x))))>
#<alt (* (pow x 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x))))>
#<alt (* 1/4 (pow x 2))>
#<alt (+ (* -1/2 (* x y)) (* 1/4 (pow x 2)))>
#<alt (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y))))>
#<alt (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y))))>
#<alt (* 1/4 (pow y 2))>
#<alt (* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))>
#<alt (* (pow y 2) (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))>
#<alt (* (pow y 2) (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))>
#<alt (* 1/4 (pow y 2))>
#<alt (* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))>
#<alt (* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow x 2) y)) (* 1/2 x)) y))))>
#<alt (* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow x 2) y)) (* 1/2 x)) y))))>
#<alt (/ -1/2 y)>
#<alt (- (/ x (pow y 2)) (* 1/2 (/ 1 y)))>
#<alt (- (* x (+ (* -1/2 (/ x (pow y 3))) (/ 1 (pow y 2)))) (* 1/2 (/ 1 y)))>
#<alt (- (* x (+ (* x (- (* -1/2 (/ x (pow y 4))) (* 1/2 (/ 1 (pow y 3))))) (/ 1 (pow y 2)))) (* 1/2 (/ 1 y)))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/2 (/ (- (* -1 y) y) x))) x)>
#<alt (/ (+ 1/2 (+ (* -1/2 (/ (+ (* y (- (* -1 y) y)) (pow y 2)) (pow x 2))) (* 1/2 (/ (- (* -1 y) y) x)))) x)>
#<alt (/ (+ 1/2 (+ (* -1/2 (/ (+ (* -1 (* y (+ (* y (- (* -1 y) y)) (pow y 2)))) (* (pow y 2) (- (* -1 y) y))) (pow x 3))) (+ (* -1/2 (/ (+ (* y (- (* -1 y) y)) (pow y 2)) (pow x 2))) (* 1/2 (/ (- (* -1 y) y) x))))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/2 (/ (- y (* -1 y)) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1/2 (- y (* -1 y))) (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)) x))) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y)))) x)) (* 1/2 (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)))) x)) (* -1/2 (- y (* -1 y)))) x)) 1/2) x))>
#<alt (/ 1/2 x)>
#<alt (+ (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 x)))>
#<alt (+ (* y (- (* 1/2 (/ y (pow x 3))) (/ 1 (pow x 2)))) (* 1/2 (/ 1 x)))>
#<alt (+ (* y (- (* y (+ (* 1/2 (/ y (pow x 4))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 (pow x 2)))) (* 1/2 (/ 1 x)))>
#<alt (/ -1/2 y)>
#<alt (/ (- (* 1/2 (/ (- x (* -1 x)) y)) 1/2) y)>
#<alt (/ (- (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (* x (- x (* -1 x)))) (pow y 2))) (* 1/2 (/ (- x (* -1 x)) y))) 1/2) y)>
#<alt (/ (- (+ (* -1/2 (/ (+ (* -1 (* x (+ (* -1 (pow x 2)) (* x (- x (* -1 x)))))) (* (pow x 2) (- x (* -1 x)))) (pow y 3))) (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (* x (- x (* -1 x)))) (pow y 2))) (* 1/2 (/ (- x (* -1 x)) y)))) 1/2) y)>
#<alt (/ -1/2 y)>
#<alt (* -1 (/ (+ 1/2 (* -1/2 (/ (- x (* -1 x)) y))) y))>
#<alt (* -1 (/ (+ 1/2 (* -1 (/ (+ (* 1/2 (- x (* -1 x))) (* 1/2 (/ (+ (* -1 (* x (- x (* -1 x)))) (pow x 2)) y))) y))) y))>
#<alt (* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (* x (- x (* -1 x)))) (pow x 2))) (* 1/2 (/ (+ (* x (+ (* -1 (* x (- x (* -1 x)))) (pow x 2))) (* (pow x 2) (- x (* -1 x)))) y))) y)) (* 1/2 (- x (* -1 x)))) y))) y))>
#<alt (* 2 (pow y 2))>
#<alt (+ (* 2 (* x y)) (* 2 (pow y 2)))>
#<alt (+ (* 2 (pow y 2)) (* x (+ (* 2 x) (* 2 y))))>
#<alt (+ (* 2 (pow y 2)) (* x (+ (* 2 x) (* 2 y))))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 2 (+ (* 2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))))>
#<alt (* (pow x 2) (+ 2 (+ (* 2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 2 (* -1 (/ (+ (* -2 y) (* -2 (/ (pow y 2) x))) x))))>
#<alt (* (pow x 2) (+ 2 (* -1 (/ (+ (* -2 y) (* -2 (/ (pow y 2) x))) x))))>
#<alt (* 2 (pow x 2))>
#<alt (+ (* 2 (* x y)) (* 2 (pow x 2)))>
#<alt (+ (* 2 (pow x 2)) (* y (+ (* 2 x) (* 2 y))))>
#<alt (+ (* 2 (pow x 2)) (* 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)) (* 2 (/ (pow x 2) (pow y 2))))))>
#<alt (* (pow y 2) (+ 2 (+ (* 2 (/ x y)) (* 2 (/ (pow x 2) (pow y 2))))))>
#<alt (* 2 (pow y 2))>
#<alt (* (pow y 2) (+ 2 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 2 (* -1 (/ (+ (* -2 x) (* -2 (/ (pow x 2) y))) y))))>
#<alt (* (pow y 2) (+ 2 (* -1 (/ (+ (* -2 x) (* -2 (/ (pow x 2) y))) y))))>

Calls

99 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(* y (+ x y))
2.0ms	y	@	0	(/ (- (* (- x y) (* 1/4 (- x y))) (* x x)) (- (* (- x y) 1/2) x))
2.0ms	x	@	-inf	(* 2 (+ (* x x) (* y (+ x y))))
1.0ms	y	@	inf	(/ (- x y) (* 2 (+ (* x x) (* y (+ x y)))))
1.0ms	x	@	0	(/ (- (* (- x y) (* 1/4 (- x y))) (* x x)) (- (* (- x y) 1/2) x))

rewrite570.0ms (6.8%)

Memory

17.4MiB live, 992.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 498×	`accelerator-lowering-fma.f32`
5 498×	`accelerator-lowering-fma.f64`
3 982×	`/-lowering-/.f32`
3 982×	`/-lowering-/.f64`
3 890×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	129
1	211	125
2	2122	125
0	8550	114

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 1 075

Calls

Call 1

Inputs
(+ (* x 1/2) (+ (* y -1/2) x))
(+ (* y -1/2) x)
(+ (* -1/2 y) 0)
(/ 1 (/ 1 (+ (* (- x y) 1/2) x)))
(/ 1 (+ (* (- x y) 1/2) x))
(+ (* (- x y) 1/2) x)
(- x y)
(/ (- (* (- x y) (* 1/4 (- x y))) (* x x)) (- (* (- x y) 1/2) x))
(- (* (- x y) 1/2) x)
(- (* (- x y) (* 1/4 (- x y))) (* x x))
(+ (* (+ (* x x) (* y (+ x y))) (/ (- x y) (* 2 (+ (* x x) (* y (+ x y)))))) x)
(+ (* x x) (* y (+ x y)))
(* y (+ x y))
(+ x y)
(* (- x y) (* 1/4 (- x y)))
(/ (- x y) (* 2 (+ (* x x) (* y (+ x y)))))
(* 2 (+ (* x x) (* y (+ x y))))

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

simplify435.0ms (5.2%)

Memory

-23.5MiB live, 785.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8 754×	`accelerator-lowering-fma.f32`
8 754×	`accelerator-lowering-fma.f64`
5 202×	`-lowering-.f32`
5 202×	`-lowering-.f64`
3 080×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	661	4353
1	2086	3988
2	6233	3897
0	8406	3587

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 396

Calls

Call 1

Inputs
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(+ (* -1/2 y) (* 3/2 x))
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(+ (* -1/2 y) (* 3/2 x))
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x
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(* (pow x 2) (+ 1/4 (* -1/2 (/ y x))))
(* (pow x 2) (+ 1/4 (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2))))))
(* (pow x 2) (+ 1/4 (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2))))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -1/2 (/ y x))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x))))
(* 1/4 (pow x 2))
(+ (* -1/2 (* x y)) (* 1/4 (pow x 2)))
(+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y))))
(+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y))))
(* 1/4 (pow y 2))
(* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))
(* (pow y 2) (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))
(* (pow y 2) (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))
(* 1/4 (pow y 2))
(* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))
(* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow x 2) y)) (* 1/2 x)) y))))
(* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow x 2) y)) (* 1/2 x)) y))))
(/ -1/2 y)
(- (/ x (pow y 2)) (* 1/2 (/ 1 y)))
(- (* x (+ (* -1/2 (/ x (pow y 3))) (/ 1 (pow y 2)))) (* 1/2 (/ 1 y)))
(- (* x (+ (* x (- (* -1/2 (/ x (pow y 4))) (* 1/2 (/ 1 (pow y 3))))) (/ 1 (pow y 2)))) (* 1/2 (/ 1 y)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/2 (/ (- (* -1 y) y) x))) x)
(/ (+ 1/2 (+ (* -1/2 (/ (+ (* y (- (* -1 y) y)) (pow y 2)) (pow x 2))) (* 1/2 (/ (- (* -1 y) y) x)))) x)
(/ (+ 1/2 (+ (* -1/2 (/ (+ (* -1 (* y (+ (* y (- (* -1 y) y)) (pow y 2)))) (* (pow y 2) (- (* -1 y) y))) (pow x 3))) (+ (* -1/2 (/ (+ (* y (- (* -1 y) y)) (pow y 2)) (pow x 2))) (* 1/2 (/ (- (* -1 y) y) x))))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/2 (/ (- y (* -1 y)) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ (* -1/2 (- y (* -1 y))) (* -1/2 (/ (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)) x))) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* y (+ (* -1 (* y (- y (* -1 y)))) (pow y 2))) (* (pow y 2) (- y (* -1 y)))) x)) (* 1/2 (+ (* -1 (* y (- y (* -1 y)))) (pow y 2)))) x)) (* -1/2 (- y (* -1 y)))) x)) 1/2) x))
(/ 1/2 x)
(+ (* -1 (/ y (pow x 2))) (* 1/2 (/ 1 x)))
(+ (* y (- (* 1/2 (/ y (pow x 3))) (/ 1 (pow x 2)))) (* 1/2 (/ 1 x)))
(+ (* y (- (* y (+ (* 1/2 (/ y (pow x 4))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 (pow x 2)))) (* 1/2 (/ 1 x)))
(/ -1/2 y)
(/ (- (* 1/2 (/ (- x (* -1 x)) y)) 1/2) y)
(/ (- (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (* x (- x (* -1 x)))) (pow y 2))) (* 1/2 (/ (- x (* -1 x)) y))) 1/2) y)
(/ (- (+ (* -1/2 (/ (+ (* -1 (* x (+ (* -1 (pow x 2)) (* x (- x (* -1 x)))))) (* (pow x 2) (- x (* -1 x)))) (pow y 3))) (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (* x (- x (* -1 x)))) (pow y 2))) (* 1/2 (/ (- x (* -1 x)) y)))) 1/2) y)
(/ -1/2 y)
(* -1 (/ (+ 1/2 (* -1/2 (/ (- x (* -1 x)) y))) y))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* 1/2 (- x (* -1 x))) (* 1/2 (/ (+ (* -1 (* x (- x (* -1 x)))) (pow x 2)) y))) y))) y))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (* x (- x (* -1 x)))) (pow x 2))) (* 1/2 (/ (+ (* x (+ (* -1 (* x (- x (* -1 x)))) (pow x 2))) (* (pow x 2) (- x (* -1 x)))) y))) y)) (* 1/2 (- x (* -1 x)))) y))) y))
(* 2 (pow y 2))
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(+ (* 2 (pow y 2)) (* x (+ (* 2 x) (* 2 y))))
(+ (* 2 (pow y 2)) (* x (+ (* 2 x) (* 2 y))))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(* (pow x 2) (+ 2 (+ (* 2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))))
(* (pow x 2) (+ 2 (+ (* 2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(* (pow x 2) (+ 2 (* -1 (/ (+ (* -2 y) (* -2 (/ (pow y 2) x))) x))))
(* (pow x 2) (+ 2 (* -1 (/ (+ (* -2 y) (* -2 (/ (pow y 2) x))) x))))
(* 2 (pow x 2))
(+ (* 2 (* x y)) (* 2 (pow x 2)))
(+ (* 2 (pow x 2)) (* y (+ (* 2 x) (* 2 y))))
(+ (* 2 (pow x 2)) (* y (+ (* 2 x) (* 2 y))))
(* 2 (pow y 2))
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(* (pow y 2) (+ 2 (+ (* 2 (/ x y)) (* 2 (/ (pow x 2) (pow y 2))))))
(* (pow y 2) (+ 2 (+ (* 2 (/ x y)) (* 2 (/ (pow x 2) (pow y 2))))))
(* 2 (pow y 2))
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(* (pow y 2) (+ 2 (* -1 (/ (+ (* -2 x) (* -2 (/ (pow x 2) y))) y))))
(* (pow y 2) (+ 2 (* -1 (/ (+ (* -2 x) (* -2 (/ (pow x 2) y))) y))))

Outputs
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(* 3/2 x)
(*.f64 #s(literal 3/2 binary64) x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* x (+ 3/2 (* -1/2 (/ y x))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* x (+ 3/2 (* -1/2 (/ y x))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* 3/2 x)
(*.f64 #s(literal 3/2 binary64) x)
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) #s(literal -3/2 binary64))))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) #s(literal -3/2 binary64))))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) #s(literal -3/2 binary64))))
(+ x (* 1/2 x))
(*.f64 #s(literal 3/2 binary64) x)
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
x
(+ x (* -1/2 y))
(fma.f64 #s(literal -1/2 binary64) y x)
(+ x (* -1/2 y))
(fma.f64 #s(literal -1/2 binary64) y x)
(+ x (* -1/2 y))
(fma.f64 #s(literal -1/2 binary64) y x)
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* y (- (/ x y) 1/2))
(*.f64 y (+.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* y (- (/ x y) 1/2))
(*.f64 y (+.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* y (- (/ x y) 1/2))
(*.f64 y (+.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* -1 (* y (+ 1/2 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* -1 (* y (+ 1/2 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* -1 (* y (+ 1/2 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -1/2 binary64) (/.f64 x y)))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(+ x (* -1/2 y))
(fma.f64 #s(literal -1/2 binary64) y x)
(+ x (* -1/2 y))
(fma.f64 #s(literal -1/2 binary64) y x)
(+ x (* -1/2 y))
(fma.f64 #s(literal -1/2 binary64) y x)
x
(* x (+ 1 (* -1/2 (/ y x))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 1 binary64)))
(* x (+ 1 (* -1/2 (/ y x))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 1 binary64)))
(* x (+ 1 (* -1/2 (/ y x))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 1 binary64)))
x
(* -1 (* x (- (* 1/2 (/ y x)) 1)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 1 binary64)))
(* -1 (* x (- (* 1/2 (/ y x)) 1)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 1 binary64)))
(* -1 (* x (- (* 1/2 (/ y x)) 1)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 1 binary64)))
(* -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)
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(+ (* -1/2 y) (* 3/2 x))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(* 3/2 x)
(*.f64 #s(literal 3/2 binary64) x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* x (+ 3/2 (* -1/2 (/ y x))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* x (+ 3/2 (* -1/2 (/ y x))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) #s(literal 3/2 binary64)))
(* 3/2 x)
(*.f64 #s(literal 3/2 binary64) x)
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) #s(literal -3/2 binary64))))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) #s(literal -3/2 binary64))))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 y (/.f64 #s(literal 1/2 binary64) x) #s(literal -3/2 binary64))))
(+ x (* 1/2 x))
(*.f64 #s(literal 3/2 binary64) x)
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
(/ -2 y)
(/.f64 #s(literal -2 binary64) y)
(- (* -6 (/ x (pow y 2))) (* 2 (/ 1 y)))
(/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 x #s(literal -6 binary64)) y)) y)
(- (* x (- (* -18 (/ x (pow y 3))) (* 6 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))
(fma.f64 x (fma.f64 #s(literal -18 binary64) (/.f64 x (.f64 y (.f64 y y))) (/.f64 #s(literal -6 binary64) (*.f64 y y))) (/.f64 #s(literal -2 binary64) y))
(- (* x (- (* x (- (* -54 (/ x (pow y 4))) (* 18 (/ 1 (pow y 3))))) (* 6 (/ 1 (pow y 2))))) (* 2 (/ 1 y)))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -54 binary64) (/.f64 x (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal -18 binary64) (.f64 y (.f64 y y)))) (/.f64 #s(literal -6 binary64) (*.f64 y y))) (/.f64 #s(literal -2 binary64) y))
(/ 2/3 x)
(/.f64 #s(literal 2/3 binary64) x)
(/ (+ 2/3 (* 2/9 (/ y x))) x)
(/.f64 (fma.f64 (/.f64 y x) #s(literal 2/9 binary64) #s(literal 2/3 binary64)) x)
(/ (- (+ 2/3 (* 2/27 (/ (pow y 2) (pow x 2)))) (* -2/9 (/ y x))) x)
(/.f64 (+.f64 #s(literal 2/3 binary64) (/.f64 (fma.f64 y #s(literal 2/9 binary64) (/.f64 (.f64 (.f64 y y) #s(literal 2/27 binary64)) x)) x)) x)
(/ (- (+ 2/3 (* 2/81 (/ (pow y 3) (pow x 3)))) (+ (* -2/9 (/ y x)) (* -2/27 (/ (pow y 2) (pow x 2))))) x)
(/.f64 (+.f64 (fma.f64 #s(literal 2/81 binary64) (/.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))) #s(literal 2/3 binary64)) (/.f64 (fma.f64 y #s(literal 2/9 binary64) (/.f64 (.f64 (.f64 y y) #s(literal 2/27 binary64)) x)) x)) x)
(/ 2/3 x)
(/.f64 #s(literal 2/3 binary64) x)
(* -1 (/ (- (* -2/9 (/ y x)) 2/3) x))
(/.f64 (fma.f64 (/.f64 y x) #s(literal 2/9 binary64) #s(literal 2/3 binary64)) x)
(* -1 (/ (- (* -1 (/ (- (* 2/27 (/ (pow y 2) x)) (* -2/9 y)) x)) 2/3) x))
(/.f64 (-.f64 #s(literal -2/3 binary64) (/.f64 (fma.f64 y #s(literal 2/9 binary64) (/.f64 (.f64 (.f64 y y) #s(literal 2/27 binary64)) x)) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -2/81 (/ (pow y 3) x)) (* 2/27 (pow y 2))) x)) (* -2/9 y)) x)) 2/3) x))
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (fma.f64 (.f64 y y) #s(literal -2/27 binary64) (.f64 #s(literal -2/81 binary64) (/.f64 (.f64 y (.f64 y y)) x))) x) (*.f64 y #s(literal -2/9 binary64))) x) #s(literal -2/3 binary64)) (-.f64 #s(literal 0 binary64) x))
(/ 1 (+ x (* 1/2 x)))
(/.f64 #s(literal 2/3 binary64) x)
(+ (* 1/2 (/ y (pow (+ x (* 1/2 x)) 2))) (/ 1 (+ x (* 1/2 x))))
(fma.f64 y (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 9/4 binary64))) (/.f64 #s(literal 2/3 binary64) x))
(+ (* y (+ (* 1/4 (/ y (pow (+ x (* 1/2 x)) 3))) (* 1/2 (/ 1 (pow (+ x (* 1/2 x)) 2))))) (/ 1 (+ x (* 1/2 x))))
(fma.f64 y (fma.f64 y (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 27/8 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 9/4 binary64)))) (/.f64 #s(literal 2/3 binary64) x))
(+ (* y (+ (* y (+ (* 1/8 (/ y (pow (+ x (* 1/2 x)) 4))) (* 1/4 (/ 1 (pow (+ x (* 1/2 x)) 3))))) (* 1/2 (/ 1 (pow (+ x (* 1/2 x)) 2))))) (/ 1 (+ x (* 1/2 x))))
(fma.f64 y (fma.f64 y (fma.f64 #s(literal 1/8 binary64) (/.f64 y (pow.f64 (.f64 #s(literal 3/2 binary64) x) #s(literal 4 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 27/8 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 9/4 binary64)))) (/.f64 #s(literal 2/3 binary64) x))
(/ -2 y)
(/.f64 #s(literal -2 binary64) y)
(/ (- (* -4 (/ (+ x (* 1/2 x)) y)) 2) y)
(/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 x #s(literal -6 binary64)) y)) y)
(/ (- (* -8 (/ (pow (+ x (* 1/2 x)) 2) (pow y 2))) (+ 2 (* 4 (/ (+ x (* 1/2 x)) y)))) y)
(/.f64 (+.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 9/4 binary64)) (/.f64 #s(literal -8 binary64) y) (*.f64 x #s(literal -6 binary64))) y) #s(literal -2 binary64)) y)
(/ (- (* -16 (/ (pow (+ x (* 1/2 x)) 3) (pow y 3))) (+ 2 (+ (* 4 (/ (+ x (* 1/2 x)) y)) (* 8 (/ (pow (+ x (* 1/2 x)) 2) (pow y 2)))))) y)
(/.f64 (fma.f64 #s(literal -16 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 27/8 binary64)) (.f64 y (.f64 y y))) (+.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 9/4 binary64)) (/.f64 #s(literal -8 binary64) y) (.f64 x #s(literal -6 binary64))) y) #s(literal -2 binary64))) y)
(/ -2 y)
(/.f64 #s(literal -2 binary64) y)
(* -1 (/ (+ 2 (* 4 (/ (+ x (* 1/2 x)) y))) y))
(/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 x #s(literal -6 binary64)) y)) y)
(* -1 (/ (+ 2 (* -1 (/ (- (* -8 (/ (pow (+ x (* 1/2 x)) 2) y)) (* 4 (+ x (* 1/2 x)))) y))) y))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 9/4 binary64)) (/.f64 #s(literal -8 binary64) y) (*.f64 x #s(literal -6 binary64))) y)) (-.f64 #s(literal 0 binary64) y))
(* -1 (/ (+ 2 (* -1 (/ (- (* -1 (/ (- (* 16 (/ (pow (+ x (* 1/2 x)) 3) y)) (* -8 (pow (+ x (* 1/2 x)) 2))) y)) (* 4 (+ x (* 1/2 x)))) y))) y))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (-.f64 (.f64 x #s(literal -6 binary64)) (/.f64 (fma.f64 #s(literal 16 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 27/8 binary64)) y) (.f64 (.f64 (*.f64 x x) #s(literal 9/4 binary64)) #s(literal 8 binary64))) y)) y)) (-.f64 #s(literal 0 binary64) y))
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(/ (- (* 1/2 (/ (- x (* -1 x)) y)) 1/2) y)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 x x) y) #s(literal -1/2 binary64)) y)
(/ (- (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (* x (- x (* -1 x)))) (pow y 2))) (* 1/2 (/ (- x (* -1 x)) y))) 1/2) y)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 x (-.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 x x))) (.f64 y y)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 x x) y) #s(literal -1/2 binary64))) y)
(/ (- (+ (* -1/2 (/ (+ (* -1 (* x (+ (* -1 (pow x 2)) (* x (- x (* -1 x)))))) (* (pow x 2) (- x (* -1 x)))) (pow y 3))) (+ (* -1/2 (/ (+ (* -1 (pow x 2)) (* x (- x (* -1 x)))) (pow y 2))) (* 1/2 (/ (- x (* -1 x)) y)))) 1/2) y)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (fma.f64 x (fma.f64 x x (.f64 x (.f64 x #s(literal -2 binary64)))) (.f64 x (.f64 x (+.f64 x x)))) (.f64 y (.f64 y y))) (/.f64 (fma.f64 x (-.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 x x))) (.f64 y y))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 x x) y) #s(literal -1/2 binary64))) y)
(/ -1/2 y)
(/.f64 #s(literal -1/2 binary64) y)
(* -1 (/ (+ 1/2 (* -1/2 (/ (- x (* -1 x)) y))) y))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 x x) y) #s(literal 1/2 binary64))) y)
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* 1/2 (- x (* -1 x))) (* 1/2 (/ (+ (* -1 (* x (- x (* -1 x)))) (pow x 2)) y))) y))) y))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 x #s(literal 2 binary64) (/.f64 (fma.f64 x x (.f64 x (.f64 x #s(literal -2 binary64)))) y)) y) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) y))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (* x (- x (* -1 x)))) (pow x 2))) (* 1/2 (/ (+ (* x (+ (* -1 (* x (- x (* -1 x)))) (pow x 2))) (* (pow x 2) (- x (* -1 x)))) y))) y)) (* 1/2 (- x (* -1 x)))) y))) y))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x (fma.f64 x x (.f64 x (.f64 x #s(literal -2 binary64)))) (.f64 x (.f64 x (+.f64 x x)))) y) (.f64 #s(literal -1/2 binary64) (fma.f64 x x (.f64 x (.f64 x #s(literal -2 binary64)))))) y)) y)) (-.f64 #s(literal 0 binary64) y))
(* 2 (pow y 2))
(*.f64 y (+.f64 y y))
(+ (* 2 (* x y)) (* 2 (pow y 2)))
(*.f64 (+.f64 y y) (+.f64 y x))
(+ (* 2 (pow y 2)) (* x (+ (* 2 x) (* 2 y))))
(fma.f64 y (+.f64 y y) (*.f64 (+.f64 x x) (+.f64 y x)))
(+ (* 2 (pow y 2)) (* x (+ (* 2 x) (* 2 y))))
(fma.f64 y (+.f64 y y) (*.f64 (+.f64 x x) (+.f64 y x)))
(* 2 (pow x 2))
(*.f64 x (+.f64 x x))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(.f64 (.f64 x x) (fma.f64 y (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)))
(* (pow x 2) (+ 2 (+ (* 2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 2 binary64) (fma.f64 y (/.f64 y (*.f64 x x)) (/.f64 y x)) #s(literal 2 binary64)))
(* (pow x 2) (+ 2 (+ (* 2 (/ y x)) (* 2 (/ (pow y 2) (pow x 2))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 2 binary64) (fma.f64 y (/.f64 y (*.f64 x x)) (/.f64 y x)) #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (+.f64 x x))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(.f64 (.f64 x x) (fma.f64 y (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)))
(* (pow x 2) (+ 2 (* -1 (/ (+ (* -2 y) (* -2 (/ (pow y 2) x))) x))))
(.f64 (.f64 x x) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 y (/.f64 y x) y) x) #s(literal 2 binary64)))
(* (pow x 2) (+ 2 (* -1 (/ (+ (* -2 y) (* -2 (/ (pow y 2) x))) x))))
(.f64 (.f64 x x) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 y (/.f64 y x) y) x) #s(literal 2 binary64)))
(* 2 (pow x 2))
(*.f64 x (+.f64 x x))
(+ (* 2 (* x y)) (* 2 (pow x 2)))
(*.f64 (+.f64 x x) (+.f64 y x))
(+ (* 2 (pow x 2)) (* y (+ (* 2 x) (* 2 y))))
(fma.f64 y (+.f64 y y) (*.f64 (+.f64 x x) (+.f64 y x)))
(+ (* 2 (pow x 2)) (* y (+ (* 2 x) (* 2 y))))
(fma.f64 y (+.f64 y y) (*.f64 (+.f64 x x) (+.f64 y x)))
(* 2 (pow y 2))
(*.f64 y (+.f64 y y))
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(.f64 y (.f64 y (fma.f64 x (/.f64 #s(literal 2 binary64) y) #s(literal 2 binary64))))
(* (pow y 2) (+ 2 (+ (* 2 (/ x y)) (* 2 (/ (pow x 2) (pow y 2))))))
(.f64 (.f64 y y) (fma.f64 #s(literal 2 binary64) (fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 x y)) #s(literal 2 binary64)))
(* (pow y 2) (+ 2 (+ (* 2 (/ x y)) (* 2 (/ (pow x 2) (pow y 2))))))
(.f64 (.f64 y y) (fma.f64 #s(literal 2 binary64) (fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 x y)) #s(literal 2 binary64)))
(* 2 (pow y 2))
(*.f64 y (+.f64 y y))
(* (pow y 2) (+ 2 (* 2 (/ x y))))
(.f64 y (.f64 y (fma.f64 x (/.f64 #s(literal 2 binary64) y) #s(literal 2 binary64))))
(* (pow y 2) (+ 2 (* -1 (/ (+ (* -2 x) (* -2 (/ (pow x 2) y))) y))))
(.f64 (.f64 y y) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 x (/.f64 x y) x) y) #s(literal 2 binary64)))
(* (pow y 2) (+ 2 (* -1 (/ (+ (* -2 x) (* -2 (/ (pow x 2) y))) y))))
(.f64 (.f64 y y) (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 x (/.f64 x y) x) y) #s(literal 2 binary64)))

eval377.0ms (4.5%)

Memory: 27.7MiB live, 522.1MiB allocated
Compiler: Compiled 65 818 to 3 931 computations (94% saved)

prune400.0ms (4.8%)

Memory

-0.2MiB live, 262.6MiB allocated

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	1 848	8	1 856
Fresh	7	4	11
Picked	5	0	5
Done	0	0	0
Total	1 860	12	1 872

Accuracy

100.0%

Counts

1 872 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	19.5%	(fma.f64 (fma.f64 x (.f64 x x) (.f64 y (.f64 y y))) (/.f64 #s(literal 1/2 binary64) (fma.f64 x x (.f64 y (+.f64 x y)))) x)
▶	99.8%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
	51.4%	(fma.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 x y)) x))))
▶	99.8%	(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
▶	51.7%	(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) x) x (.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64)))) (-.f64 (*.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))
	53.8%	(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 x y) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
▶	55.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2/3 binary64) x))
	88.4%	(+.f64 x (/.f64 (-.f64 (.f64 x (/.f64 #s(literal 2 binary64) y)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) y))))
	99.7%	(+.f64 x (/.f64 (.f64 (+.f64 x y) (.f64 (-.f64 x y) (/.f64 #s(literal 1 binary64) (+.f64 x y)))) #s(literal 2 binary64)))
	88.6%	(*.f64 y (fma.f64 #s(literal 3/2 binary64) (/.f64 x y) #s(literal -1/2 binary64)))
	45.5%	(*.f64 y #s(literal -1/2 binary64))
▶	55.2%	(*.f64 #s(literal 3/2 binary64) x)

Compiler

Compiled 348 to 206 computations (40.8% saved)

simplify353.0ms (4.2%)

Memory

-24.0MiB live, 533.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) x)
✓	cost-diff	0	(fma.f64 (-.f64 #s(literal 0 binary64) x) x (.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))))
✓	cost-diff	192	(-.f64 (*.f64 (-.f64 x y) #s(literal 1/2 binary64)) x)
✓	cost-diff	192	(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) x) x (.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64)))) (-.f64 (*.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))
✓	cost-diff	0	(/.f64 #s(literal 2/3 binary64) x)
✓	cost-diff	1024	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2/3 binary64) x))
✓	cost-diff	0	(-.f64 y x)
✓	cost-diff	0	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
✓	cost-diff	-64	(*.f64 #s(literal 3/2 binary64) x)
✓	cost-diff	-64	(*.f64 #s(literal 3/2 binary64) x)
✓	cost-diff	192	(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))

Rules

10 646×	`accelerator-lowering-fma.f32`
10 646×	`accelerator-lowering-fma.f64`
3 204×	`-lowering-.f32`
3 204×	`-lowering-.f64`
1 956×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	113
1	47	113
2	97	111
3	291	111
4	783	107
5	2037	107
6	4651	107
0	8423	104

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* -1/2 y) (* 3/2 x))
-1/2
y
(* 3/2 x)
3/2
x
(* 3/2 x)
3/2
x
(+ (* (- y x) -1/2) x)
(- y x)
y
x
-1/2
(/ 1 (/ 2/3 x))
1
(/ 2/3 x)
2/3
x
(/ (+ (* (- 0 x) x) (* (- x y) (* (- x y) 1/4))) (- (* (- x y) 1/2) x))
(+ (* (- 0 x) x) (* (- x y) (* (- x y) 1/4)))
(- 0 x)
0
x
(* (- x y) (* (- x y) 1/4))
(- x y)
y
(* (- x y) 1/4)
1/4
(- (* (- x y) 1/2) x)
(* (- x y) 1/2)
1/2

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

localize150.0ms (1.8%)

Memory

16.9MiB live, 360.6MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64)))
✓	accuracy	100.0%	(-.f64 (*.f64 (-.f64 x y) #s(literal 1/2 binary64)) x)
✓	accuracy	82.4%	(fma.f64 (-.f64 #s(literal 0 binary64) x) x (.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))))
✓	accuracy	68.5%	(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) x) x (.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64)))) (-.f64 (*.f64 (-.f64 x y) #s(literal 1/2 binary64)) x))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2/3 binary64) x))
✓	accuracy	99.6%	(/.f64 #s(literal 2/3 binary64) x)
✓	accuracy	100.0%	(-.f64 y x)
✓	accuracy	100.0%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 3/2 binary64) x)
✓	accuracy	100.0%	(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 3/2 binary64) x)

Samples

73.0ms	89×	5	exit
38.0ms	166×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 116 to 28 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 17.0ms (22.9% of total)

const: 16.0ms (21.5% of total)

ival-div: 14.0ms (18.8% of total)

adjust: 13.0ms (17.5% of total)

ival-add: 7.0ms (9.4% of total)

ival-sub: 6.0ms (8.1% of total)

exact: 1.0ms (1.3% of total)

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

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

series9.0ms (0.1%)

Memory

21.4MiB live, 21.4MiB allocated

Counts

11 → 216

Calls

Call 1

Inputs
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (+ (* (- y x) -1/2) x)>
#<alt (- y x)>
#<alt (/ 1 (/ 2/3 x))>
#<alt (/ 2/3 x)>
#<alt (/ (+ (* (- 0 x) x) (* (- x y) (* (- x y) 1/4))) (- (* (- x y) 1/2) x))>
#<alt (- (* (- x y) 1/2) x)>
#<alt (+ (* (- 0 x) x) (* (- x y) (* (- x y) 1/4)))>
#<alt (- 0 x)>
#<alt (* (- x y) (* (- x y) 1/4))>

Outputs
#<alt (* 3/2 x)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* -1/2 y)>
#<alt (* y (- (* 3/2 (/ x y)) 1/2))>
#<alt (* y (- (* 3/2 (/ x y)) 1/2))>
#<alt (* y (- (* 3/2 (/ x y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -3/2 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -3/2 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -3/2 (/ x y)))))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (+ x (* 1/2 x))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (+ x (+ (* -1/2 y) (* 1/2 x)))>
#<alt (* -1/2 y)>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 x)>
#<alt (- y x)>
#<alt (- y x)>
#<alt (- y x)>
#<alt y>
#<alt (* y (+ 1 (* -1 (/ x y))))>
#<alt (* y (+ 1 (* -1 (/ x y))))>
#<alt (* y (+ 1 (* -1 (/ x y))))>
#<alt y>
#<alt (* -1 (* y (- (/ x y) 1)))>
#<alt (* -1 (* y (- (/ x y) 1)))>
#<alt (* -1 (* y (- (/ x y) 1)))>
#<alt y>
#<alt (+ y (* -1 x))>
#<alt (+ y (* -1 x))>
#<alt (+ y (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ y x) 1))>
#<alt (* x (- (/ y x) 1))>
#<alt (* x (- (/ y x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1 (/ y x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ y x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ y x)))))>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (* 3/2 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (/ 2/3 x)>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (- (+ 3/2 (/ y x)) (* 3/2 (/ y x))))>
#<alt (* x (- (+ 3/2 (+ (* -1/2 (/ (pow y 2) (pow x 2))) (/ y x))) (+ (* 3/2 (/ y x)) (/ (* y (- y (* 3/2 y))) (pow x 2)))))>
#<alt (* x (- (+ 3/2 (+ (* -1 (/ (* y (- (* -1/2 (pow y 2)) (* y (- y (* 3/2 y))))) (pow x 3))) (+ (* -1/2 (/ (pow y 2) (pow x 2))) (/ y x)))) (+ (* 3/2 (/ y x)) (/ (* y (- y (* 3/2 y))) (pow x 2)))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* -1 (/ (- y (* 3/2 y)) x)) 3/2)))>
#<alt (* -1 (* x (- (* -1 (/ (- (+ y (* -1 (/ (- (* 1/2 (pow y 2)) (* -1 (* y (- y (* 3/2 y))))) x))) (* 3/2 y)) x)) 3/2)))>
#<alt (* -1 (* x (- (* -1 (/ (- (+ y (* -1 (/ (- (+ (* -1 (/ (* y (- (* 1/2 (pow y 2)) (* -1 (* y (- y (* 3/2 y)))))) x)) (* 1/2 (pow y 2))) (* -1 (* y (- y (* 3/2 y))))) x))) (* 3/2 y)) x)) 3/2)))>
#<alt (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (- (* 1/2 x) x))>
#<alt (+ (* -1 (/ (pow x 2) (- (* 1/2 x) x))) (+ (* 1/4 (/ (pow x 2) (- (* 1/2 x) x))) (* y (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))))))>
#<alt (+ (* -1 (/ (pow x 2) (- (* 1/2 x) x))) (+ (* 1/4 (/ (pow x 2) (- (* 1/2 x) x))) (* y (- (+ (* -1/2 (/ x (- (* 1/2 x) x))) (* y (- (* 1/4 (/ 1 (- (* 1/2 x) x))) (* -1/2 (/ (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))) (- (* 1/2 x) x)))))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))))))>
#<alt (+ (* -1 (/ (pow x 2) (- (* 1/2 x) x))) (+ (* 1/4 (/ (pow x 2) (- (* 1/2 x) x))) (* y (- (+ (* -1/2 (/ x (- (* 1/2 x) x))) (* y (- (+ (* 1/4 (/ 1 (- (* 1/2 x) x))) (* 1/2 (/ (* y (- (* 1/4 (/ 1 (- (* 1/2 x) x))) (* -1/2 (/ (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))) (- (* 1/2 x) x))))) (- (* 1/2 x) x)))) (* -1/2 (/ (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))) (- (* 1/2 x) x)))))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))))))>
#<alt (* -1/2 y)>
#<alt (* y (- (* 2 (/ x y)) (+ 1/2 (* 1/2 (/ x y)))))>
#<alt (* y (- (+ (* -2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow y 2))) (* 2 (/ x y))) (+ 1/2 (+ (* -2 (/ (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))) (pow y 2))) (* 1/2 (/ x y))))))>
#<alt (* y (- (+ (* -2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow y 2))) (+ (* 2 (/ x y)) (* 2 (/ (* (- (* -2 (+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))) (* -2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))))) (- (* 1/2 x) x)) (pow y 3))))) (+ 1/2 (+ (* -2 (/ (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))) (pow y 2))) (* 1/2 (/ x y))))))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 2 x) (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (+ (* -1 (/ (- (* 2 (+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))) (* 2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))))) y)) (* 2 x)) (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))) (* 2 (/ (* (- (* 1/2 x) x) (- (* 2 (+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))) (* 2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x)))))) y))) (* 2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))))) y)) (* 2 x)) (* 1/2 x)) y)))))>
#<alt (* -1/2 y)>
#<alt (+ (* -1/2 x) (* -1/2 y))>
#<alt (+ (* -1/2 x) (* -1/2 y))>
#<alt (+ (* -1/2 x) (* -1/2 y))>
#<alt (* -1/2 x)>
#<alt (* x (- (* -1/2 (/ y x)) 1/2))>
#<alt (* x (- (* -1/2 (/ y x)) 1/2))>
#<alt (* x (- (* -1/2 (/ y x)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ y x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ y x)))))>
#<alt (- (* 1/2 x) x)>
#<alt (- (+ (* -1/2 y) (* 1/2 x)) x)>
#<alt (- (+ (* -1/2 y) (* 1/2 x)) x)>
#<alt (- (+ (* -1/2 y) (* 1/2 x)) x)>
#<alt (* -1/2 y)>
#<alt (* y (- (* 1/2 (/ x y)) (+ 1/2 (/ x y))))>
#<alt (* y (- (* 1/2 (/ x y)) (+ 1/2 (/ x y))))>
#<alt (* y (- (* 1/2 (/ x y)) (+ 1/2 (/ x y))))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 1/2 x) x) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 1/2 x) x) y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ (- (* 1/2 x) x) y)))))>
#<alt (* 1/4 (pow y 2))>
#<alt (+ (* -1/2 (* x y)) (* 1/4 (pow y 2)))>
#<alt (+ (* 1/4 (pow y 2)) (* x (+ (* -3/4 x) (* -1/2 y))))>
#<alt (+ (* 1/4 (pow y 2)) (* x (+ (* -3/4 x) (* -1/2 y))))>
#<alt (* -3/4 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ y x)) 3/4))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2)))) 3/4))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2)))) 3/4))>
#<alt (* -3/4 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ y x)) 3/4))>
#<alt (* (pow x 2) (- (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x)) 3/4))>
#<alt (* (pow x 2) (- (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x)) 3/4))>
#<alt (+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))>
#<alt (+ (* -1 (pow x 2)) (+ (* -1/2 (* x y)) (* 1/4 (pow x 2))))>
#<alt (+ (* -1 (pow x 2)) (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y)))))>
#<alt (+ (* -1 (pow x 2)) (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y)))))>
#<alt (* 1/4 (pow y 2))>
#<alt (* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))>
#<alt (* (pow y 2) (+ 1/4 (+ (* -1 (/ (pow x 2) (pow y 2))) (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2)))))))>
#<alt (* (pow y 2) (+ 1/4 (+ (* -1 (/ (pow x 2) (pow y 2))) (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2)))))))>
#<alt (* 1/4 (pow y 2))>
#<alt (* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))>
#<alt (* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) y)) (* 1/2 x)) y))))>
#<alt (* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) y)) (* 1/2 x)) y))))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* 1/4 (pow y 2))>
#<alt (+ (* -1/2 (* x y)) (* 1/4 (pow y 2)))>
#<alt (+ (* 1/4 (pow y 2)) (* x (+ (* -1/2 y) (* 1/4 x))))>
#<alt (+ (* 1/4 (pow y 2)) (* x (+ (* -1/2 y) (* 1/4 x))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (+ 1/4 (* -1/2 (/ y x))))>
#<alt (* (pow x 2) (+ 1/4 (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/4 (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2))))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (+ 1/4 (* -1/2 (/ y x))))>
#<alt (* (pow x 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x))))>
#<alt (* (pow x 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x))))>
#<alt (* 1/4 (pow x 2))>
#<alt (+ (* -1/2 (* x y)) (* 1/4 (pow x 2)))>
#<alt (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y))))>
#<alt (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y))))>
#<alt (* 1/4 (pow y 2))>
#<alt (* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))>
#<alt (* (pow y 2) (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))>
#<alt (* (pow y 2) (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))>
#<alt (* 1/4 (pow y 2))>
#<alt (* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))>
#<alt (* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow x 2) y)) (* 1/2 x)) y))))>
#<alt (* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow x 2) y)) (* 1/2 x)) y))))>

Calls

54 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(/ (+ (* (- 0 x) x) (* (- x y) (* (- x y) 1/4))) (- (* (- x y) 1/2) x))
1.0ms	y	@	inf	(/ (+ (* (- 0 x) x) (* (- x y) (* (- x y) 1/4))) (- (* (- x y) 1/2) x))
0.0ms	y	@	-inf	(/ (+ (* (- 0 x) x) (* (- x y) (* (- x y) 1/4))) (- (* (- x y) 1/2) x))
0.0ms	x	@	0	(/ 2/3 x)
0.0ms	x	@	-inf	(* 3/2 x)

rewrite454.0ms (5.4%)

Memory

-20.0MiB live, 838.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 272×	`accelerator-lowering-fma.f32`
6 272×	`accelerator-lowering-fma.f64`
4 434×	`/-lowering-/.f32`
4 434×	`/-lowering-/.f64`
3 570×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	80
1	145	60
2	1340	60
0	8895	57

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 707

Calls

Call 1

Inputs
(+ (* -1/2 y) (* 3/2 x))
(* 3/2 x)
(+ (* (- y x) -1/2) x)
(- y x)
(/ 1 (/ 2/3 x))
(/ 2/3 x)
(/ (+ (* (- 0 x) x) (* (- x y) (* (- x y) 1/4))) (- (* (- x y) 1/2) x))
(- (* (- x y) 1/2) x)
(+ (* (- 0 x) x) (* (- x y) (* (- x y) 1/4)))
(- 0 x)
(* (- x y) (* (- x y) 1/4))

Outputs
(+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 3/2 binary64) x))
(+.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal -1/2 binary64) y))
(+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal -3/2 binary64) x))) (neg.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64)) (fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal -3/2 binary64) x)))))
(-.f64 (.f64 #s(literal -1/2 binary64) y) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 3/2 binary64) x)))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal -3/2 binary64) x))) (/.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64)) (fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal -3/2 binary64) x))))
(-.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64)) (-.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal -1/2 binary64) y))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.f64 (.f64 #s(literal 3/2 binary64) x) (*.f64 #s(literal -1/2 binary64) y))))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(fma.f64 y #s(literal -1/2 binary64) (*.f64 #s(literal 3/2 binary64) x))
(fma.f64 (.f64 #s(literal -1/2 binary64) y) #s(literal 1 binary64) (.f64 #s(literal 3/2 binary64) x))
(fma.f64 #s(literal 3/2 binary64) x (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 (.f64 #s(literal 3/2 binary64) x) #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 3/2 binary64) x)) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal -3/2 binary64) x))) (neg.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64)) (fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal -3/2 binary64) x)))))
(fma.f64 (pow.f64 (.f64 #s(literal 3/2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 3/2 binary64) x) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal -3/2 binary64) (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 (pow.f64 (/.f64 #s(literal 2/3 binary64) (.f64 x (fma.f64 x x #s(literal 0 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 (pow.f64 (/.f64 #s(literal 2/3 binary64) (fma.f64 x x #s(literal 0 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x) (*.f64 #s(literal -1/2 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 3/4 binary64) (.f64 y (-.f64 #s(literal 0 binary64) x)))))) (fma.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) #s(literal 27/8 binary64) (.f64 (.f64 y (*.f64 y y)) #s(literal -1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal -1/2 binary64) y)) (-.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64)) (.f64 #s(literal 1/4 binary64) (*.f64 y y)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x)))))
(/.f64 (fma.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) #s(literal 27/8 binary64) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))) (fma.f64 (.f64 #s(literal 3/2 binary64) x) (-.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal -1/2 binary64) y)) (.f64 #s(literal 1/4 binary64) (*.f64 y y))))
(/.f64 (fma.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) #s(literal 27/8 binary64) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 3/4 binary64) (*.f64 y (-.f64 #s(literal 0 binary64) x)))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64))) (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal -3/2 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) #s(literal 27/8 binary64) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 #s(literal 3/2 binary64) x) (-.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal -1/2 binary64) y)) (.f64 #s(literal 1/4 binary64) (*.f64 y y)))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) #s(literal 27/8 binary64) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 y y) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 3/4 binary64) (*.f64 y (-.f64 #s(literal 0 binary64) x))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal -3/2 binary64) x))))
(/.f64 (-.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 y y))) (-.f64 (.f64 #s(literal 3/2 binary64) x) (*.f64 #s(literal -1/2 binary64) y)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 y y)) (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal -3/2 binary64) x))) (.f64 (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal -3/2 binary64) x)) (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 9/4 binary64)))) (.f64 (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal -3/2 binary64) x)) (fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal -3/2 binary64) x))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) #s(literal 27/8 binary64) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 #s(literal 3/2 binary64) x) (-.f64 (.f64 #s(literal 3/2 binary64) x) (.f64 #s(literal -1/2 binary64) y)) (.f64 #s(literal 1/4 binary64) (*.f64 y y))))))
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(.f64 (fma.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (-.f64 x y))) (.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/64 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/16 binary64) (-.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 x (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (-.f64 x y) (*.f64 (-.f64 x y) #s(literal 1/4 binary64)))))))))
(.f64 (fma.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (-.f64 x y))) (.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/64 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/16 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) (.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (fma.f64 x x #s(literal 0 binary64)))))))
(.f64 (-.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/16 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) (.f64 (-.f64 x y) (*.f64 (-.f64 x y) #s(literal 1/4 binary64))))))
(*.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) x) (-.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64)) x))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (-.f64 x y))) (.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/64 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (fma.f64 (-.f64 x y) (*.f64 (-.f64 x y) #s(literal 1/4 binary64)) (fma.f64 x x #s(literal 0 binary64))) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/16 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) (.f64 (-.f64 x y) (*.f64 (-.f64 x y) #s(literal 1/4 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 (.f64 (-.f64 x y) (-.f64 x y)) (.f64 (-.f64 x y) (-.f64 x y))) #s(literal 1/16 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (fma.f64 x x #s(literal 0 binary64)))))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x))
(+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) x)
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x #s(literal 0 binary64))
(fma.f64 (*.f64 x (fma.f64 x x #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 x x #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))) #s(literal 0 binary64))
(neg.f64 x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal -1 binary64) x)))
(/.f64 (*.f64 x (fma.f64 x x #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (fma.f64 x x #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (fma.f64 x x #s(literal 0 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 x x #s(literal 0 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (fma.f64 x x #s(literal 0 binary64))))) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) x) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 x x (-.f64 #s(literal 0 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64)))))
(pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) x)
(.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))))
(*.f64 (fma.f64 x x #s(literal 0 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (fma.f64 x x #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) x) (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y)))
(+.f64 (.f64 x (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (log.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64))) #s(literal 2 binary64)))
(fma.f64 x (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (.f64 (-.f64 #s(literal 0 binary64) y) (*.f64 (-.f64 x y) #s(literal 1/4 binary64))))
(fma.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) x (.f64 (*.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (*.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (-.f64 x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y x) (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (*.f64 (+.f64 y x) (-.f64 x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (.f64 (.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (-.f64 x y)) (*.f64 (-.f64 x y) #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y x) (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (*.f64 (-.f64 x y) #s(literal 1/4 binary64)))))
(/.f64 (*.f64 (-.f64 x y) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(/.f64 (*.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(/.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (*.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (-.f64 x y))) (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (*.f64 (+.f64 y x) (-.f64 x y))) (+.f64 y x))
(/.f64 (.f64 (.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (-.f64 x y)) (*.f64 (-.f64 x y) #s(literal 1/4 binary64))) (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (*.f64 (-.f64 x y) #s(literal 1/4 binary64))) (+.f64 y x))
(/.f64 (neg.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (*.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (-.f64 x y)))) (-.f64 #s(literal 0 binary64) (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (*.f64 (+.f64 y x) (-.f64 x y)))) (-.f64 #s(literal 0 binary64) (+.f64 y x)))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (-.f64 x y)) (*.f64 (-.f64 x y) #s(literal 1/4 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (*.f64 (-.f64 x y) #s(literal 1/4 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 y x)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) x) (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) x) (-.f64 (.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y)) (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y))) (.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) x) (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 (-.f64 x y) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (.f64 x (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (-.f64 x y) #s(literal 1/4 binary64)))) (.f64 (.f64 x (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (-.f64 x y) #s(literal 1/4 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) x) (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) x)) (.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y)) (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y)))) (-.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) x) (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (.f64 x (.f64 (-.f64 x y) #s(literal 1/4 binary64)))) (.f64 (.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (-.f64 x y) #s(literal 1/4 binary64))))) (-.f64 (.f64 x (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (-.f64 x y) #s(literal 1/4 binary64)))))
(pow.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 2 binary64))
(.f64 (-.f64 x y) (.f64 (-.f64 x y) #s(literal 1/4 binary64)))
(.f64 (-.f64 x y) (.f64 #s(literal 1/2 binary64) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64))))
(.f64 #s(literal 1/4 binary64) (.f64 (-.f64 x y) (-.f64 x y)))
(.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (-.f64 x y))
(.f64 #s(literal 1/2 binary64) (.f64 (-.f64 x y) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64))))
(*.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64)) (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64))
(.f64 (.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64)) (-.f64 x y)) #s(literal 1/2 binary64))
(.f64 (.f64 (fma.f64 (-.f64 x y) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)) (-.f64 x y))
(.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64)))))
(.f64 (.f64 (.f64 (-.f64 x y) #s(literal 1/4 binary64)) (.f64 (+.f64 y x) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (+.f64 y x)))
(.f64 (.f64 (.f64 (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64))) (-.f64 x y)) (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y (+.f64 y x) (fma.f64 x x #s(literal 0 binary64)))))
(.f64 (.f64 (.f64 (+.f64 y x) (-.f64 x y)) (.f64 (-.f64 x y) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 y x)))

simplify472.0ms (5.6%)

Memory

-8.9MiB live, 713.8MiB allocated

Algorithm

1×	egg-herbie

Rules

13 738×	`accelerator-lowering-fma.f32`
13 738×	`accelerator-lowering-fma.f64`
5 852×	`-lowering-.f32`
5 852×	`-lowering-.f64`
4 080×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	300	2181
1	976	1989
2	3141	1874
0	8213	1740

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(* 3/2 x)
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(* -1/2 y)
(* y (- (* 3/2 (/ x y)) 1/2))
(* y (- (* 3/2 (/ x y)) 1/2))
(* y (- (* 3/2 (/ x y)) 1/2))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -3/2 (/ x y)))))
(* -1 (* y (+ 1/2 (* -3/2 (/ x y)))))
(* -1 (* y (+ 1/2 (* -3/2 (/ x y)))))
(* -1/2 y)
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(* 3/2 x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(* x (+ 3/2 (* -1/2 (/ y x))))
(* x (+ 3/2 (* -1/2 (/ y x))))
(* 3/2 x)
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(+ x (* 1/2 x))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(+ x (+ (* -1/2 y) (* 1/2 x)))
(* -1/2 y)
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* y (- (+ (* 1/2 (/ x y)) (/ x y)) 1/2))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ x (* 1/2 x)) y)))))
(* -1/2 y)
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(* 3/2 x)
(* x (+ 3/2 (* -1/2 (/ y x))))
(* x (+ 3/2 (* -1/2 (/ y x))))
(* x (+ 3/2 (* -1/2 (/ y x))))
(* 3/2 x)
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 (* x (- (* 1/2 (/ y x)) 3/2)))
(* -1 x)
(- y x)
(- y x)
(- y x)
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(* 3/2 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(/ 2/3 x)
(* -1/2 y)
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(+ (* -1/2 y) (* 3/2 x))
(* 3/2 x)
(* x (- (+ 3/2 (/ y x)) (* 3/2 (/ y x))))
(* x (- (+ 3/2 (+ (* -1/2 (/ (pow y 2) (pow x 2))) (/ y x))) (+ (* 3/2 (/ y x)) (/ (* y (- y (* 3/2 y))) (pow x 2)))))
(* x (- (+ 3/2 (+ (* -1 (/ (* y (- (* -1/2 (pow y 2)) (* y (- y (* 3/2 y))))) (pow x 3))) (+ (* -1/2 (/ (pow y 2) (pow x 2))) (/ y x)))) (+ (* 3/2 (/ y x)) (/ (* y (- y (* 3/2 y))) (pow x 2)))))
(* 3/2 x)
(* -1 (* x (- (* -1 (/ (- y (* 3/2 y)) x)) 3/2)))
(* -1 (* x (- (* -1 (/ (- (+ y (* -1 (/ (- (* 1/2 (pow y 2)) (* -1 (* y (- y (* 3/2 y))))) x))) (* 3/2 y)) x)) 3/2)))
(* -1 (* x (- (* -1 (/ (- (+ y (* -1 (/ (- (+ (* -1 (/ (* y (- (* 1/2 (pow y 2)) (* -1 (* y (- y (* 3/2 y)))))) x)) (* 1/2 (pow y 2))) (* -1 (* y (- y (* 3/2 y))))) x))) (* 3/2 y)) x)) 3/2)))
(/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (- (* 1/2 x) x))
(+ (* -1 (/ (pow x 2) (- (* 1/2 x) x))) (+ (* 1/4 (/ (pow x 2) (- (* 1/2 x) x))) (* y (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))))))
(+ (* -1 (/ (pow x 2) (- (* 1/2 x) x))) (+ (* 1/4 (/ (pow x 2) (- (* 1/2 x) x))) (* y (- (+ (* -1/2 (/ x (- (* 1/2 x) x))) (* y (- (* 1/4 (/ 1 (- (* 1/2 x) x))) (* -1/2 (/ (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))) (- (* 1/2 x) x)))))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))))))
(+ (* -1 (/ (pow x 2) (- (* 1/2 x) x))) (+ (* 1/4 (/ (pow x 2) (- (* 1/2 x) x))) (* y (- (+ (* -1/2 (/ x (- (* 1/2 x) x))) (* y (- (+ (* 1/4 (/ 1 (- (* 1/2 x) x))) (* 1/2 (/ (* y (- (* 1/4 (/ 1 (- (* 1/2 x) x))) (* -1/2 (/ (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))) (- (* 1/2 x) x))))) (- (* 1/2 x) x)))) (* -1/2 (/ (- (* -1/2 (/ x (- (* 1/2 x) x))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))) (- (* 1/2 x) x)))))) (* -1/2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow (- (* 1/2 x) x) 2)))))))
(* -1/2 y)
(* y (- (* 2 (/ x y)) (+ 1/2 (* 1/2 (/ x y)))))
(* y (- (+ (* -2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow y 2))) (* 2 (/ x y))) (+ 1/2 (+ (* -2 (/ (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))) (pow y 2))) (* 1/2 (/ x y))))))
(* y (- (+ (* -2 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) (pow y 2))) (+ (* 2 (/ x y)) (* 2 (/ (* (- (* -2 (+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))) (* -2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))))) (- (* 1/2 x) x)) (pow y 3))))) (+ 1/2 (+ (* -2 (/ (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))) (pow y 2))) (* 1/2 (/ x y))))))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1 (/ (- (* 2 x) (* 1/2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (- (+ (* -1 (/ (- (* 2 (+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))) (* 2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))))) y)) (* 2 x)) (* 1/2 x)) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (- (+ (* -1 (/ (- (+ (* 2 (+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))) (* 2 (/ (* (- (* 1/2 x) x) (- (* 2 (+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))) (* 2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x)))))) y))) (* 2 (* (- (* 1/2 x) x) (- (* 2 x) (* 1/2 x))))) y)) (* 2 x)) (* 1/2 x)) y)))))
(* -1/2 y)
(+ (* -1/2 x) (* -1/2 y))
(+ (* -1/2 x) (* -1/2 y))
(+ (* -1/2 x) (* -1/2 y))
(* -1/2 x)
(* x (- (* -1/2 (/ y x)) 1/2))
(* x (- (* -1/2 (/ y x)) 1/2))
(* x (- (* -1/2 (/ y x)) 1/2))
(* -1/2 x)
(* -1 (* x (+ 1/2 (* 1/2 (/ y x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ y x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ y x)))))
(- (* 1/2 x) x)
(- (+ (* -1/2 y) (* 1/2 x)) x)
(- (+ (* -1/2 y) (* 1/2 x)) x)
(- (+ (* -1/2 y) (* 1/2 x)) x)
(* -1/2 y)
(* y (- (* 1/2 (/ x y)) (+ 1/2 (/ x y))))
(* y (- (* 1/2 (/ x y)) (+ 1/2 (/ x y))))
(* y (- (* 1/2 (/ x y)) (+ 1/2 (/ x y))))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* -1 (/ (- (* 1/2 x) x) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (- (* 1/2 x) x) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (- (* 1/2 x) x) y)))))
(* 1/4 (pow y 2))
(+ (* -1/2 (* x y)) (* 1/4 (pow y 2)))
(+ (* 1/4 (pow y 2)) (* x (+ (* -3/4 x) (* -1/2 y))))
(+ (* 1/4 (pow y 2)) (* x (+ (* -3/4 x) (* -1/2 y))))
(* -3/4 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ y x)) 3/4))
(* (pow x 2) (- (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2)))) 3/4))
(* (pow x 2) (- (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2)))) 3/4))
(* -3/4 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ y x)) 3/4))
(* (pow x 2) (- (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x)) 3/4))
(* (pow x 2) (- (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x)) 3/4))
(+ (* -1 (pow x 2)) (* 1/4 (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* -1/2 (* x y)) (* 1/4 (pow x 2))))
(+ (* -1 (pow x 2)) (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y)))))
(+ (* -1 (pow x 2)) (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y)))))
(* 1/4 (pow y 2))
(* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))
(* (pow y 2) (+ 1/4 (+ (* -1 (/ (pow x 2) (pow y 2))) (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2)))))))
(* (pow y 2) (+ 1/4 (+ (* -1 (/ (pow x 2) (pow y 2))) (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2)))))))
(* 1/4 (pow y 2))
(* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))
(* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) y)) (* 1/2 x)) y))))
(* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow x 2)) (* 1/4 (pow x 2))) y)) (* 1/2 x)) y))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* 1/4 (pow y 2))
(+ (* -1/2 (* x y)) (* 1/4 (pow y 2)))
(+ (* 1/4 (pow y 2)) (* x (+ (* -1/2 y) (* 1/4 x))))
(+ (* 1/4 (pow y 2)) (* x (+ (* -1/2 y) (* 1/4 x))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -1/2 (/ y x))))
(* (pow x 2) (+ 1/4 (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2))))))
(* (pow x 2) (+ 1/4 (+ (* -1/2 (/ y x)) (* 1/4 (/ (pow y 2) (pow x 2))))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -1/2 (/ y x))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x))))
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow y 2) x)) (* 1/2 y)) x))))
(* 1/4 (pow x 2))
(+ (* -1/2 (* x y)) (* 1/4 (pow x 2)))
(+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y))))
(+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/4 y))))
(* 1/4 (pow y 2))
(* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))
(* (pow y 2) (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))
(* (pow y 2) (+ 1/4 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))
(* 1/4 (pow y 2))
(* (pow y 2) (+ 1/4 (* -1/2 (/ x y))))
(* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow x 2) y)) (* 1/2 x)) y))))
(* (pow y 2) (+ 1/4 (* -1 (/ (+ (* -1/4 (/ (pow x 2) y)) (* 1/2 x)) y))))

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

eval154.0ms (1.8%)

Memory: 43.1MiB live, 265.3MiB allocated
Compiler: Compiled 31 632 to 2 254 computations (92.9% saved)

prune102.0ms (1.2%)

Memory

-3.6MiB live, 237.3MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	961	2	963
Fresh	6	1	7
Picked	3	2	5
Done	0	0	0
Total	970	5	975

Accuracy

100.0%

Counts

975 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
▶	54.8%	(fma.f64 y #s(literal -1/2 binary64) x)
▶	100.0%	(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
▶	45.5%	(*.f64 y #s(literal -1/2 binary64))
✓	55.2%	(*.f64 #s(literal 3/2 binary64) x)

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify5.0ms (0.1%)

Memory

-30.7MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(fma.f64 y #s(literal -1/2 binary64) x)
✓	cost-diff	(*.f64 #s(literal -1/2 binary64) y)
✓	cost-diff	(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
✓	cost-diff	(*.f64 y #s(literal -1/2 binary64))

Rules

12×	`accelerator-lowering-fma.f32`
12×	`accelerator-lowering-fma.f64`
8×	`+-lowering-+.f64`
8×	`-lowering-.f32`
8×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	14	27
0	14	25

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize29.0ms (0.3%)

Memory

29.5MiB live, 68.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 y #s(literal -1/2 binary64) x)
✓	accuracy	100.0%	(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) y)
✓	accuracy	100.0%	(*.f64 y #s(literal -1/2 binary64))

Samples

14.0ms	228×	0	valid
2.0ms	14×	1	valid
2.0ms	11×	2	valid
1.0ms	3×	3	valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

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

ival-mult: 6.0ms (61.7% of total)

ival-add: 3.0ms (30.8% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#<alt (* y -1/2)>
#<alt (+ (* x 3/2) (* -1/2 y))>
#<alt (* -1/2 y)>
#<alt (+ (* y -1/2) x)>

Outputs
#<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 (* -1/2 y)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* x (+ 3/2 (* -1/2 (/ y x))))>
#<alt (* 3/2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 3/2)))>
#<alt (* 3/2 x)>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (+ (* -1/2 y) (* 3/2 x))>
#<alt (* -1/2 y)>
#<alt (* y (- (* 3/2 (/ x y)) 1/2))>
#<alt (* y (- (* 3/2 (/ x y)) 1/2))>
#<alt (* y (- (* 3/2 (/ x y)) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -3/2 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -3/2 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -3/2 (/ x 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 (* -1/2 y)>
#<alt x>
#<alt (+ x (* -1/2 y))>
#<alt (+ x (* -1/2 y))>
#<alt (+ x (* -1/2 y))>
#<alt (* -1/2 y)>
#<alt (* y (- (/ x y) 1/2))>
#<alt (* y (- (/ x y) 1/2))>
#<alt (* y (- (/ x y) 1/2))>
#<alt (* -1/2 y)>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1/2 (* -1 (/ x y)))))>
#<alt (* -1/2 y)>
#<alt (+ x (* -1/2 y))>
#<alt (+ x (* -1/2 y))>
#<alt (+ x (* -1/2 y))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ y x))))>
#<alt (* x (+ 1 (* -1/2 (/ y x))))>
#<alt (* x (+ 1 (* -1/2 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ y x)) 1)))>

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	y	@	inf	(* y -1/2)
0.0ms	y	@	-inf	(* y -1/2)
0.0ms	y	@	0	(* y -1/2)
0.0ms	x	@	inf	(+ (* x 3/2) (* -1/2 y))
0.0ms	x	@	-inf	(+ (* x 3/2) (* -1/2 y))

rewrite395.0ms (4.7%)

Memory

-27.7MiB live, 570.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 768×	`accelerator-lowering-fma.f32`
6 768×	`accelerator-lowering-fma.f64`
4 306×	`-lowering-.f32`
4 306×	`-lowering-.f64`
4 014×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	44	18
2	299	18
3	3049	18
0	8276	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 266

Calls

Call 1

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

Outputs
(exp.f64 (log.f64 (*.f64 y #s(literal -1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 y #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 y #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) y)
(*.f64 #s(literal -1/2 binary64) (pow.f64 y #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 #s(literal -1/2 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal -1/2 binary64))) (exp.f64 (log.f64 y)))
(+.f64 (.f64 y #s(literal -1/2 binary64)) (.f64 x #s(literal 3/2 binary64)))
(+.f64 (.f64 x #s(literal 3/2 binary64)) (.f64 y #s(literal -1/2 binary64)))
(+.f64 (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/2 binary64) (.f64 x #s(literal 3/2 binary64))))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal -1/2 binary64) (.f64 x #s(literal -3/2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal -1/2 binary64) (.f64 x #s(literal -3/2 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 729/64 binary64)) (fma.f64 x (.f64 (.f64 x x) #s(literal 27/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (fma.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 x #s(literal -3/4 binary64))) (.f64 x (.f64 x #s(literal 9/4 binary64))))) (/.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))) (fma.f64 x (.f64 (.f64 x x) #s(literal 27/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (fma.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 x #s(literal -3/4 binary64))) (.f64 x (.f64 x #s(literal 9/4 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 729/64 binary64)) (fma.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (.f64 x #s(literal 9/4 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 81/16 binary64)))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))) (fma.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (.f64 x #s(literal 9/4 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 81/16 binary64)))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 81/16 binary64)) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (.f64 x #s(literal 9/4 binary64))))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (.f64 x #s(literal 9/4 binary64))))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 x #s(literal -3/4 binary64))) (.f64 x (.f64 x #s(literal 9/4 binary64)))))) (/.f64 (fma.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 27/8 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 x #s(literal -3/4 binary64))) (.f64 x (*.f64 x #s(literal 9/4 binary64)))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))))) (/.f64 (fma.f64 x (.f64 x #s(literal 9/4 binary64)) (.f64 (.f64 y y) #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 y #s(literal 1/2 binary64) (*.f64 x #s(literal 3/2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 729/64 binary64)) (.f64 (fma.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 x #s(literal -3/4 binary64))) (.f64 x (.f64 x #s(literal 9/4 binary64)))) (fma.f64 x (.f64 (.f64 x x) #s(literal 27/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))) (.f64 (fma.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 x #s(literal -3/4 binary64))) (.f64 x (.f64 x #s(literal 9/4 binary64)))) (fma.f64 x (.f64 (.f64 x x) #s(literal 27/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 729/64 binary64)) (.f64 (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))) (fma.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (.f64 x #s(literal 9/4 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 81/16 binary64))))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))) (.f64 (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))) (fma.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (.f64 x #s(literal 9/4 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 81/16 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 81/16 binary64)) (.f64 (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (.f64 x #s(literal 9/4 binary64)))))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y))) (.f64 (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (.f64 x #s(literal 9/4 binary64)))))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (.f64 (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))))) (/.f64 (.f64 (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))) (.f64 y (.f64 y #s(literal 1/4 binary64)))) (.f64 (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (.f64 (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))))) (fma.f64 (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (fma.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (.f64 (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))))))) (/.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))))) (fma.f64 (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (fma.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (.f64 (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))))))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 9/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))))) (fma.f64 (.f64 x x) (/.f64 #s(literal 9/4 binary64) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))))) (/.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64))))) (fma.f64 (.f64 x x) (/.f64 #s(literal 9/4 binary64) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (fma.f64 y #s(literal 1/2 binary64) (.f64 x #s(literal 3/2 binary64)))))))
(fma.f64 y #s(literal -1/2 binary64) (*.f64 x #s(literal 3/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 x #s(literal 3/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (pow.f64 y #s(literal 1 binary64)) (*.f64 x #s(literal 3/2 binary64)))
(fma.f64 x #s(literal 3/2 binary64) (*.f64 y #s(literal -1/2 binary64)))
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(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -1/2 binary64)) x)))) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 x x) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x x))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -1/2 binary64)) x)))) (neg.f64 (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (*.f64 x x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/2 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 x (.f64 y #s(literal 1/2 binary64))) (fma.f64 x x (.f64 (*.f64 y y) #s(literal -1/4 binary64)))) #s(literal -1 binary64))
(.f64 (fma.f64 y #s(literal -1/2 binary64) x) (.f64 (-.f64 (.f64 y #s(literal -1/2 binary64)) x) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -1/2 binary64)) x))))
(.f64 (fma.f64 y #s(literal -1/2 binary64) x) (/.f64 (-.f64 (.f64 y #s(literal -1/2 binary64)) x) (-.f64 (*.f64 y #s(literal -1/2 binary64)) x)))
(.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64)))))))
(.f64 (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64))))) (.f64 (fma.f64 y #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64))))))))
(.f64 (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64))))) (/.f64 (fma.f64 y #s(literal -1/2 binary64) x) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (*.f64 y #s(literal 1/2 binary64)))))))
(.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 y #s(literal -1/2 binary64)) x)))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64))))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 y #s(literal -1/2 binary64)) x))))
(*.f64 #s(literal 1 binary64) (fma.f64 y #s(literal -1/2 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64)))))) (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -1/2 binary64)) x)) (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y #s(literal -1/2 binary64)) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))) #s(literal -1 binary64)))
(.f64 (fma.f64 x x (.f64 (.f64 y y) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (.f64 y #s(literal 1/2 binary64)))))
(.f64 (/.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (*.f64 x x))) (fma.f64 y #s(literal -1/2 binary64) x))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (.f64 y #s(literal 1/2 binary64))) (.f64 (+.f64 x (.f64 y #s(literal 1/2 binary64))) (+.f64 x (.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))))) (fma.f64 (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64)))) (-.f64 (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64)))) (.f64 y (.f64 y #s(literal 1/4 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y))) (.f64 x (.f64 (+.f64 x (.f64 y #s(literal 1/2 binary64))) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64)))))))) (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64))))))
(.f64 (/.f64 (-.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 x x)) (fma.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) x))) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (fma.f64 y #s(literal -1/2 binary64) x))))
(.f64 (pow.f64 (/.f64 (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal -1/512 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (*.f64 y y)) #s(literal 1/64 binary64))))))
(.f64 (pow.f64 (/.f64 (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x (+.f64 x (.f64 y #s(literal 1/2 binary64))))) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y (.f64 y y)) #s(literal -1/8 binary64) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) x))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 y #s(literal -1/2 binary64)) x) (-.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 x x) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 y #s(literal -1/2 binary64)) x) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y))) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 y #s(literal 1/4 binary64)) (*.f64 x x))))

simplify373.0ms (4.4%)

Memory

11.2MiB live, 489.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8 340×	`accelerator-lowering-fma.f32`
8 340×	`accelerator-lowering-fma.f64`
3 392×	`/-lowering-/.f32`
3 392×	`/-lowering-/.f64`
2 280×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	318
1	109	318
2	291	318
3	720	318
4	1675	318
5	3273	318
6	4576	318
7	5114	318
8	5321	318
9	5482	318
10	7149	318
0	8013	282

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

eval41.0ms (0.5%)

Memory: 14.4MiB live, 95.0MiB allocated
Compiler: Compiled 10 433 to 786 computations (92.5% saved)

prune43.0ms (0.5%)

Memory

-10.3MiB live, 105.6MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	337	1	338
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	337	6	343

Accuracy

100.0%

Counts

343 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
✓	54.8%	(fma.f64 y #s(literal -1/2 binary64) x)
✓	100.0%	(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
✓	45.5%	(*.f64 y #s(literal -1/2 binary64))
✓	55.2%	(*.f64 #s(literal 3/2 binary64) x)
	12.5%	x

Compiler

Compiled 390 to 120 computations (69.2% saved)

regimes43.0ms (0.5%)

Memory

-22.4MiB live, 70.6MiB allocated

Counts

28 → 1

Calls

Call 1

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

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

Calls

3 calls:

23.0ms	y
11.0ms	x
8.0ms	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

25.7MiB live, 25.7MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
x
(*.f64 #s(literal 3/2 binary64) x)
(*.f64 y #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) y #s(literal 0 binary64))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 0 binary64))
(fma.f64 y #s(literal -1/2 binary64) x)
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))

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

Calls

3 calls:

3.0ms	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))
3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`y`
99.8%	1	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

-14.8MiB live, 24.1MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
x
(*.f64 #s(literal 3/2 binary64) x)
(*.f64 y #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) y #s(literal 0 binary64))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 0 binary64))
(fma.f64 y #s(literal -1/2 binary64) x)
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)

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

Calls

3 calls:

5.0ms	y
3.0ms	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))
3.0ms	x

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`y`
99.8%	1	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

6 → 3

Calls

Call 1

Inputs
x
(*.f64 #s(literal 3/2 binary64) x)
(*.f64 y #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) y #s(literal 0 binary64))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 0 binary64))
(fma.f64 y #s(literal -1/2 binary64) x)

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

Calls

3 calls:

3.0ms	x
3.0ms	(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))
3.0ms	y

Results

Accuracy	Segments	Branch
76.5%	3	`x`
79.7%	3	`y`
62.1%	2	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0.1%)

Memory

-31.4MiB live, 7.6MiB allocated

Counts

5 → 3

Calls

Call 1

Inputs
x
(*.f64 #s(literal 3/2 binary64) x)
(*.f64 y #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) y #s(literal 0 binary64))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 0 binary64))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
78.4%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes5.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
x
(*.f64 #s(literal 3/2 binary64) x)

Outputs
(*.f64 #s(literal 3/2 binary64) x)

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
55.2%	1	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`
55.2%	1	`x`
55.2%	1	`y`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

11.9MiB live, 11.9MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
12.5%	1	`x`
12.5%	1	`y`
12.5%	1	`(+.f64 x (/.f64 (-.f64 x y) #s(literal 2 binary64)))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch70.0ms (0.8%)

Memory

-15.0MiB live, 29.4MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
66.0ms	1.4556081784137928e+48	9.536834300795325e+51
2.0ms	-6.384832272777584e+86	-5.313289226956957e+86

Samples

62.0ms	151×	0	valid
1.0ms	5×	2	valid
0.0ms	4×	1	valid

Compiler

Compiled 142 to 111 computations (21.8% saved)

Precisions

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

ival-div: 1.0ms (29.8% of total)

ival-add: 1.0ms (29.8% of total)

ival-sub: 1.0ms (29.8% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

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

bsearch14.0ms (0.2%)

Memory

8.6MiB live, 47.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	1.4556081784137928e+48	9.536834300795325e+51
3.0ms	-6.384832272777584e+86	-5.313289226956957e+86

Samples

6.0ms	149×	0	valid
1.0ms	8×	1	valid
0.0ms	3×	2	valid

Compiler

Compiled 132 to 111 computations (15.9% saved)

Precisions

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

ival-div: 1.0ms (29.9% of total)

ival-add: 1.0ms (29.9% of total)

ival-sub: 1.0ms (29.9% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

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

simplify9.0ms (0.1%)

Memory

-11.1MiB live, 28.3MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
4×	`if-if-or-not_binary32`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	53
1	32	53
2	37	53
3	39	53
4	40	53

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
(if (<=.f64 y #s(literal -550000000000000021850375070452307741903035367879611187505453877284161110663179966349312 binary64)) (fma.f64 y #s(literal -1/2 binary64) x) (if (<=.f64 y #s(literal 13500000000000000510789242693921982591770638155776 binary64)) (*.f64 #s(literal 3/2 binary64) x) (fma.f64 y #s(literal -1/2 binary64) x)))
(if (<=.f64 y #s(literal -550000000000000021850375070452307741903035367879611187505453877284161110663179966349312 binary64)) (.f64 y #s(literal -1/2 binary64)) (if (<=.f64 y #s(literal 1550000000000000027396237512564765051788271288320 binary64)) (.f64 #s(literal 3/2 binary64) x) (*.f64 y #s(literal -1/2 binary64))))
(*.f64 #s(literal 3/2 binary64) x)
x

Outputs
(fma.f64 x #s(literal 3/2 binary64) (*.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 #s(literal 3/2 binary64) x))
(fma.f64 #s(literal -1/2 binary64) y (*.f64 x #s(literal 3/2 binary64)))
(fma.f64 (-.f64 y x) #s(literal -1/2 binary64) x)
(if (<=.f64 y #s(literal -550000000000000021850375070452307741903035367879611187505453877284161110663179966349312 binary64)) (fma.f64 y #s(literal -1/2 binary64) x) (if (<=.f64 y #s(literal 13500000000000000510789242693921982591770638155776 binary64)) (*.f64 #s(literal 3/2 binary64) x) (fma.f64 y #s(literal -1/2 binary64) x)))
(if (<=.f64 y #s(literal -550000000000000021850375070452307741903035367879611187505453877284161110663179966349312 binary64)) (fma.f64 y #s(literal -1/2 binary64) x) (if (<=.f64 y #s(literal 13500000000000000510789242693921982591770638155776 binary64)) (*.f64 x #s(literal 3/2 binary64)) (fma.f64 y #s(literal -1/2 binary64) x)))
(if (<=.f64 y #s(literal -550000000000000021850375070452307741903035367879611187505453877284161110663179966349312 binary64)) (.f64 y #s(literal -1/2 binary64)) (if (<=.f64 y #s(literal 1550000000000000027396237512564765051788271288320 binary64)) (.f64 #s(literal 3/2 binary64) x) (*.f64 y #s(literal -1/2 binary64))))
(if (<=.f64 y #s(literal -550000000000000021850375070452307741903035367879611187505453877284161110663179966349312 binary64)) (.f64 #s(literal -1/2 binary64) y) (if (<=.f64 y #s(literal 1550000000000000027396237512564765051788271288320 binary64)) (.f64 x #s(literal 3/2 binary64)) (*.f64 #s(literal -1/2 binary64) y)))
(*.f64 #s(literal 3/2 binary64) x)
(*.f64 x #s(literal 3/2 binary64))
x

soundness1.2s (14.6%)

Memory

17.5MiB live, 883.5MiB allocated

Rules

13 738×	`accelerator-lowering-fma.f32`
13 738×	`accelerator-lowering-fma.f64`
8 754×	`accelerator-lowering-fma.f32`
8 754×	`accelerator-lowering-fma.f64`
8 340×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	129
1	211	125
2	2122	125
0	8550	114
0	300	2181
1	976	1989
2	3141	1874
0	8213	1740
0	26	80
1	145	60
2	1340	60
0	8895	57
0	39	318
1	109	318
2	291	318
3	720	318
4	1675	318
5	3273	318
6	4576	318
7	5114	318
8	5321	318
9	5482	318
10	7149	318
0	8013	282
0	58	351
1	176	351
2	487	351
3	1348	315
4	2968	315
5	4585	315
6	6569	315
7	7592	315
0	8078	297
0	6	15
1	45	15
2	397	15
3	5077	15
0	8178	14
0	661	4353
1	2086	3988
2	6233	3897
0	8406	3587

Stop Event

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

Compiler

Compiled 194 to 115 computations (40.7% saved)

preprocess49.0ms (0.6%)

Memory: 11.8MiB live, 126.8MiB allocated
Compiler: Compiled 156 to 68 computations (56.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	19	48
1	51	42
2	153	42
3	406	42
4	715	42
5	909	42
6	951	42
0	6	7
1	12	7
2	23	7
3	44	7
4	83	7
5	154	7
6	278	7
7	435	7
8	543	7
9	604	7
10	608	7
0	608	6

Iter	Nodes	Cost
0	6	18
1	12	18
2	23	18
3	44	18
4	83	18
5	154	18
6	278	18
7	435	18
8	543	18
9	604	18
10	608	18
0	608	17

Iter	Nodes	Cost
0	19	48
1	51	42
2	153	42
3	406	42
4	715	42
5	909	42
6	951	42
0	6	7
1	12	7
2	23	7
3	44	7
4	83	7
5	154	7
6	278	7
7	435	7
8	543	7
9	604	7
10	608	7
0	608	6

Iter	Nodes	Cost
0	6	18
1	12	18
2	23	18
3	44	18
4	83	18
5	154	18
6	278	18
7	435	18
8	543	18
9	604	18
10	608	18
0	608	17

analyze0.0ms (0%)

sample931.0ms (11.1%)

preprocess78.0ms (0.9%)

explain70.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify28.0ms (0.3%)

localize35.0ms (0.4%)

series3.0ms (0%)

rewrite331.0ms (3.9%)

simplify311.0ms (3.7%)

eval86.0ms (1%)

prune57.0ms (0.7%)

simplify489.0ms (5.8%)

localize155.0ms (1.8%)

series28.0ms (0.3%)

rewrite570.0ms (6.8%)

simplify435.0ms (5.2%)

eval377.0ms (4.5%)

prune400.0ms (4.8%)

simplify353.0ms (4.2%)

localize150.0ms (1.8%)

series9.0ms (0.1%)

rewrite454.0ms (5.4%)

simplify472.0ms (5.6%)

eval154.0ms (1.8%)

prune102.0ms (1.2%)

simplify5.0ms (0.1%)

localize29.0ms (0.3%)

series2.0ms (0%)

rewrite395.0ms (4.7%)

simplify373.0ms (4.4%)

eval41.0ms (0.5%)

prune43.0ms (0.5%)

regimes43.0ms (0.5%)

regimes10.0ms (0.1%)

regimes12.0ms (0.1%)

regimes8.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

bsearch70.0ms (0.8%)

bsearch14.0ms (0.2%)

simplify9.0ms (0.1%)

soundness1.2s (14.6%)

preprocess49.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	19	48
1	51	42
2	153	42
3	406	42
4	715	42
5	909	42
6	951	42
0	6	7
1	12	7
2	23	7
3	44	7
4	83	7
5	154	7
6	278	7
7	435	7
8	543	7
9	604	7
10	608	7
0	608	6

Iter	Nodes	Cost
0	6	18
1	12	18
2	23	18
3	44	18
4	83	18
5	154	18
6	278	18
7	435	18
8	543	18
9	604	18
10	608	18
0	608	17